I? 8-W CIVIL ENGINEERING STUDIES SANITARY ENGINEERING SERIES NO. 31 APPLICABILITY OF PREVAILING GRAVITY THICKENING THEORIES TO ACTIVATED SLUDGE o o Eh o t " © p= 2s c O Hi o o C3 o 00 H oo M o M Hi (-3 S £> pq By RICHARD IRWIN DICK Supported By DIVISION OF WATER SUPPLY AND POLLUTION CONTROL U. S. PUBLIC HEALTH SERVICE RESEARCH FELLOWSHIP 5-F1-WP-21, 613-02 DEPARTMENT OF CIVIL ENGINEERING UNIVERSITY OF ILLINOIS URBANA, ILLINOIS OCTOBER, 1965 APPLICABILITY OF PREVAILING GRAVITY THICKENING THEORIES TO ACTIVATED SLUDGE by RICHARD IRWIN DICK September 1 965 Digitized by the Internet Archive in 2013 http://archive.org/details/applicabilityofp31dick APPLICABILITY OF PREVAILING GRAVITY THICKENING THEORIES TO ACTIVATED SLUDGE Richard Irwin Dick, Ph„D Department of Civil Engineering University of Illinois, 1965 It was hypothesized that the present criteria for evaluating mass loading capabilities of settling basins were inadequate when applied to activated sludge because of their failure to consider the rheologicai properties of the material „ The basis of the prevailing criteria is the Kynch theory which maintains that the rate of subsidence of a suspension is a function only of the local particle concentration,, The credibility of the basic hypothesis was shown by experiments designed to influence the sludge=water interface subsidence rate while leaving the concentration of particles at the interface unaltered „ The experiments involved varying the initial depth of sludge and mixing the underlying sludge. Analysis of the relationship between initial suspension depth and initial settling velocity provided a measure of the extent to which the behavior of activated sludge deviated from the behavior of the ideal suspension considered by thickening theories „ This parameter was called the retardation factor,, The relationship between the rheologicai properties of activated sludge and the deviations from prevailing thickening theory was confirmed both theoretically and experimentally „ A mathematical model of thickening was developed based on an analysis of the forces acting on a subsiding column of sludge „ The model indicated that the observed settling behavior could be explained by the existence of a structural support force within the sludge „ Studies with a viscometer were then undertaken to show that activated sludge did possess such internal structure „ Finally, the relative magnitude of the structural support force as' computed from settling data with the help of the mathematical model was shown to be related to the yield strength of the sludge as determined from viscometric analysis, confirming the relationship between rheological properties and the deviations from prevailing thickening theories. The more important implications of the results are that the area of the thickening portion of a settling basin need not be considered to be immutably established by the settling velocity of the rate-limiting con- centration of sludge, and that settling tests for collection of design data must be conducted at depths and mixing conditions representative of plant operation. The area requirement for thickening can be reduced (or the capacity of an existing settling basin can be increased) by minimizing the structural support of the sludge to reduce retardation. Suggestions are made for further investigation of the distribution of excess hydrostatic pressure during the subsidence of activated sludge and for study of the influence of biological variables on the rheological properties of activated sludge. Ill ACKNOWLEDGEMENTS The author is grateful to Dr, Ben B, Ewing, Professor of Sanitary Engineerings, for his counsel during the conception, planning and performance of this researcho Rather than imposing his will on the course of the study, Dr, Ewing offered advice and constructive criticism in a manner which encouraged the author to explore his own ideas. The cooperation and suggestions of numerous others have contributed to the investigation „ The contribution of some warrants particular acknowl- edgement o Dr Roy E, Olson, Associate Professor of Civil Engineering gave generously of his time to discuss problems in his specialty, soil mechanics, Dr, John H, Austin, Assistant Professor of Sanitary Engineering, maintained a continued interest in the study, and reviewed portions of the thesis as they were prepared, Mr Vincent J, McDonald, Associate Professor of Civil Engineering, and his staff willingly assisted the author with measurement problems. Members of the hydraulic engineering staff, notably Dr, Harry G Wenzel s Assistant Professor of Civil Engineering, provided help in their area of specialization. This investigation was supported by a research fellowship (number 5-F1-WP-21, 613-02) from the Division of Water Supply and Pollution Control, Public Health Service, IV TABLE OF CONTENTS Page ACKNOWLEDGEMENTS iii LIST OF TABLES vii LIST OF FIGURES viii I. INTRODUCTION 1 THE THICKENING OPERATION 1 THICKENING IN THE ACTIVATED SLUDGE PROCESS 2 PRESENT THICKENING THEORIES 6 Area Requirement 6 Volume Requirement 22 Unified Concepts of Thickening 28 APPLICABILITY OF THICKENING THEORIES TO ACTIVATED SLUDGE 29 PREVIOUS EVALUATIONS OF THE KYNCH ANALYSIS 31 PURPOSE AND NATURE OF STUDY 33 II o EXPERIMENTAL EQUIPMENT AND TECHNIQUES 35 MEASUREMENT OF SETTLING PROPERTIES 35 Apparatus for Settling Tests 35 Effect of Column Diameter 39 Initial Dispersion of Solids in Settling Tests 40 Nature of the Problem 40 Preliminary Investigations 43 General Procedure 43 Aeration 46 Filling from Top 47 Filling from Bottom 49 Development of Bottom Fill Procedure 51 Page Initial Mixing Procedure in Unusual Columns 56 MEASUREMENT OF RHEOLOGICAL PROPERTIES 60 Properties of Interest 60 Viscometry 60 Type of Viscometer 60 Theory of Rotational Viscometers 61 Modifications to Commercial Viscometer 62 Calibration of Viscometer 75 Procedure for Investigating Rheological Properties of Activated Sludge 78 In situ Investigation of Rheological Properties 81 MEASUREMENT OF OTHER PROPERTIES OF SLUDGE 87 Determination of Suspended Solids Concentration 87 Procedure 87 Comparison with Other Methods 89 Reliability 92 Temporal Variation in Sludge Characteristics 94 IIIo DEVIATIONS FROM PRESENT THEORIES OF THICKENING 99 PURPOSE OF INVESTIGATION 99 EFFECT OF DEPTH 100 EFFECT OF STIRRING UNDERLYING SLUDGE 112 EFFECT OF LARGE LOWER COLUMN 116 OTHER EVIDENCE OF NON-IDEAL BEHAVIOR 118 SIGNIFICANCE OF RESULTS 118 IV. RELATIONSHIP BETWEEN RHEOLOGICAL AND SETTLING BEHAVIOR 121 INTRODUCTION 121 MATHEMATICAL MODEL OF THICKENING 121 VI Page Development of Model 121 Assumptions of Mathematical Model of Thickening 131 Predictions of the Mathematical Model 132 General Form of Model 132 Defect in Model 135 Fitting of Observed Data to the Mathematical Model 138 EXPERIMENTAL RELATIONSHIP BETWEEN THICKENING BEHAVIOR AND RHEOLOGICAL PROPERTIES 146 Introduction 146 Determination of Structural Support Characteristics from Sedimentation Behavior 146 Nature of Structural Support Force 148 Experimental Results 152 Activated Sludges Examined 152 Sedimentation Properties 153 Rheological Properties 157 Comparison of Rheological and Sedimentation Data 163 SIGNIFICANCE OF RESULTS 170 Vo CONCLUSIONS 174 VI „ REFERENCES 178 VII. APPENDICES 184 APPENDIX A, A REVIEW OF RHEOLOGY 185 APPENDIX Bo THEORY OF ROTATIONAL VISCOMETRY 194 APPENDIX Co SOURCES OF ACTIVATED SLUDGE 204 APPENDIX Do SYMBOLS 208 VITA 214 Vll LIST OF TABLES Table Page I Comparison of Viscosities Determined with Cylinder Pairs of Differing Roughnesses 66 II Comparison of Yield Strengths Determined with Cylinder Pairs of Differing Roughnesses 69 III Dimensions and Geometric Constants for Mat-Roughened Cylinders 77 IV Comparison of Suspended Solids Determination Techniques 91 V Comparison of Retardation of Several Activated Sludges 108 VI Properties of Activated Sludges Employed 153 VII Constants in Expression Relating Retardation Factors to Concentration 157 VIII Constants in Expression Relating Yield Strength to Concentration 160 IX Constants in Expression Relating Retardation Factor to Yield Strength 163 Vlll LIST OF FIGURES Figure Page 1 Influence of Return Sludge Solids Concentration on Size of Waste Treatment Plant Components 3 2 Zones Formed During Subsidence of a Suspension 7 3 Definition Sketch for Determination of Solids Handling Capacity 10 4 Determination of Limiting Solids Handling Capacity 10 5 Definition Sketch for Kynch Analysis 13 6 The Kynch Interpretation of a Batch Settling Curve 13 7 Determination of Concentration-Velocity Relationship from Batch Settling Curve 16 8 Determination of Unit Area by Construction Technique 16 9 Solids Flux Plot 20 10 Logarithmic Compression Relationship 26 11 Arbitrary Determination of Time of Compaction 26 12 Settling Test Apparatus 36 13 Diagram of Apparatus for Settling Tests 37 14 Effect of Column Diameter on Settling Velocity 41 15 Illustration of Apparent Flocculation Time 44 16 Suspended Solids Profiles from Columns Mixed with Diffused Air 48 17 Suspended Solids Profiles from Columns Mixed by Filling from the Bottom 50 18 Rate of Filling Columns from Bottom by Pumping 52 19 Complete Suspended Solids Profiles from Columns Filled from Bottom 53 20 Suspended Solids Profiles and Settling Curves for Two Concentrated Activated Sludges 55 IX Figure Page 21 Suspended Solids Profiles at End of Apparent Flocculation Time in Columns of Various Configurations 58 22 Apparatus for Initial Dispersion of Suspended Solids in Shallow Columns 59 23 Modification of Rotational Viscometer 64 24 Determination of Viscosity of Newtonian Fluid Using Cylinders of Various Roughnesses 67 25 Comparison of Inner and Outer Cylinder Rotation 73 26 Error in Torque Produced by Rotation of Outer Cylinder 74 27 Effect of Flocculation Time on Viscometer Reading 80 28 Thixotropic Change of Activated Sludge in Viscometer 80 29 Techniques for in i itu Measurement of Rheological Properties 83 30 Scheme for Investigating Rheological Properties with Weighing Device 84 31 Reliability of Suspended Solids Determinations 93 32 Change in Activated Sludge Settling Properties During Endogenous Respiration 96 33 Representative Settling Curves 101 34 Effect of Sludge Depth on Initial Settling Velocity 103 35 Extent of Retardation -- Urbana-Champaign Activated Sludge 105 36 Extent of Retardation -- Tuscola and Sullivan Activated Sludges 106 37 Settling Behavior of Sand Suspensions 110 38 Device for Stirring Bottom of Settling Column 113 39 Effect of Stirring Underlying Sludge 115 40 Apparatus for Observing Effect of Large Lower Column 117 41 Effect of Large Lower Column 117 42 Abnormal Suspended Solids Profile During Thickening 119 43 Definition Sketch for Mathematical Model of Thickening 123 Figure Page 44 General Form of Mathematical Model 134 45 — vso D Plots Predicted by Model 134 v J 46 Comparison of Model Predictions and Observed Behavior. Urbana-Champaign Activated Sludge at 2400 mg/1 142 47 Comparison of Model Predictions and Observed Behavior, Urbana-Champaign Activated Sludge at 4210 mg/1 143 48 Comparison of Model Predictions and Observed Behavior., Urbana-Champaign Activated Sludge at 6280 mg/1 144 49 Settling Properties of Urbana-Champaign Activated Sludge 154 50 -vs, D Curves for Urbana-Champaign Activated Sludge 154 51 Settling Properties of Tuscola Activated Sludge 155 52 — vs, D Curves for Tuscola Activated Sludge 155 53 Settling Properties of Sullivan Activated Sludge 156 54 -vs, D Curves for Sullivan Activated Sludge 156 v to 55 Variation of Retardation Factor with Solids Concentration 158 56 Typical Viscometer Data 161 57 Variation of Yield Strength with Solids Concentration 162 58 Relationship Between Retardation Factor and Yield Strength 164 59 Relationship Between Observed Yield Strength and Pre- dictions of Laminar Model 166 60 Relationship Between Observed Yield Strength and Pre- dictions of Turbulent Model 167 61 Types of Time-Independent Rheological Behavior 188 62 Types of Time-Dependent Rheological Behavior 188 63 Schematic Representation of Coaxial Cylinder Viscometer 195 64 Behavior of Plastic Material in a Rotational Viscometer 200 I. INTRODUCTION THE THICKENING OPERATION In sanitary engineering $ the gravity thickening operation is ordinarily thought of as a special treatment given sludges prior to subse- quent treatment or disposal. Yet, thickening occurs along with clarifi- cation in any sedimentation operation. In most applications, satisfactory performance of a sedimentation basin requires production of both a clari- fied overflow and a concentrated underflow. The name given to a sedimentation basin depends upon whether one is more concerned with the thickening or clarifying function. In sanitary engineering applications, the production of an effluent with a low concen- tration of suspended solids is often the paramount consideration, and thus the name "clarifier" is common , In chemical and mining engineering problems, where the production of a concentrated underflow is frequently the principal concern, a similar tank would be called a "thickener „" Regardless of the name given to the operation, both clarification and thickening take place, and proper design of a settling basin requires analysis of both functions,, Depending on the suspension and the purpose of sedimentation 9 only cursory consideration may be required for one of the functions,, The term "thickening," as considered in this study, refers to gravity-induced concentration of flocculent microbiological suspensions primarily as it occurs in the final settling basins of the activated sludge process o The same fundamental principles apply to thickening as the treat- ment given to waste sludge prior to its subsequent treatment or disposal. THICKENING IN THE ACTIVATED SLUDGE PROCESS Waste treatment by the activated sludge process is possible only because microorganisms have the characteristic of flocculating under proper conditions o This allows removal of the biological mass by sedimentation, permitting it to be retained in the system, and makes possible the discharge of a treated effluent which is essentially free of suspended matter,, The fundamental parameter in the design of activated sludge systems is the amount of organic material per unit time applied per unit weight of sludge solids o Since, with adequate aeration and pumping capacity, the concentra- tion of mixed liquor suspended solids which can be maintained in the aeration tanks is controlled by the degree of thickening which can be accomplished in the final settling tank, the thickening function is a cardinal factor regulating the size of an activated sludge plant. The influence of the thickening function on the size of an activated sludge plant can be readily illustrated by means of an example „ Consider a plant receiving a flow, Q,* and returning activated sludge at a rate 9 R 9 as shown in Figure la„ If sludge is withdrawn from the final settling tank at a concentration of 1 percent, which according to Heukelekian and Weisburg (1956) is the normal limit for good activated sludge, and the mixed liquor suspended solids concentration is 2500 mg/1, then it may be seen that R equals 33 percent of Q (presuming that Q contains negligible solids )„ One-third of the organic matter in the raw waste will be considered to be removed as settleable solids in primary treatment, one-third as synthesized biological mass from the secondary portion of the plant s and one-third as carbon dioxide resulting from biological oxidation „ "Symbols are defined where they first appear and again, with dimensions, in Appendix D„ (a) RETURN SLUDGE =99% WATER Q PRIMARY SETTLING T L T AERATION TANK V = l.33 QT R =0.33 Q RETURN SLUDGE PUMP NOTE : SEE TEXT REGARDING ASSUMTIONS AND DIGESTER SIZE. (b) RETURN SLUDGE = 96 % WATER Q PRIMARY SETTLING JL 3 L AERATION TANK V=l.08 QT R = 0.08Q FINAL ^SETTLINGl T L ^a> STREAM k! RETURN SLUDGE PUMP Q = RAW WASTE FLOW RATE L = ORGANIC LOAD R = RETURN SLUDGE FLOW RATE q = RELATIVE WASTE SLUDGE VOLUME V = RELATIVE VOLUMETRIC CAPACITY T = DETENTION TIME FIGURE INFLUENCE OF RETURN SLUDGE SOLIDS CONCENTRATION ON SIZE OF WASTE TREATMENT PLANT COMPONENTS . If raw sludge is removed at a concentration of 4 percent, and activated sludge is wasted directly to the digesters, the volume of waste activated sludge may be roughly approximated as four times the volume of raw sludge, q s as indicated in Figure la. This presumes that the two forms of organic material are basically similar,, Figure lb shows the plant as it would appear if return sludge could somehow be removed from the final settling tank at a suspended solids concentration of 4 percent „ It is seen that the return sludge and piping facilities could be reduced to 25 percent of their former capacity and still return the same amount of biological material,, Because less water would be returned to the aeration tank, its relative volume could be reduced from 1,33 QT to 1„08 QT, or by almost 20 percent . The total volume of sludge pumped to the digesters would be reduced 2,5 times. Limitations on the volatile solids loading on the digester might prevent a major change in its volume, but piping and pumping capacities could certainly be reduced, The area of the final settling tank would be the same in either case. In an existing activated sludge plant where the size of the facilities is fixed, inadequate thickening results in a reduction in the weight of solids returned to the process, if the volume of return sludge is maintained constant If the rate of return based on weight of biologi- cal solids is held constant, then the aeration time must be somewhat reduced because of the higher flow rate. In either case, the net effect is that the microorganisms will not have progressed as far along their growth curve when they enter the final settling tank as they would have if thickening were adequate. Their flocculant nature and settleability is thus impaired (McKinney, 1956), and the problem is compounded. In spite of its influence on the sizing and performance of activated sludge plants, conventional design procedures do not recognize the thickening function of final settling tanks „ Conventional procedures are typified by the recommendations of the Great Lakes-Upper Mississippi River Board of Sanitary Engineers (1960) which advocates design of final settling tanks on the basis of a surface settling rate, Lesperance (1957) noted that proper analysis of any sedimentation problem requires the determination of an area and a volume for both the clarification and the thickening functions. The area required for clarifi- cation may be determined from the classical overflow rate considerations as described by Hazen (1904) and Camp (1936), while the area required for thickening is determined by the solids transmitting capacity of the limiting concentration of the suspension as hereinafter discussed „ The larger of the two areas must be provided if the basin is to satisfactorily perform both its clarifying and thickening duties. The volume required for clarification is established by considering the flocculating charac- teristics of the dispersion as described by O'Connor and Eckenfelder (1957), or by considering the interface subsidence velocity in the case of zone settling,, The volume required for thickening may be determined from the compaction characteristics of the sludge (Roberts, 1949 ) Because of the tendency to consider only the clarification function of final settling tanks 9 few data are available regarding the thickening properties of activated sludge Lesperance (1957) indicated that, for an activated sludge of given concentration, either the thickening or clarification functions might regulate the required area of a settling tank depending on the biological condition of the sludge. The thickening requirement was found to control the size of the final settling tank in two of three plants studied by the author „ As illustrated in the preceding example by the effect of activated sludge concentration on the required digester capacity, the problem of thickening of activated sludge is pertinent, not only in the process per se, but also in the handling of the excess sludge resulting from synthesis in the process o The problem of treatment and/or disposal of this waste sludge can be minimized by further thickening of the solids wasted from the final settling tank underflow,, The economic feasibility of thickening waste activated sludge prior to anaerobic digestion has frequently been shown -- notably by Torpey (1954) and Nelson and Budd (1959) The need for addi- tional thickening of activated sludge prior to other types of treatment has also been noted — as, for example, by Hurwitz and Katz (1959) „ The principles of thickening of activated sludge considered in the sections which follow apply equally well to thickening as it occurs in final settling tanks and in special thickeners „ PRESENT THICKENING THEORIES Area R equirement Modern thickening practice is founded on work by Coe and Clevenger (1916)„ These authors described the thickening mechanism by defining four distinct settling zones as shown in Figure 2„ Proceeding from the top to the bottom of a container filled with a settling suspension, the zones were as follows : a„ zone of clarified liquor,, bo zone of uniform concentration which settles at a constant Y7 b •I:::::::::: c CLARIFIED LIQUID ZONE SETTLING TRANSITION COMPRESSION FIGURE 2. ZONES FORMED DURING SUBSIDENCE OF A SUSPENSION . 8 rate j frequently termed the zone settling velocity,, This velocity is less than that predicted by expressions for the settling velocity of individual particles because of the increase in drag occasioned by the presence of other particles „ In addition to this hindered settling, particles in zone settling are considered to remain in fixed positions relative to one another,, Co transition zone in which the solids concentration increases from that of zone b to the concentration at the top of zone d„ do compression zone in which the particles rest upon each other Coe and Clevenger introduced the concept that each concentration of a suspension has a certain capacity to discharge its solids. Figure 3 illustrates a column of sludge with unit cross sectional area which is initially at a concentration (weight per volume), c.„ After elapse of time, T, the suspension subsides a distance, vT, and a portion of the solids are considered to concentrate from concentration c. to concentration c „ Pre- 1 u suming T to be unity, the weight of water which has been clarified, W, is W = vy where y is the unit weight of water „ Obviously, this water came from the sludge which was compacted from c. to c „ Thus, if the weight of solids which was so compacted was C, then the weight of clarified water may also be expressed as '' c. c Y 1 u/ Equating Equations 1 and 2 yields C = c. c 1 u in which C is the solids handling capacity of the suspension at concentra- tion c. in weight of solids per unit area per unit time,, Coe and Clevenger explained that if a layer has a lower solids handling capacity than the overlying layer, it will not be able to dis- charge solids as fast as they are received and will necessarily increase in thickness „ Accordingly, if a layer is able to transmit solids at a higher rate than they are received from the overlying area, its thickness will remain infinitesimal. It follows that the basis for determining the area required for the thickening function of a sedimentation basin is to provide sufficient area to assure that solids are applied at a rate less than the solids handling capacity of the limiting layer. Coe and Clevenger prescribed a series of batch settling tests at various concentrations to identify this limiting layer. In general, while the settling velocity of a suspension decreases with an increase in particle concentration, the rate of decrease may be less than the rate of increase of concentration over some range of concentration. Thus, the solids handling capacity, C, is normally found to pass through some minimum value when the suspension concentration is varied. Figure 4 shows the relationship between concen- tration and solids handling capacity, and illustrates the selection of the limiting solids handling capacity, C , for use in determining the required L area of a thickener, Kynch (1952) performed a mathematical analysis of the thickening 10 FIGURE 3. DEFINITION SKETCH FOR DETERMINATION OF SOLIDS HANDLING CAPACITY. c, weight /unit volume FIGURE 4. DETERMINATION OF LIMITING SOLIDS HANDLING CAPACITY . 11 operation predicated on the basic assumption that "at any point in a dis- persion the velocity of fall of a particle depends only on the local con- centration of particles „" This is interpreted to mean that for each type of suspension there is a unique curve relating velocity of fall and local concentration (Kynch, 1964) „ Kynch wrote a continuity equation describing solids entering and leaving an infinitely thin element at the surface of a layer of given concentration in a batch settling test. He then showed that, if his assumption that settling velocity depends only on local par- ticle concentration was correct, the surface of the layer would move upward at a uniform velocity,, Figure 5 shows the infinitely thin layer examined in the Kynch analysis o The layer, of concentration, c, is presumed to be at the upper surface of a stratum of sludge which receives solids at a rate faster than it can transmit them to the underlying strata „ Thus, the stratum increases in thickness, and the layer is propagated upward at a rate, u Since the layer in Figure 5 is presumed to remain infinitely thin, the rate at which solids enter its upper surface must equal the rate at which solids exit from its lower surface The concentration and settling velocity of sludge above and below the layer is illustrated in Figure 5„ From this information, the solids balance for the layer may be written as (c - dc)(v t dv + u) AT = (c)(v + u) AT 4 where A is the area of the layer, T is time, and other terms are described in Figure 5„ Simplifying, dropping the second order infinitesimal, and solving for u gives u = c -r— - v 5 dc 12 In accordance with the basic assumption that v = f(c), do"" f (C) But, since the concentration within the layer is constant, both f(c) and f (c) are constant,, It follows from Equation 5 that u, the upward rate of propagation of the layer of concentration c, is a constant ■ Kynch went on to show that the continually decreasing slope of the suspension-liquid interface vs„ time curve in batch settling tests could be interpreted to represent the successive intersection of slower- subsiding, more-concentrated layers with the interface „ This implication of the Kynch analysis is illustrated in Figure 6 A suspension of initial concentration "a" settles at a uniform rate as indicated by the slope of the line AB At the same time, a layer of concentration "b" is propagated up from the bottom of the vessel at a constant velocity equal to the slope of line OBo At point B, the subsidence velocity of the interface is reduced to that of the settling rate of the suspension at concentration "b" (slope of the line BC) At point C, the layer of concentration "b" has expired, and the interface subsides at a rate equal to the slope of line CD which is the characteristic settling rate for the suspension at ;ion "c," and so forth „ It is interesting to note that, if science would progress in a more orderly fashion, Kynch *s work in 1952 would have preceded that of Coe and Clevenger in 1916„ Coe and Clevenger 1 s concept of a limiting solids handling capacity is a logical outgrowth of Kynch' s contribution „ It is obvious that Coe and Clevenger were tacitly aware of the upward propagation 13 v + dv c-dc \ ^ I c = CONCENTRATION v = SETTLING VELOCITY OF SUSPENSION u = RATE OF UPWARD PROPAGATION OF LAYER FIGURE 5. DEFINITION SKETCH FOR KYNCH ANALYSIS. TIME FIGURE 6. THE KYNCH INTERPRETATION OF A BATCH SETTLING CURVE. 14 of layers of higher concentration at a uniform velocity „ This is evident from their discussion of the growth of a layer which receives solids at a faster rate than it can pass them Coe and Clevenger failed, however to recognize Kynch u s concept, or s at least, did not develop it„ Talmage and Fitch (1955) also noted this similarity between Kynch's analysis and the work of Coe and Clevenger „ Kynch's contribution — even though it is relatively recent -- may, then, be considered as the fundamental basis for present procedures for determining the area required for thickening Talmage and Fitch (1955) showed that, according to the Kynch analysis, multiple batch settling tests for determining the limiting solids handling capacity, as advocated by Coe and Clevenger, were unnec- essary,, Since all layers with less capacity than the layer above are ultimately propagated to the surface, their settling rates may be deter- mined from the slope of the interface-time curve, The concentration associated with any segment of the batch settling curve can be deduced by back extrapolation of the tangent to the segment as shown in Figure 7 If a layer of concentration c. is considered to be propagated upward at a constant velocity, u., then at time, T., when the layer reaches the sur- face, all solids in the container have passed through the top of the layer, This total weight of solids can be represented as c H A, where c is the & r o o ' o concentration at the beginning of test, H is the initial depth, and A is the cross -sectional area of the test column „ The total weight can also be expressed in terms of u, and v., the settling velocity of the suspension at concentration c, as follows; c H A = c.AT. (v. + u.) o O 111 1 15 The back extrapolate, H, , may be substituted for T.(v. + u.), and Equation 7 becomes c H o o Equation 8 provides a basis for determining the critical solids handling capacity of a suspension from a single settling test„ Having determined the settling velocity from the slope of the settling curve and the corre- sponding concentration from Equation 8, the solids handling capacity of the suspension at that concentration may be computed from Equation 3„ Repetition of this procedure for several points on the settling curve permits development of the relationship between concentration and settling velocity o A curve such as shown in Figure 4 may be plotted, and the con- centration with the limiting solids handling capacity may be selected for determining the required area of the thickener, Talmage and Fitch also proposed a technique for establishing the area requirement for an arbitrarily-selected, rate-limiting layer „ This procedure is illustrated in Figure 8„ If the point at which the tangent is drawn is presumed to correspond to the layer with the smallest solids transmitting capacity, it may be seen that the slope of the tangent is dH _ b i dT T. l This represents the rate at which the solids subside, or, considering the solids as the datum s the rate at which water passes through the solids „ Note the H, may be considered as the depth to which the total solids in 16 CO o Q. LU (J a: LU FIGURE 7. TIME DETERMINATION OF CONCENTRATION VELOCITY RELATIONSHIP FROM BATCH SETTLING CURVE . CO O CL UJ O cr LU H; A = T " " c H X. T| T u TIME FIGURE 8. DETERMINATION OF UNIT AREA BY CONSTRUCTION TECHNIQUE . 17 the column would stand if they were at the concentration represented by point i s c. (see Equation 8) If H is considered to be the depth to which the solids would stand at the desired underflow concentration, the total depth of water through which the solids must settle is H ~ H „ The time required to eliminate this much water is H, - H m b u T = H-nr 10 b 1 T. 1 T. _!_ = _i — ii H b - H u H b ~ H i From similar triangles, T = T 12 u The total weight of solids in a settling column of unit area is c H , and to to o o' the rate at which these solids could be passed through the layer of concen- tration, c, would be c H /T o Now defining the "unit area," A , of a ' 1* o o u ' u' layer as the area required to allow a given weight of solids to pass through the layer in a given time permits one to write T u c H o o According to Talmage and Fitch, A in Equation 13 is expressed in sq ft per ton per day, T is in days, and c is in tons per cu ft. The value of A as determined from Equation 13 is to be multiplied by the amount of solids to be handled in tons per day to obtain the required area of a thickener„ 18 In spite of the fact that no sound basis has been advanced for selecting the rate limiting concentration , the technique has gained wide acceptance o Empirical methods for selecting the rate-limiting layer have been prescribed (Eckenfelder and Melbinger 9 1957 )„ In presenting their adaptation of the Kynch analysis for use in thickener design s Talmage and Fitch (1955) argued that values of solids handling capacity obtained from analysis of a single settling curve were more accurate than those obtained from multiple settling curves at various initial concentrations according to Coe and Clevenger's technique „ They explained that Coe and Clevenger's method presumed that the settling characteristics of a floe were independent of the initial concentration of solids in the sludge in which they are formed Talmage and Fitch found that j at high concentrations , settling velocities determined by use of the Kynch analysis were lower than those determined by the Coe and Clevenger technique — presumably because of differences in the characteristics of the two flocculent suspensions of equal concentration „ Shannon et al„ (1964), who worked with a suspension of glass beads, reported that the settling velocities of solids concentrations formed in the curved portion of the settling curve were the same as the initial settling velocities of suspen- sions at corresponding initial concentrations „ Shannon and Tory (1965) found differences in the settling velocities of calcium carbonate slurries determined by the two methods They maintained that the deviation was caused by the fact that the maximum solids concentration at the bottom of the bed changed with time so that the concentration determined by graphical extrapolation was not the true concentration of the interface „ They felt that the slurry did settle at a velocity corresponding to the true inter- face concentration o 19 Hassett (1958b) found that settling velocities obtained from the curved portion of a batch settling curve were less than the corresponding velocities obtained from the initial straight-line portion of a settling curve of corresponding concentration, and concluded that the work of Kynch (1952) and Talmage and Fitch (1955) was in error. Alderton (1963), who worked with gold mine slurries, found that area requirements based on the Kynch-Talmage and Fitch method were much larger than requirements of the Coe and Clevenger technique „ Plant-scale operation in a 50-ft diameter basin indicated the Coe and Clevenger value to be more nearly correct Fitch (1962) seemingly reversed his position and advocated the use of multiple batch settling tests to determine the limiting solids handling capacity rather than single settling curves as he had previously recom- mended Several recent workers (Kynch, 1952; Yoshioka et al , 1957; Hassett, 1964, and Shannon et al„, 1963, 1964, and 1965) have employed plots of solids flux vs„ concentration in analysis of the sedimentation of suspensions o Such a curve is shown in Figure 9 The doubly concave shape resembles that obtained by Shannon et al„ (1961) for rigid glass sphereso The solids fiux s S s is defined as the weight of solids passing through a unit of cross-sectional area per unit time,, In batch settling operations, it is S, = cv 14 D where v is the settling velocity of the suspension, and c is its concen- tration j expressed as weight per unit volume „ In the case of continuous thickening operations, the solids flux is increased because of the 20 X q _i o CO SOLIDS CONCENTRATION FIGURE 9. SOLIDS FLUX PLOT. 21 downward movement of the sludge and becomes S = (v + u)c 15 c where u is the downward velocity of the sludge (the sludge withdrawal rate, Q , divided by the cross-sectional area, A)„ In a continuous thickener which is at equilibrium, u in Equation 15 is equivalent to u in Figure 5 for the rate-limiting layer That is, the downward velocity in a continuous thickener at equilibrium must equal the rate of upward propagation of the rate-limiting layer in a batch settling test„ Since the sludge withdrawal rate may be written as S A Q = — 16 u c u where c is the underflow concentration, then u ' S u = -£■ 17 c u Substituting this expression into Equation 15 gives 18 which is the same as Equation 3 -- Coe and Clevenger's expression for the solids handling capacity of a suspension. It may be seen that the slope of a line from the origin to a point on the flux curve is the settling velocity of the suspension at that concentration,, Also, Kynch (1952) showed that the slope of the tangent at 22 any point on the flux plot, dS/dc, was the velocity at which a layer of the corresponding concentration was propagated upward from the bottom of a vessel in batch settling tests „ Shannon et al„ (1964) employed these principles to accurately predict batch settling curves for suspensions of rigid spheres from flux plots. Flux plots have also been employed to determine the area required in a thickener to accomplish a desired underflow concentration (Yoshioka et al , 1957, and Shannon and Tory, 1965)., Referring to Figure 9, the allowable solids flux to withdraw solids at a concentration c from a con- u tinuous thickener would be S , the intersection on the ordinate axis of x the tangent to the flux curve originating at c , The required area of a thickener receiving solids at a rate, R, would be R , „ A = _ 19 x It should be noted that flux plots are used as a method of data analysis The technique does not represent any deviation from, or expansion of, the basic thickening concepts developed previously. The approach has been advocated (Shannon and Tory, 1965) as a convenient means of relating batch and continuous thickening and as a tool in gaining insight into the thickening operation., Volume Requirement Classical thickening theory maintains that, while the area required in a thickener is determined by the solids handling capacity of the rate-limiting layer, the volume is determined by the time needed for further compaction beyond the concentration of the limiting layer. In 23 terms of the settling regimes described by Coe and Clevenger (see Figure 2), the area requirement is considered to be determined by the transition zone, while the volume requirement is determined by the compaction zone. Analysis of compaction has been largely empirical — it has not enjoyed the rational approach given to the determination of solids handling capacity,, Although early workers such as Coe and Clevenger (1916) recom- mended laboratory tests to determine the required time in compression just as current practice prescribes, the foundation for modern concepts of com- paction is commonly considered to have been laid by Roberts in 1949," He noted that the rate of elimination of water in the compression zone was proportional to the amount of water yet to be eliminated „t §= "k cr < Q. Q_ < O < o: e> < ro o ~ — or X LU i— cr Z) e? 38 10 gal of sludge , and was continually aerated to maintain aerobic conditions and to uniformly distribute the solids „ The pump discharge line was equipped with a throttling valve to regulate the rate of filling columns and with a check valve to prevent backflow when the pump was shut off when a column became filled to the desired level,, After completion of a settling test, suspended solids were redistributed in the settling column by intro- ducing air through a sampling tap at the bottom of a column „ Sludge was then allowed to flow by gravity back to the reservoir by opening the valve in the check valve bypass line a The air conditioner, windows, radiators, and exhaust fan in the room in which experiments were conducted were manually regulated to maintain constant temperature. Sludge was brought to equilibrium temperature before tests commenced. Settling tests in the first phase of the study were con- ducted at a constant sludge temperature of 20°C. The second phase was conducted during a warmer season, and it was necessary to operate at tem- peratures as high as 25°C, although the temperature variation during individual experiments did not exceed 2°C. It has been noted frequently that rakes should be employed in batch settling tests (Behn, 1957)„ Typically, such rakes are built of 1/8-in. wire, extend the entire depth of the column, and rotate at about 1 rpm Because the structural properties of sludge were of interest, rakes were not appropriate in this investigation as they would disrupt the very structure which was to be studied. In the absence of rakes, data from the few experiments employing concentrated sludge were erratic. It was presumed that this behavior was caused by the fact that pronounced bridging or arching occurred during subsidence of the concentrated sludge and that failure of one bridge catalyzed a chain reaction resulting in the 39 obliteration of many void spaces „ Settling was thus alternately slow and rapid, corresponding to the formation and destruction of bridges „ The initial solids concentration at which this erratic behavior occurred varied with the source and character of the activated sludge, but with ordinary sludges it was expected to occur at concentrations greater than 6000 or 7000 mg/1,, This observation is in agreement with Mancini's finding (1962) that rake action was not important in batch settling tests with activated sludge if the initial solids concentration was less than 5000 mg/lo Effect of Column Diameter Laboratory settling tests differ from sedimentation as it occurs in practice in that the container boundaries are more prevalent,, As the diameter of the container is reduced, the "wall effect" becomes more pro- nounced,, Ordinarily, in sedimentation studies, this wall effect is con- sidered to manifest itself in a reduction in particle settling velocities due to interference with the normal streamlines about a falling particle. However, in settling tests employing suspensions such as activated sludge which exhibit zone settling, the effect of the wall is — as will be shown by the data which follow — to increase the settling velocity,, It is pro- posed that this is because the water which is being displaced by the sub- sidence of solids encounters less resistance flowing upward along the wall than by the more tortuous route between particles „ While this effect cannot readily be eliminated in laboratory studies, it is well to minimize it and to inquire as to its magnitude „ Numerous investigators have indicated that wall effects are not of particular importance in laboratory suspension settling tests, Coe 40 and Clevenger (1916) indicated that column diameters greater than 2 in„ had little effect on settling rates Kammermeyer (1941) found that 1„57 in was sufficient o Mancini (1962), who worked with activated sludge, investi- gated diameters from 2 25 to 12 in„ and could not discern that column diameter had any effect on settling rates „ Clifford and Windridge (1932) studied the rate of subsidence of activated sludge in columns from 1„34 to 4 19 in„ in diameter and found that settling velocity increased with column diameter — the antithesis of the results reported here. Initial settling velocities of sludges of various concentrations and sources^ were observed in columns ranging in diameter from o 62 to 7„5 in„ Initial sludge depths were 3 5 ft„ The results, shown in Figure 14, indicate that column diameter is of more importance than the literature suggests o It is seen that the most severe effect of diameter is in sizes smaller than 2 or 3 in , but that the wall effect continues to influence settling velocity in larger columns „ The results indicate that laboratory columns should definitely be greater than, say, 2,5 in., and cast doubt on the common sanitary engineering practice of observing the settling proper- ties of suspensions in 1-liter graduated cylinders „ The desirability of using settling columns which are as large as possible is offset by laboratory space limitations, the cost of large columns, and the large sludge volumes required. The 3 5-in diameter columns employed in this study were considered to be a reasonable compromise, Initial Dispersion of Solids in Settling Tests Nature of the Problem „ Although failure to obtain uniform initial distribution of suspended solids is often offered as a possible cause of "See Appendix C for descriptions of plants from which activated sludge was obtained o 41 c E o o _) UJ > 1.0 0.8 0.6 04 0.2 0.10 008 006h 0.04 002- LU _l 0010 < P 0.008 ? 0006 0.004 0002 - 0001 - URBANA- CHAMPAIGN, 2380 mg// □ -TUSCOLA, 5290 mg// A-- URBANA- CHAMPAIGN, 6490 mg// COLUMN DIAMETER, in. FIGURE 14. EFFECT OF COLUMN DIAMETER ON SETTLING VELOCITY. 42 otherwise unexplainable behavior in batch settling tests (Shannon et al. , 1964, Gaudin, Fuerstenau, and Mitchell, 19 59), the literature offers no satisfactory remedy to the problem„ Many writers failed to report their technique for distributing solids (Mancini, 1962; Gaudin et al, , 1959; Comings, 1940; Behn, 1953; Shroepfer and Ziemke, 1959; and Talmage and Fitch, 1955), and those who mention their technique refrained from com- menting on its efficacy o Coe and Clevenger (1916) employed shaking to initially disperse solids and allowed 1/8 in„ of subsidence to occur before starting the batch test„ Clifford (1932) and Kearsey and Gill (1963) also employed hand shaking,, Michaels and Bolger (1962a) compared inversion by hand and mechanical mixing as methods of dispersing clay slurries and concluded that the methods produced different floe sizes and settling velocities, but that either method gave reproducible results. Daily and Bugliarello (1958) employed stirring. Hassett (1958a) used fluidization, but speculated that classification might occur. Shannon, Stroupe, and Tory (1963) used aeration. While several of these investigators worked with flocculent materials, none of them dealt with the unique problems of dispersing such suspensions, Uniform distribution of solids is ordinarily obtained by creating turbulent conditions. Such conditions produce shearing forces which destroy the very floe which is to be studied. After the dispersing mechanism is discontinued at the start of the settling test, velocity gradients subside, and an opportunity for reformation of the flocculent particles is afforded. It is the uniformity of the distribution of sus- pended solids after they are reformed which is of interest. Sedimentation of solids during the period of reformation must be minimized. This pro- duction of nonhomogeneous conditions during the period of reformation of 43 floe particles is referred to herein as "separation of solids „" A typical batch settling curve for a flocculent material such as activated sludge, as is shown in Figure 15, illustrates the problem of distributing flocculent solids „ It is seen that the material did not sub- side appreciably at the onset of the test, but that a lag period occurred before constant-rate zone settling commenced „ The back extrapolate of the constant settling rate portion of the curve was taken as a measure of the time required — 2„4 min. in this case — for the suspended solids to reagglomerate, and was termed the apparent flocculation time„ Although some flocculation took place after the end of the apparent flocculation period, as indicated by the increase in the slope of the settling curve after 2 4 min, the back extrapolate provided a convenient measure of the effective time of reflocculation -- hence the term "apparent," The test shown in Figure 15 employed activated sludge with a suspended solids con- centration of 2080 mg/lo Dispersion was accomplished by aerating for 10 min at a rate of 1„5 1/min in a column 3„5 in„ in diameter,, While solids were ideally distributed at the beginning of the test, the solids concen- tration increased at the bottom and decreased at the top during the first 2„4 min Hence, little reliance could be placed on data obtained from such a testo Preliminary Investigations , General Procedure. --To obtain perfect distribution of suspended solids at the end of the apparent floc- culation period, it would be necessary for turbulence to subside uniformly, and for floe particles to instantaneously and simultaneously reform throughout the column <, Such conditions obviously cannot be created. It was necessary, however, to develop a technique which would minimize the 44 C £ LU LU I- 3 O o o LU cr < Q_ < o h- < H co 3 in LU q: 3 W 'NOIllSOd 30VJd31NI 45 extent of nonhomogeneity which existed at the end of the apparent floccu- lation periodo A 3 5-ft sludge depth in columns 3,5 in, in diameter was used for the preliminary studies „ Activated sludge from the Urbana-Champaign plant was employed „ Dispersion of suspended solids by hand shaking, raising and lowering of a plunger, aeration, filling from the top, and filling from the bottom were considered,, The first two possibilities were dismissed after cursory trials due to difficulties in reproducibility and because of the tendency for production of localized regions of high turbu- lence which persisted long after discontinuance of mixing,, Aeration and top and bottom filling showed promise in early trials and were studied more extensively. Some optimum rate of mixing could be expected to exist for each technique o Aerating or filling too slowly would not create homogeneous conditions during the initial mixing period. Aerating or filling too rapidly would create extensive turbulence. This would produce a long apparent flocculation time due to the long period required for decay of turbulent eddies, and afford an opportunity for separation of solids. The technique for evaluating initial mixing techniques was to obtain a sus- pended solids profile at time, T = 0, at the end of the mixing period, plot the interface height vs. time curve to determine the apparent floc- culation time, and then to obtain a solids profile at the end of the apparent flocculation period (T = T f )„ Variations from the mean solids concentration in the column were evaluated by use of the 95 percent confi- dence interval obtained from the study of the precision of the suspended solids determination technique (Figure 31), This procedure provided a basis for discerning meaningful variations in solids concentration from 46 random variations. Points falling outside of the 95 percent confidence limits were not , however, necessarily indicative of improper distribution. While the 95 percent confidence limits reflect only the variation in the suspended solids determination, variations in points on the suspended solids profiles of the columns were caused by several additional factors. The solids profiles were obtained by successive repetition of the mixing procedure until samples had been withdrawn from all desired locations in the column „ Aliquots were then withdrawn from the samples for solids determination,, Thus, the variation in points on the solids profile in- cludes measure of the reproducibility of the initial dispersion technique and of the precision of obtaining samples and withdrawing aliquots. In addition, the observed mean solids concentration determined for the column might be different than the true mean because of the limited number of samples employed Aeration o— Aeration was the most convenient of the dispersion techniques studied „ Compressed air was introduced through diff users situated in the bottom of columns, and the intensity of mixing was con- trolled by adjusting the air flow rate The diff user employed was a 3.5-in. plugged piece of 0„375~in. diameter Plexiglas tubing through which fourteen 1/16-in. holes were drilled. In one series of tests, a porous stone diff user was employed. During the aeration period a homogeneous suspension was readily maintained. Only at extremely low air flow rates did separation of solids occur during mixing. Unfortunately, aeration at a rate sufficient to uni- formly disperse solids created a high degree of turbulence with an accom- panying long apparent flocculation time. In all tests, air flow rates above the minimum required to maintain homogeneity during the mixing 47 period were attended by severe separation of solids during the apparent flocculation period„ An attempt to reduce the magnitude of turbulent eddies by employing fine bubble diffusion was unsatisfactory because of flotation of solids „ Figure 16 illustrates the difficulties encountered with aeration as a means of distributing solids „ Points on the curves are connected for purposes of illustration and not to suggest a continuous gradient in solids concentration from one sampling point to the next,, Part a of the figure demonstrates the difficulty in obtaining uniform initial distribution of suspended solids with a very low air flow rate. Part b shows that the distribution at the end of the mixing period could readily be improved by increasing the air flow rate, but that separation occurred during the apparent flocculation period „ The data in Figure 16b correspond to the settling curve shown in Figure 15 „ Part c of Figure 16 shows the effect of flotation when fine bubbles were employed. It was concluded that aeration could not be relied upon as a means of distributing solids at the start of batch settling tests „ Air flow rates high enough to disperse the solids were accompanied by long apparent flocculation times during which separation occurred. Filling from Top u — Initial distribution of suspended solids by filling from the top was accomplished by siphoning the contents of a vigorously aerated container of sludge Into a column „ The degree of tur- bulence in the column was controlled by altering the filling rate. During the filling period, solids tended to become more highly concentrated at the bottom of the column while the concentration in the middle of the column fell below the mean At the top, suspended solids remained sheared and did not separate during filling . During the apparent flocculation 48 < o_ hi ^ c en — L±J E fc v. c _l o ^A E UJ CD 00 CO in O Z> CM O CO GD ii n ii ( > o \-? LlI 2 U. o UJ < q: ^ ^ \ c o _i E E c u. O *Sk E or 00 o in sr — r\| CO < n ii n ( ) o P _L e> "^ cf E E m O — rO c ii UJ <3" <\l E in 1- < 2 2 or o o 1- O o i— 2 II l- _i LlI o < u. O 7* _l 3 cr O f 1 _l Ll. o < CO cc o _J CO < Ll O o o h" o o c o CD E «4- o ■♦— o c GO CO CO o o 2 o (T U_ CO . UJ cc _l < u_ o ce n Q UJ to 3 CO h Q U_ _i n o CO X i- o UJ £ Q 2 UJ Q CL UJ CO X ~> ^~ CO ^ CD UJ CC 3 IO wouoq wojj u 'NIAiniOO Nl NOIllSOd 49 period, separation did occur „ Attempts to establish the optimum rate of filling from the top to minimize nonhomogeneity were abandoned when the technique of filling from the bottom was perfected „ Filling from Bottom, =~The technique of distributing solids by- filling settling columns from the bottom employed a reservoir in which sludge was maintained in a sheared, homogeneous condition by aeration and a pump which forced the sludge through o 5-in o piping into the bottom of the columns o The degree of mixing was controlled by throttling a valve to vary the filling rate. Sludge in the lower portion of the column was maintained in a sheared state during the filling operation due to the turbulence induced by the entering sludge „ At depths over one to two ft (depending on the filling rate), turbulence subsided to such an extent that the upper por- tion of the column started to reagglomerate during the filling operation. The flocculated suspension was then carried upward in laminar flow„ When filling was too slow, sedimentation commenced in the upper portion of the column producing a high suspended solids concentration at an intermediate level with a low concentration at the top„ Such a situation is shown in Part a of Figure 17. More rapid filling gave uniform distribution at the end of the filling period , but produced so much turbulence that solids were able to separate during the apparent flocculation period as illustrated in Figure 17b. An intermediate filling rate, illustrated in Figure 17c, maintained homogeneous conditions during the filling period, and yet did not create sufficient turbulence to permit separation during the apparent flocculation period. On the basis of these results the bottom filling technique was selected for more extensive study to establish a standard procedure for initial dispersion of suspended solids. 50 UJ < or _3 I- Q_ O o E O O CVI ii o or e c c E E o C\J c\J O c\J n n o u_ h=" 0_ < or en E O <£> en C\J UJ s 5 Or q: i w o o CO CD c E 10 c o F II UJ CD ^ — H n UJ Z O - ,- o CO <-> o o 3 Ll ii UJ , H — UJ *£ o ± o c o CD E o c GO CO o L. o CD *- Q. h- O < or \- -z. UJ CJ o 2 o o o CO Q _J o o CO CO o n 5: UJ o 2 UJ CL CO o :d C\J CO CO o . o 5 o 5 1- 1- o o ir GO u_ UJ CO X UJ h- _l u. o or 5 o rr LL li- CO es o z _l _i o _i CO u. n UJ O > 00 z UJ Q Q. UJ CO X => CO ^ UJ IO ujouoq wojj u 'NIAimOO Nl NOIllSOd 51 Development of Bottom Fill Procedure „ The filling procedure was standardized utilizing a 3 5-ft sludge depth in columns 3 5 in in diameter. The pump originally employed gave the declining-rate filling curve illus- trated in Figure 18, This pump was incapable of filling deeper columns or columns of larger diameter at a suitable rate $ and when large columns were used, it was necessary to employ a high capacity pump which gave the more constant rate filling curve shown in Figure 18 „ A comparison of solids profiles and settling curves from columns filled by the two pumps in the same interval of time revealed no appreciable differences. With sludge from the Urbana-Champaign plant, filling times less than 1.5 min normally gave satisfactory distribution at the end of the filling period, and little separation normally occurred during the apparent flocculation period when the filling period was greater than 1 min. Thus, the range of filling times from 1 to 1 5 min was studied, with emphasis on filling times of 1„1 to 1„2 min. The mere fact that an interface appeared during the apparent flocculation period demonstrates that some alteration of suspended solids distribution occurred during that time The severity of the alteration in the upper 6 in. was of particular interest and was investigated by filling the column to varying depths between 3„5 and 4 ft and withdrawing samples from the sampling tube at the 3.5=ft level „ Such profiles are shown in Figure 19. Little reliance could be placed on samples withdrawn near the interface at the end of the apparent flocculation period because of like- lihood that clarified liquid was withdrawn with the sample . In one series of tests the effect of the possible reduction in solids concentration near the surface was checked by overfilling columns to 3.75 ft and then with- drawing the upper 0.25 ft at the end of the apparent flocculation period. 52 O Q_ LlI Q SMALL PUMP \— LARGE PUMP 60 80 100 PORTION OF TOTAL FILLING TIME, percent FIGURE 18. RATE OF FILLING COLUMNS FROM BOTTOM BY PUMPING. 53 1 SLUDGE CONFIDENCE INTERVAL I i *•- ii 1 Q 5« UJ H & < u /C-° — "V" — — — rO- 2S j*' z _ [ / V, o r — 0_ H 1 ^s* t- — u-5 i E o c E o H- •z. < <£> sr If) ST — 2 N ^ < C\J o rO rO GD II H ii ii jqi o h^ o Q d" - ^^ 13 « — i i 1 UJ 4: -i i i 1 o ^ UJ < 2 <-> > o ■s* t z or *■ o _j \ N*) UJ UJ i— II - CO Q UJ 6 o b 10 d ii Oh i i 1- 1- on II »_ K° < > CM UJ *" < 5? UJ i= II z. h- O in Zvf) ' O CT) ^^ — < o rO .«-* ^ a -»— \- c ■> ii t u^ * E 3^ — o--o— ^ ^o" N n^ LING MPAIGIS < or i- Z UJ o _i u. »- I 1- CL UJ o CO 2 - UJ 4 *f j _l < o Z o I.I MIN Fl URBANA-CH z o o CO CO II CJ UJ or < CL < n < Z ii < or UJ f- z ii d" - , , o 1 — ■* 1 1 en C D E c o Q. < l- z UJ o o o CO 9 _i o CO Q UJ Q z UJ Q_ CO Z> CO CO o o O cc u_ CO LU _J U. O CC Q_ CO Q _l o CO UJ Q UJ 0_ CO CO UJ I- Ul _l CL o o & UJ cr => o h- H O CD O OC U. Q UJ ujouoq ujojj u 'NWniOO Nl NOIllSOd 54 The resulting settling curves did not differ from those obtained by filling to 3 5 ft initially o It might be expected that heavier suspended solids would fall to the bottom during the filling and apparent flocculation periods „ Pro- ceeding on the supposition that such particles would be higher in nonvolatile material than the average solids present in the column, profiles of nonvola- tile suspended solids were conducted,, No preferential separation of non- volatile matter could be detected. Even in the preliminary tests where severe separation of solids occurred , the percentage of volatile material remained constant throughout the columns „ In general^ an increase in suspended solids concentration was accompanied by an increase in the apparent flocculation time For example, when a sample of Urbana-Champaign activated sludge was increased in concen- tration from 2800 to 4240 mg/1, the apparent flocculation time increased from 0,6 to 3„8 min„ While 3„8 min seems an incredible time for suspended solids to remain without appreciable subsidence, the suspended solids pro- file at the end of the apparent flocculation period, as shown in Figure 20, demonstrates that no objectionable redistribution of suspended solids occurred Due to differences in biological characteristics, considerable variation in the apparent flocculation time occurred between different activated sludges Figure 20 includes a comparison of concentrated sludges from the Urbana-Champaign and Lake Park plants „ The flocculation and settling characteristics of the Lake Park sludge were so good that subsi- dence commenced during the filling period, and the apparent flocculation time was negative While the suspended solids distribution in the case shown was satisfactory, the rapid flocculation and sedimentation of the 55 c 1 lj o o c_> c CO Q o E _l o «♦- CO o ^_ o c III 0) Q o -z. oc 3 O CO LU o O 2 O _l 1- 3 _J (0 H UJ CO Q LU \- LJ < z > < \- O CO < LU _J o CL Q LU H < CC 1- (7) 2 Q LU _l O o 2 CO O o Q LU o o LU 1- CL CO cc 3 o CO u_ d CO LU or 3 O wojjoq wojj ^ 'NKimOD Nl NOIllSOd 56 Lake Park sludge resulted in some separation in suspended solids when more dilute suspensions were investigated with a 1.2~min filling time. The problem could readily be corrected by employing a shorter filling time. While a filling time of I 1 to 1.2 min for a 3.5-ft sludge depth in columns 3.5 in in diameter normally produced satisfactory suspended solids distribution j it was concluded that absolute standardization of the filling procedure was not desirable „ The tendency for suspended solids to separate during the filling and apparent flocculation periods varied with the source g condition and concentration of the sludge . Thus, it was necessary to be constantly vigilant of the initial solids distribution being attained in settling tests. Suspended solids profiles were routinely observed in each series of tests, and special attention was given sludges which exhibited unusual apparent flocculation times. Initial Mixing Procedure in Unusual Columns . Several experiments required use of sludge depths or column diameters different than the 3.5-ft depth and 3.5-in. diameter considered in the previous discussions. It was necessary to adapt the basic filling procedure for use in these instances. Columns with diameters less than 3.5 in. were filled by reducing the flow rate to give a fill time equal to that used in 3.5-in. columns. The Reynolds number characterizing the nature of upward flow in the smallest column used (0.62-in. diameter) was less than 300. This is far below the lower limit of turbulent flow (about 2000), which shows that turbulent mass transport did not occur above the disturbed area at the inlet. This method was not successful in a column 7.5 in. in diameter — the only size larger than 3.5 in. employed. When an activated sludge was pumped into five columns of various diameters at a rate of 3.5 ft per 1.2 min, the 57 apparent flocculation time was less than o 7 min in all cases except for the 7.5-in. column in which it was 2.8 min. This suggested that the high flow rate required to fill this large column produced high turbulence above the outlet of the 0„5-in. filling pipe and resulted in a long apparent flocculation time. The profile of suspended solids at the end of the apparent flocculation period confirmed that separation of solids did occur. The difficulty could be corrected by increasing the filling time to 2,2 min which reduced the apparent flocculation time to 0,7 min and gave the sus- pended solids profile shown in Figure 21a „ Figure 21b shows the distribution of solids which was accomplished in columns with increased diameter in the lower section. In this case solids were dispersed in a 3.5-ft section of a column 3.5 in. in diameter placed on top of a 2.5-ft section of a column 7.5 in. in diameter. The technique employed was to fill the large lower section in a 1-min period, and then to reduce the flow rate to fill the upper section in the normal filling period of about 1.2 min. The procedure devised for filling columns deeper than 3.5 ft involved adjustment of the throttling valve on the pump discharge line so that filling of the column was accomplished in the normal filling time of about 1.2 min. The resulting profile of suspended solids in a column with a 7.5-ft sludge depth — the largest depth employed — is illustrated in Figure 21c. Initial distribution of suspended solids in columns with sludge depths less than 3.5 ft was accomplished by use of the device shown in Figure 22. The 0„5=in„ diameter filling line was extended a distance A into the column to discharge through a Plexiglas disc which formed a false bottom in the column. A butterfly valve fabricated of Plexiglas was 58 £ o •4— ■♦— o E o O (J CO o Q_ 1 1 1 1 1 1 1 (a) 3.5 FT DEPTH IN 7.5 IN. COLUMN. C =SS CONCENTRATION =2360 mg// T f = APPARENT FLOC- CULATION TIME = 0.5 mm 8- 7 - 6 - 5- 4- 3- I - j I (b) LOWER 2.5 FT, 7.5 IN. COLUMN. UPPER 3.5 FT, 3.5 IN. COLUMN. C = 2390 mg// T f =0.0 min ± I L — i — i — i — i — i — i — r (c)7.5 FT DEPTH IN 3.5 IN. COLUMN. C = 2180 mg// Tf = 0.7 min 95 % CONFIDENCE INTERVAL J I L 97 99 101 103 97 99 101 103 97 99 101 SUSPENDED SOLIDS CONCENTRATION, percent of mean 103 FIGURE 21 SUSPENDED SOLIDS PROFILES AT END OF APPARENT FLOCCULATION TIME IN COLUMNS OF VARIOUS CONFIGURATIONS. 3.5 in. COLUMN- BUTTERFLY VALVE PLATFORM DEAD SPACE -\ V o CD FILLING LINE 59 FIGURE 22. APPARATUS FOR INITIAL DISPERSION OF SUSPENDED SOLIDS IN SHALLOW COLUMNS 60 inserted between two sections of column as shown, A 3.5-ft section of column above the platform was then filled in accordance with standard procedure o At the end of the filling period, the butterfly valve was closed to isolate the test section of depth C, To vary the test section in subsequent tests, the distance A was variedo The butterfly valve remained at a fixed elevation , In this way, a shallow column of uniformly dispersed sludge was obtained in which the conditions for flocculation were identical to those in deeper columns, and the turbulent conditions at the point of discharge of the filling line were avoided,, MEASUREMENT OE RHEOLOGICAL PROPERTIES Properties of Interest Inasmuch as it was postulated that the internal structure formed by activated sludge was a significant property in relation to thickening, the yield strength of the sludge was a rheological property of primary concern. In the course of determining yield strength, it was also neces- sary to investigate the plastic viscosity and the thixotropic properties of the materialo The reader is referred to Appendix A for a discussion of the meaning of these and other terms relating to rheology Viscometry Type of Viscometer o The basic tool of rheologists is the viscometer, A wide variety of viscometers is available commercially (Aronson and Nelson, 1964, and Van Wazer et al„, 1963), Many are empirical devices in which flow behavior cannot be accurately described. Those amenable to mathematical description employ flow about rotational devices, in capillary tubes, or around falling spheres. The basic design of 61 rotational viscometers offers significant advantages for study of materials such as activated sludge „ Most models can be operated continuously so that time-dependent properties can be evaluated , In some models, multiphase systems with appreciable particle sizes can be studied by employing a large sample width, Also s complete shearing of plastic materials can be effected to produce a straight line relationship between shear stress and shear rate to permit evaluation of yield stress „ As will be discussed later, none of the commercially available rotational viscometers was considered completely suitable for use with activated sludge , Hence a model which could be readily modified, the Brookfield Synchro-Lectric,* was selected for use in this study. Further discussion of viscometry is limited to rotational viscometers of the coaxial cylinder type. Theory of Rotational Viscometers , The annular space between the two right cylinders in a coaxial viscometer is occupied by the material being investigated. When one cylinder is rotated relative to the other, velocity gradients and, hence, shearing forces are created in the material. The relationship between the rate of shear and the shearing stress can be computed from fundamental principles for wholly viscous motion. Knowing the geometric properties of the viscometer, the shearing stress at the surface of one of the cylinders can be deduced from observation of the torque on the cylinder. The shear rate can be determined from knowledge of the instrument geometry and observation of the general flow properties of the material being investigated, A more complete development of the theory of rotational viscometry is contained in Appendix B, "Model LVT, manufactured by Brookfield Engineering Laboratories, Stoughton, Massachusetts, 62 Modifications to Commercial Viscometer „ As previously noted, none of the commercial viscometers investigated were considered to be suitable for measurement of the rheological properties of activated sludge „ The properties of activated sludge which rendered rheological measurements difficult were the relatively large size of floe particles, the relatively low apparent viscosity, and the tendency for separation of water at smooth surfaces o Commercial rotational viscometers designed to permit accurate measurement of relatively low viscosities employ extremely narrow gaps between the inner and outer cylinders (for example, the Hercules viscometer employs a o 5 mm gap, and the Haake Rotovisco viscometer may be used with gaps less than 0„1 mm wide) Use of narrow gaps permits high shear rates to be developed (with correspondingly high, and easily measureable, torques) without developing turbulent flow Use of such narrow gaps is not permis- sible in investigations of the rheology of activated sludge because of the large particle size All commercial viscometers considered employed smooth surfaces on the cylinders Suspensions tend to separate into two phases at such surfaces so that one actually measures the characteristics of the dispersing medium and not the true properties of the suspension (Van Wazer et al s 1963 ) The required modifications to the Brookfield instrument which are discussed in the following paragraphs were: roughening of sur- faces to prevent phase separation and slippage, increasing the diameter of the inner cylinder to increase the sensitivity of the instrument to low shearing stresses, controlling the width of the gap between cylinders to permit complete shear of plastic substances and to avoid turbulence, rotating the outer cylinder to stabilize flow, using a continuously variable speed drive to increase the number of possible observations of torque vs rotational speed j and limiting the maximum rate of rotation to 63 avoid turbulence „ Figure 23 shows the viscometer before and after modifi- cation,, In the modified viscometer, the Brookfield instrument served only as a convenient method of measuring torque „ Crude measurements of the rheological properties of various con- centrations of activated sludge were made with the unmodified viscometer to establish preliminary design criteria for the cylinders of the modified instrument o On this basis, six inner cylinders with radii varying from l o 90 to 4 15 cm and 13 outer cylinders with radii varying from 2 65 to 6 85 cm were fabricated Various combinations of these cylinders were used in future studies „ Inner cylinders were made from 10 o 16-cm long pieces of Plexiglas tubingo Both ends of the cylinder were plugged with Plexiglas discs and a shaft was placed through the center of the cylinder „ The top end of the shaft was tapped to permit attachment of the cylinder on the Brookfield viscometer in place of the standard inner cylinder,, In all cases the space between the bottom of the inner cylinder and the bottom of the outer cylinder (1) was 2„54 cm, and the depth of immersion of the inner cylinder (h) was 7 62 cm (see Figure 63, Appendix B)„ Because of their buoyancy, the large cylinders were not heavier than those provided by the viscometer manufacturer Where necessary, the modified inner cylinders were weighted so that their operating weight was within the range of operating weights of the various "spindles" (inner cylinders) which accompanied the commercial viscometer „ Outer cylinders were labora- tory beakers or were fabricated from Plexiglas tubingo Van Wazer et al„ (1963) recommended that the viscometer gap be "at least 10 times greater than the diameter of the largest particle or strongly agglomerated unit of the material comprising the body,," Although aggregate particles with diameters of the order of 3 mm can ordinarily be 64 1- z LLi 5 3 tr or i- z LU o LU 2 o u. CO Q O > S _J «--» < .o z o h- < H o cr Ll. O z o H h- Z < Ld V 5 3 u_ a: Q i- o z 2 _i . < ro o C\J a: LU LU 2 a: 2 Z> o O o ii 65 observed in activated sludge s Finstein and Heukelekian (1965) reported that the diameters of basic floe particles in various activated sludges varied from 0„03 to o 34 mm Probably Finstein and Heukelekian 's measure- ments come closer to defining the size of "strongly agglomerated" units „ As has been noted, the desirability of using as large a gap as possible is offset by the necessity of producing shear across the complete gap, and of avoiding turbulence „ When extremely wide gaps were used, the torque pro- duced at shear rates sufficient to cause shearing stresses at the outer cylinder in excess of the yield strength of the sludge exceeded the torque measuring capacity of the viscometer , and, in addition, turbulent condi- tions were created„ The width of the gaps in the three combinations of inner and outer cylinders which were found from the studies described in this section to be satisfactory for measurement of the rheological proper- ties of sludge were o 83 s CL85, and o 95 cm u The solids concentration of a two-phase system is necessarily lower at boundaries than within the suspension., The relationship between shear rate and shearing stress is correspondingly different, and thus "slippage" occurs at the wall The situation can be remedied by placing protrusions at the surfaces to hold particles at the surface „ The effective boundary is then at the end of protrusions, and the suspension, not merely the liquid phase, is shearedo Van Wazer et al„ (1963) suggested roughening by driving finishing nails into wooden cylinders or by attaching carding cloth to cylinders „ In this study, sand and mat roughened surfaces were tried. Sand roughening was accomplished by gluing Ottawa sand (passing number 16 and retained on number 30 U„ S series seives) in a mono-granular layer on the surfaces of the inner and outer cylinders „ The mat roughening 66 was coarser, and was accomplished by gluing rubber mat" with an open mesh onto the inner and outer cylinders „ In both cases, the bottom surfaces of the two cylinders were left smooths, Before employing the roughened surfaces with activated sludge, it was necessary to ascertain that the roughening did not change the flow characteristics between the cylinders aside from its effect of reducing the gap Aqueous glycerol solutions and sucrose solutions were used for this purpose o This work with Newtonian standards was done at 20°C in a constant temperature room, Representative results are shown in Figure 24 Plots are shown for the unmodified viscometer as well as for the modified viscometer using unroughened Plexiglas cylinders and sand and mat roughened cylinders o The differences in slopes of the several curves reflect the differences in diameters and gaps of the cylinder combinations „ The vis- cosities as determined by Equation 110 (Appendix B) for the three pairs of modified cylinders are shown in Table I„ The spring constant of the viscometer was 6„737 dyne -cm per Brookfield unit TABLE I COMPARISON OF VISCOSITIES DETERMINED WITH CYLINDER PAIRS OF DIFFERING ROUGHNESSES R R Texture i o Viscosity ( cm ) ( cm ) ( cp s ) smooth lo90 4 o 20 41 sand roughened 2 o 00 4 C 15 40 mat ro ughened _ 2 Q 22 4„05 40 The straightness of the curves in Figure 24 and the agreement between the viscosities determined by the three modified cylinder pairs confirms that "No 3070 Neotex Protective Mesh, distributed by Research Products Corpora- tion, Madison, Wisconsin 67 — 1 1 V 1 1 1 or UJ i- UJ 5 CO O < Q — O J UJ Q 2 WO ZUJ O < 1— ^ u H UJ Q ^ 'Z x uj a. z> e> o ,- ° ^> q; ^ x o: o UNMOD SMOOT SAND MAT R q: UJ Q _j > x o < a a: UJ t- r> o UJ t- o z UJ o CO 2 — o a. a _i o "* X *^«^ CO — 1 1 *" x^. i If) o CO O o o if) or LU Q o Z (T» _l >- u o O z 00 MM en z> Q 3 O _J Ll (/> c 3 o - £ .5; uj O m £ CD UJ o O * a: o uJdJ c Q33dS 3AI1V10U Li_ O O w c/? Lu > z X Ll & O 3 §2 I- if) < 3 Z O or < LU > QO CVJ LU or z> o 68 the roughening of cylinders did not interfere with viscosity determinations „ The viscosity determinations shown in Table I are uncorrected for end effect (viscous drag on the bottom of the inner cylinder) and are subject to error because of the difficulty of measuring the effective radius of roughened cylinders The viscosity determined with the unmodified vis- cometer was 36 cps Figure 2^ also illustrates the desirability of using large inner cylinders o The inner cylinder used with the unmodified viscometer was the largest supplied by the manufacturer (No„ LV-1), yet the torque produced by it was considerably less than that on the smooth Plexiglas cylinder (the smallest of the modified cylinders). The viscometer manufacturer guarantees the accuracy of the spring used to measure torque to *1 Brook- field unit regardless of its deflection Thus the accuracy of the viscosity determination in Figure 24 for the unmodified viscometer at 30 rpm was 1 part in 18 or *5<,5 percent s while that for the smooth modified cylinder at the same speed was 1 part in 84 or ± 1 2 percent „ Having established that the roughened surfaces used did not interfere with measurement of the rheological properties of Newtonian materials.- the effect upon measurements with suspensions could be evaluated„ When the mat roughened cylinders were used, unsheared floe particles could be observed in the voids of the mat, and the surface of shear could be seen to correspond to the outer extremity of the mat Table II shows the yield strength of a 5650-mg/l sample of Urbana-Champaign activated sludge as determined by cylinders of various roughnesses (Equation 116, Appendix B)„ It is seen that considerable slippage occurred when smooth cylinders were used and that sand roughening was only partially effective in prevent- ing it The excellent agreement of the three determinations using different 69 combinations of mat roughened cylinders is encouraging , but suggests better reproducibility than was actually possible in the yield strength determination o On the basis of these findings s mat roughened cylinders were used in all subsequent yield strength determinations It should be noted that previous investigators who have used rotational viscometers to study the rheology of sanitary engineering sludges (Hatfield, 1938; Babbitt and Caldwell, 1939; Behn, 1962; and Geinopolos and Katz, 1964) have used smooth cylinders TABLE II COMPARISON OF YIELD STRENGTHS DETERMINED WITH CYLINDER PAIRS OF DIFFERING ROUGHNESSES Texture R. l R o (cm) (cm) l o 90 3„38 2o00 3o25 2c22 3„05 2o85 3„80 3 o 20 4 o 05 y (dynes/ s q cm) smooth sand roughened mat roughened (I) mat roughened (II) mat roughened (III) 103 0„158 o 264 0„259 0o261 The equations which form the basis of rotational viscometry (see Appendix B) are predicated on the assumption that flow is laminar, and are invalidated when turbulent conditions are producedo In addition to the normal factors which affect the onset of turbulence, the flow regime in rotational viscometers is also influenced by centrifugal forces „ When the inner cylinder is rotated and the outer cylinder is stationary, particles near the inner cylinder have a larger centrifugal force (prto 2 ) than those farther out „ The result is the production of "Taylor vortices" (Taylor, 1923 ) The disturbance takes the form of cellular toroidal vortices spaced 70 regularly along the axis of the cylinders (Merrill, Mickley, and Ram, 1962 ) In contrast, rotation of the outer cylinder while holding the inner cylinder stationary stabilizes flow u The fluid particles at the outer cylinder are subjected to the highest centrifugal force and they have no inclination to change position,, Schlichting (1955) likened the situation to the stability of a temperature inversion in meteorology, and reported experimental obser- vations of laminar flow between concentric cylinders at Reynolds numbers of 200,000 when the outer cylinder was rotatedo The critical Reynolds number above which secondary motion is considered to occur when the inner cylinder is rotated has been reported- (Van Wazer et al„ s 1953) as 28 R - R. o 1 where v. is the linear velocity of the inner cylinder, R and R. are the l J J ' o 1 radii of the outer and inner cylinders, and p and u are the mass density and viscosity of the fluid „ Equation 28 shows that increasing the diameter of cylinders and increasing the gap between them (as was done in modifying the viscometer) reduces the speed at which the viscometer may be operated. In studies employing Newtonian standards, turbulence was observed to be produced at rotative speeds so slow as to render the viscometer with inner cylinder rotation useless for investigation of the rheology of activated sludge. To remedy the situation, a device was constructed to permit rotation of the outer cylinder „ As noted in Appendix B, the relative velocity distribution between cylinders is not dependent upon which of the two cylinders is rotatedo The equations which describe the behavior of materials in rotational viscometers apply to rotation of either cylinder. 71 Figure 24 illustrates this facto The open points correspond to rotation of the inner cylinder , while the solid points were obtained by rotating the outer cylinder,, The device for rotating the outer cylinder consisted of a turn- table connected to a variable speed motor" by means of a system of reducing pulleys Pulleys were selected to give a maximum rotative speed of 50 rpm» Outer cylinder rotation offered the additional advantage of permitting rheological observations at any speed between and 50 rpm rather than only at the eight speeds of the commercial viscometer,, The modified vis- cometer was equipped with an electrical impulse counter which totalized the revolutions of the turntable, and a stop watch which was used to measure time intervals and permit calculation of rotational speed A Plexiglas collar, which was larger in diameter than all of the outer cylinders , was mounted on the turntable „ Six long set screws were used to firmly hold the outside cylinders within the collar and to accu- rately center them over the axis of rotation, A level bubble was mounted on the turntable and the chassis housing the turntable was equipped with leveling screws „ In these ways 5 the eccentricity between the two cylinders was maintained within closer limits than was possible with the unmodified viscometer,, As shown in Figure 23 , the Brookfield instrument was situated on the same framework which housed the turntable „ The torque registered on the viscometer was found to be sensitive to vibrations caused by the mech- anism rotating the outer cylinder „ To minimize this effect, the whole apparatus was placed on a rigid bench, the variable speed drive and impulse counter were isolated from the main body of the viscometer, about 95 lb of "Type 10E400M Motorized Zero-Max Drive, manufactured by the Zero-Max Com- pany 9 Minneapolis s Minnesota,, 72 lead were attached to the framework supporting the turntable and Brookfield viscometer $ and the Brookfield instrument was mounted on rubber vibration arresters , Figure 25 illustrates the improvement in viscometer performance resulting from rotation of the outer cylinder , The cylinder dimensions represented by combinations I and III are included in the following sec- tion. The fluid employed in part a of the figure was a sucrose solution with a viscosity of 7„5 centipoise (cps), and in part b, water was used As seen in Figure 25 , deviations from theoretical behavior occurred with outer cylinder rotation as well as with inner rotation,, The deviations with outer cylinder rotation were 9 however, less severe and commenced at higher speeds. The onset of turbulence with inner cylinder rotation was in essential agreement with Equation 28, but the deviations from theoretical behavior in the case of outer cylinder rotation occurred at much lower speeds than expected It is postulated that the reason for this behavior was the lack of perfect concentricity between the two cylin- ders. The speed at which the deviations began was strongly dependent on the size of the cylinder. The diameter of the inner cylinder of the unmodified instrument was small enough to prevent any deviations within the speed range of the viscometer. Although deviations with outer cylinder rotation were more pronounced with fluids of low viscosity than with more viscous liquids (compare Figures 24 and 25a), the speed at the onset of turbulence could not readily be related to Reynolds number. Instead, the limiting speeds for the various combinations of mat roughened cylinders with fluids of various viscosities were determined to permit construction of curves such as shown in Figure 26, The data in Figure 26 are for combination I of the 73 50 E Q. Q UJ UJ a. if) UJ > O en 40 - 30 - 20 - T 1 1 1 - (a) COMBINATION I, /* = 7.5 cps THFORFTir/M — -a-- — z^— OUTER ROTATION -- -0-- -o-- INNER ROTATION / - yy J* ' --o • | 1 1 10 - 20 30 40 50 25 20 — 15 - 10 — 1 1 1 1 (b) COMBINATION m, A* = 1.0 cps / / / * / / / / / / / / / / // p.- /' // / ^ / .*' f .* _ [ +' 1 * i • A / ' CJ * 7 v 1 * 1 / // /' i i i i 5 10 15 20 25 TORQUE, Brookfield Units FIGURE 25. COMPARISON OF INNER AND OUTER CYLINDER ROTATION. 74 en cr LU Q Z _J o >- GO o cr UJ O 3 O Ll (fl O •*— O 10 c 3 z o T3 ^~ 1- CD < 1- O o o O or in CD >- UJ CD Z> O O or UJ o o O ^ h- 3 Q O or 0_ o TO UJ 3 O or o or o or or UJ C0 CM UJ cc 3 wdj c Q33dS 3AI1V10U 75 mat roughened cylinders and were obtained by using Newtonian fluids with viscosities ranging from 1 to 13„7 cps As a matter of conveniences the maximum permissible speed for this combination was taken as 20 rpm More restrictive speed limits had to be imposed on the larger pairs of cylinders Combination II was limited to 12 „ 5 rpm 9 and combination III to 8 rpm As seen in Figure 26 9 the potential for error was greatest at low torques „ Operation in this range was avoided by changing to a larger pair of cylin- ders o Calibration of Viscometer „ Basically, the modified cylinder pairs were calibrated by application of the theoretical equations developed in Appendix B„ However , these equations do not account for the torque caused by viscous drag on the bottom of the inner cylinder, and experimental modification of the theoretical calibration was required,, The normal pro- cedure for establishing this end effect (Van Wazer et^ al » 1963) is to vary the immersion of the inner cylinder (h in Figure 63, Appendix B) to obtain a plot of torque vs„ immersion at a single speed with a single fluid „ Back extrapolation of this straight line to zero torque gives the effect of the end in terms of an apparent depth of immersion 9 h The theoretical equa- tions are then usedj, and h + h Is substituted for h„ This technique was not effective in the present case because reduction of cylinder immersion reduced the buoyant force and increased the operating weight of the cylin- der beyond the range employed in the Brookfield instrument Instead, the correction for end effect was made by observing the difference between the known viscosity of Newtonian standards and the viscosity calculated from theoretical treatment of observed data The correction determined in this manner also contained the error resulting from the difficult measurement 76 of the effective diameter of roughened cylinders. The maximum correction for the three combinations of mat roughened cylinders employed in the study was 5.7 percent. As noted in Appendix B (Equation 110), the geometric properties of a rotational viscometer can conveniently be combined into a single constant. For Newtonian fluids, T Br » ■ \ ir- 29 rpm Similarly, for plastic substances, Equation 116 may be written as x = K n T 30 y b x^ J Br T D - T „ J* *Br and n = K c — 31 rpm In these expressions, \i is viscosity in centipoise, x is yield strength in dynes per sq cm, and n is plastic viscosity in dyne sec per sq cm. The term ft r is the rotational speed in rpm and T is the corresponding torque in Brookfield units, T is the back extrapolate of the ft vs. T^ curve x_ r rpm Br for a plastic material in Brookfield units (see Figure 64, Appendix B). K , K , and K are constants determined by the viscometer geometry. Table III shows the dimensions of the three combinations of mat roughened cylinders used in the study together with their geometric con- stants. 77 u PQ < CO 05 M Q M J >- o Q W w o o5 t- < o Cu, CO H < E-i CO O O O M 05 E-> W o w u CO o CO o CQ ^ bO C ■H c O O o r» ID LO 3- in ID 00 CM O o o CM o CM a CM H o in <£> J" CO ID CM H ID CO CO CM O CM in o CM 00 /—N 00 in in Q* 6 00 CD CO «J o o • O v^* o o o ^ CM m o •H £ CM 00 CM 4 O O e • in o CO o oo co in o 78 Procedure for Investigating Rheological Properties of Activated Sludge , In addition to the difficulties discussed in the preceding sec- tions, determination of the rheological properties of activated sludge was complicated by the fact that sludge exhibited thixotropy and settled in the viscometer. The procedure developed involved aerating the viscometer contents to disperse the sludge solids, allowing a period of quiescence for reflocculation, starting the viscometer, and recording the maximum observed torque. Samples for viscometric analysis were passed through a 16-mesh screen to remove any gross solids. In cases where rheological and settling behavior were being compared, all sludge was screened. Aeration to disperse suspended solids was accomplished by removing the inner cylinder and submerging a compressed air line in the contents of the outer cylinder. The length and intensity of aeration could not be shown to influence the subsequent rheological measurement, nor could a change in rheological properties be noted in consecutive measurements. The characteristics of the reflocculated sludge appeared to be independent of the sludge's previous history of shear. Fifteen seconds of vigorous aeration was adopted as the standard method of dis- persing solids. After aerating, the inner cylinder was replaced. It was then necessary to ascertain visually that no foam bubbles remained, A single bubble which bridged the gap between the inner and outer cylinders could increase the torque reading several fold,' Antifoam compounds were not employed because the film resulting from their use altered the vis- cometer reading. Serious problems with bubbles were not encountered with any of the sludges used. The period of quiescence following aeration permitted the uni- formly distributed sludge to flocculate and reform its internal structure. 79 Viscometer readings were only slightly dependent on the time allowed for reflocculation. The relationship is illustrated in Figure 27 , As noted in the discussion of settling tests, appreciable sedimentation does not occur during the actual period of flocculation„ The reduction in observed torque for the long flocculation periods in Figure 27 does, however, probably reflect sedimentation,, A 45-sec period for flocculation was selected as a standard. During about the first 10 sec of the period, the inner cylinder was replaced, and at the end of 45 sec the motor which turned the outer cylinder was actuated. The torque value recorded was the peak value observed before it was reduced by thixotropic decay. Although some of the more sophisticated viscometers for studying time dependent effects record this reading within a fraction of a second after starting the viscometer, the instrument used in this investigation was not so responsive. About 15 sec elapsed before a reading could be made. During start-up, it was necessary to manipulate the clutch on the viscometer to ascertain that the instrument was respond- ing to the drag on the inner cylinder and not to its inertia. Figure 28 illustrates the time dependency of viscometer readings. The rise from zero torque is shown only for the Sullivan sample. The rapid initial decrease in torque is attributed to thixotropy. The long-term gradual decrease may be caused by sedimentation. The peculiar shape of the Sullivan curve was typical for that sludge. The behavior was not thought to be caused by oscillation of the viscometer cylinder, as efforts were made to prevent this by use of the viscometer clutch. The curve suggests a rapid thixotropic breakdown of the sludge particles with subsequent rheopectic reformation. No explanation of why such behavior should exist is offered. 80 CO "E g> o o l_ CD III Z3 O or o 40 X 30 20 10 -o- -o- -o- 1T URBANA-CHAMPAIGN, 9120 mg/JJ, COMB. I AT 6.00 rpm _D SULLIVAN, 1565 mg/Jc , COMB, m AT 6.63 rpm A TUSCOLA, 5020 mg/J?, COMB HE AT 3.46 rpm J3 20 40 60 80 FL0CCULATI0N TIME, sec 100 FIGURE 27. EFFECT OF FLOCCULATION TIME ON VISCOMETER READING. (20 25 CO "c 3 - >*- O o CD UJ ID O or o i- 20 15 10 TJ O D SULLIVAN, 1565 mg/.{ , COMB, m AT 6.63 rpm A TUSCOLA, 5020 mg/jl, COMB. TJ1 AT 3.46 rpm URBANA - CHAMPAIGN , 2190 mg//, COMB. I AT 12 rpm -o- 30 60 180 210 FIGURE 28 90 120 150 READING TIME, sec THIXOTROPIC CHANGE OF ACTIVATED SLUDGE IN VISCOMETER . 240 81 To summarize, sludge solids were uniformly dispersed in the viscometer by 15 sec of aeration. Then a 45-sec period was allowed for reformation of floe after which the viscometer was started and the highest torque which was developed without inertial assistance was recorded „ The entire procedure was repeated for each determination. At each rotational speed investigated j three such determinations were made, and the average was used in plotting rotational speed vs torque. The resulting curves were then analyzed as explained in the preceding section and in Appendix B. In Situ Investigation of Rheological Properties As will be discussed in Chapter IV, the structural characteristics of activated sludge may be expected to be related to the sludge's yield strength as determined from a viscometer, but no method is available to directly associate the two. In addition, the rheological properties of sludge in a viscometer may differ from the properties of sludge in a settling column because of thixotropic change and because of the absence of a normal force in the viscometer. Thus, in evaluating the effect of the rheological characteristics of sludge upon its subsidence characteris- tics, it was desirable to determine the structural properties of the sludge as it existed in the settling columns. Unfortunately no workable procedure for the in situ measurement was devised, and, in the comparison of rheologi- cal and settling behavior, the rheological characteristics had to be repre- sented by viscometer data, A number of satisfactory methods for in situ measurements were conceived, but, in each case, instrumentation problems prevented consummation of the procedure, A few of the techniques con- sidered will be briefly discussed in this section. 82 Each of the methods considered was based on the observation that, although the pressure on the bottom of a container holding a subsiding column of sludge is constant, it is comprised of varying proportions of hydrostatic pressure and pressure due to the weight of solids being physi- cally supported by the container bottom,, At the onset of sedimentation, the pressure due to the weight of solids is minimal, and the hydrostatic pressure is at its maximum,, As sedimentation progresses the hydrostatic pressure decreases as solids transfer their weight directly to the con- tainer bottom. Finally, when no more subsidence occurs, the excess hydrostatic pressure becomes zero (the hydrostatic pressure is now caused only by the weight of the column of water) and the weight of the solids is borne entirely by the bottom of the container. If, as has been hypothe- sized, activated sludge possesses internal structure, then it is not necessary for solids to descend to the bed at the bottom of the column before transferring their weight directly to the container. Subsiding solids at the top of the column may transfer a portion of their weight to the bottom of the container through the continuous structure of sludge particles. Figure 29 shows two of the devices which were fabricated in attempts to measure the excess hydrostatic pressure or the weight of solids being supported by the container bottom. A weighing device is illustrated in Figure 29a „ A hole was drilled in the bottom of the case of a chainomatic precision balance and the balance beam was connected to a pan near the bottom of the settling column. Hydrostatic pressure was exerted on both the top and bottom of the balance pan so the net weight registered by the balance was the weight of solids being supported by it. Figure 30 shows the type of data which 83 co CO ^^^^^ UJ O X £ _____ _______ 3 U. ^ ' ' '• r ' «•».*"-* ** „ '» ^ • • " '* • ■ . ' U UJ _, a: >>;. >.•:;>. vV^-i:^:::; S Q- V~c "••'•' V- - •;• •: -.■'V:- •• ." ';" o 'V ';■'. *•••:'"-• :■• V- ■*.".V. 1 '. ••-'»• NATI ATIC 1' ,V '"'. ' ; -,, - V ' y — i— S CO or o uj q: 1- Q UJ > Q X JD CO Q _l o CO u. o X K3 ¥ 5 < Ul o >.. ..v. •■•."••■ '■'..•;'; t.V.'f ' : ,- 1 £ H ' ■-.',.' ■ '- '',■*■'■'■•■■•"■>> h- • ■ . . ' ,-'..»• ■■-. ; .". • U. O O CD i ■z. or t> \ £ y>.' ■'■/^Vi o ui i= 2 $ < z i- ERMI CON t- UJ 2 Q O o CO UJ or uj o. o or Q. < 3 O UJ X or u. o UJ UJ or GO < UJ Z> _• CO or o co UJ Z> o I o UJ OJ UJ or 84 X UJ ** - / ^ — w, w 2 W i 1 V - REMOVED AT f T < { H , H 2 f." % \ J TIME FIGURE 30. SCHEME FOR INVESTIGATING RHEOLOGICAL PROPERTIES WITH WEIGHING DEVICE. 85 was expected from the balance „ At time T after the start of a settling test ? when the sludge-water interface was at level H , the upper portion of sludge would be quickly drained off to lower the interface to H , If the sludge possessed internal structure, and was transmitting part of its weight to the container bottom, the weight of the sludge on the pan would decrease from W to W The difference between W and W would represent the weight of sludge which was supported by the structure of the sludge at level H„, and the difference between that weight and the total effective weight of solids between H and H 9 would be the excess hydrostatic pressure at H^ o Although the magnitudes of the pressures involved were extremely small, the balance pan could be made sufficiently large so that sensitivity was not a problem. The problem was in design of the balance pan near the bottom of the sedimentation column,, Difficulties included support of the sludge by the column walls, bridging of sludge over the pan, friction between the pan and the column, and leakage of solids through gaps intended to assure that hydrostatic pressure existed above and below the pan. The most successful attempt at devising a suitable pan utilized a 3,375-in, diameter pan in a 7,5-in,. settling column The pan fit inside a 3,875-in, hole in the center of a plate which was inserted between two sections of column. The gap between the pan and the plate was covered with 0,001-in o thick latex rubber membrane. The membrane was fitted sufficiently loose to prevent it from supporting the load on the pan, but tight enought to prevent the pan and plate from contacting one another. Numerous small holes were drilled in the plate to equalize the hydrostatic pressure on either side of the pan. When the column was filled with water, the standard deviation of 15 successive weight determinations was 3,2 mg„ 86 This was considered to be sufficient reliability to construct a curve of the type shown in Figure 30 Yet when sludge was placed in the column reliable weights could not be obtainedo After a layer of sludge had been deposited over the pan s individual weight measurements varied as much as 100 mg depending upon whether equilibrium was approached by lowering the pan or raising the pan„ This occurred in spite of the fact that total pan travel was limited to 1 mm c An attempt to eliminate any appreciable pan travel by replacing the balance with a single strand of strain gage wire and ancillary equip- ment was not successful because the "noise level" masked the change in resistance of the strain gage wire due to the weight of solids „ The device shown in Figure 29b was designed to measure the excess hydrostatic pressure profile in a column of subsiding sludge „ The dif- ference between the effective weight of solids above a point in the column and the excess hydrostatic pressure at the point would represent the weight of solids being transmitted by the sludge structure at that point „ The piezometer tubes were filled with supernatant liquid s and were periodically flushed by adding additional liquido The maximum excess hydrostatic pres- sure to be expected with sludge concentrations and depths such as used in this study could be computed from the specific gravity of sludge, and was in the order of 0„5 to 1„0 mm of water The sensitivity of most catheto- meters which might be used to measure the water levels in the piezometer tubes is about 0„1 mm and this was not considered to give adequate resolu- tion of the excess hydrostatic profile to yield the desired information,, Precision cathetometers which measure to o 01 mm are available „ Procure- ment of such a device should permit establishment of some detail of the profile of excess hydrostatic pressure and lend insight into the mechanism of thickening„ 87 MEASUREMENT OF OTHER PROPERTIES OF SLUDGE Determination of Suspended Solids Co ncentration Procedure o The concentration of suspended solids was determined by the glass fiber filter method described by Chanin et al„ (1958) The method employs glass fiber filters in place of the conventional asbestos mat (Standard Methods , 1960) in Gooch crucibles „ Briefly, the procedure involves placing filters in crucibles with their smoother side down and seating them by filtering a few ml of distilled water under vacuum,, The crucibles and filters are then dried in a 103°C oven, cooled in a desicca- tor and weighed „ The sample is then filtered, and the drying, cooling, and weighing steps are repeated to permit calculation of the suspended solids concentration;, Because use of the glass fiber filter-Gooch crucible technique as a research tool had not been reported, it was considered advisable to investigate sources of possible error in the procedure . Desiccation alone, oven-drying at 103°C, and firing at 600°C revealed the glass fiber filters* to be non- hygroscopic (which confirms the observations of Nusbaum, 1958) and devoid of volatile matter. The Gooch cruciblest were, of course, hygroscopic, and experiments were undertaken to determine the effect of time in the oven and in the des- iccator upon their weight „ Individual desiccators, as advocated by Winneberger, Austin, and Klett (1963), were used to avoid weight changes during the repeated openings of a conventional desiccator,, The desiccators consisted of 8-oz wide-mouth, screw-cap bottles containing about 20 gm of silica gel and a 2-oz bottle to hold the crucible above the desiccanto *No„ 934-AH, 21 -mm diameter, manufactured by Hurlbut Paper Co , Clifton, N 8 J„ tNoo 3, manufactured by Coors Co„ , Golden, Cole 88 The effect of time in the 103°C oven was studied by drying a group of crucibles and filters for 18 hr to establish their "ultimate" dry weight, and then rewetting them and determining their weight after various drying times o It was found that the entire weight change took place within the first 30 min of oven dryingo Allowing crucibles to remain for longer periods was of no consequence „ The period of weight loss might be expected to be somewhat longer when the crucibles contained wet solids „ Accordingly, a minimum drying time of 1 hr was employed as recommended in Standard Methods (1960). The temporal change of weight in desiccators was studied in a similar manner,, When crucibles were removed from the oven and placed in desiccators maintained at room temperature, the crucibles rapidly took up water for about an hour and then continued to gain weight at a slow rate throughout the 2.5-day test period „ This annoying weight change was mini- mized by placing the desiccators in the oven along with the crucibles. An equilibration still took place after the crucible and desiccator were removed from the oven This was probably due to the moisture on the plas- tic desiccator caps (which were not dried in the oven). However, essen- tially no weight gain occurred after 3 hr which was adopted as a minimum time for desiccation. To minimize the error caused by adsorption of atmospheric moisture during the weighing operation,, weights were consistently read 30 sec after the crucibles were removed from their individual desiccators, and the weighing chamber of the balance" was equipped with silica gel desiccant. "Sartorius Projecta model distributed by Brinkman Instruments, Westbury, New York. 89 During preliminary investigations of the suspended solids deter- mination technique, it was observed that when batches of crucibles and filters were rewetted, redried, redesiccated, and reweighed, on successive days s weights of all individual crucibles of the batch would increase or decrease fairly uniformly from the weight determined on the preceding day„ Weight changes of as much as plus or minus 0,5 rag were observed (as compared to a total weight of about 17 g) Presumably these uniform weight changes were caused by variables such as the weighing room humidity » To monitor such variations, at least three control crucibles, through which only water was filtered s were used in each batch of 24- crucibles „ Corrections were applied to the suspended solids determinations based on the change in weight of these control samples „ In summary, the solids determination procedure involved: a) place- ment of the glass filter in the Gooch crucible by filtering a few ml of water, b) drying at 103°C for at least one hr while in open individual desiccators, c) capping of desiccators before removing them from the oven, d) cooling in the individual desiccators for at least 3 hr, e) weighing 30 sec after removal from desiccators, f) filtering the sample, g) repeat- ing steps b through e s and h) correcting for any weight change of control crucibles o Comparison with Other Methods „ The initial interest in the glass fiber filter-Gooch crucible method of determining suspended solids was economic o The membrane filter technique frequently used in research applications employs expensive filtration apparatus and membranes., Because of the large number of suspended solids determinations to be conducted during the course of this research 9 it was desirable to use a more 90 economical method,, It was necessary, however, that the method used be comparable to other possible methods in accuracy, reliability and conven- ience o Nusbaum (1958) used glass fiber filters in Buchner funnels for suspended solids determinations with activated sludge, and found a good comparison with the conventional asbestos pad method,, Chanin et al „ (1958) could discern no difference in suspended solids concentrations of raw and settled sewage determined by glass fiber filters or asbestos pads in Gooch crucibles o No statistical difference could be shown by Smith and Greenberg (1963) between suspended solids concentrations determined by asbestos pads In Gooch crucibles 9 glass filters in Gooch crucibles, glass filters in Buchner funnels, or membrane filters „ They worked with raw, settled, and secondarily treated sewage and an industrial waste „ To establish the suitability of the glass fiber filter-Gooch crucible method, comparisons were made with the membrane filter technique, and 9 in another series of tests, with the porous crucible technique and with glass fiber filters in membrane filter holders „ The membrane filter procedure outlined by Winneberger et al„ (1963) was used„ Results are summarized in Table IV The membrane filters'" employed were 4 7 cm in diameter with 0„'-+5 y pore size The glass fiber filters were 2„1 cm in diameter with pore size varying from o 5 m to 1„0 y„ As shown in Table IV, the two methods gave comparable results „ The slightly smaller solids concentration given by the membrane filter method might reflect the problem of adequately removing solids from the filtration device „ This was not a difficulty with "Grade HA, manufactured by the Millipore Filter Company, Bedford, Mass„ 91 the Gooch crucible-glass fiber filter method since the filter was not removed from the filtration device „ The alundum porous crucible" method was investigated because of the extreme rapidity of the technique „ Unfortunately , an appreciable por- tion of the solids passed through the filter <, Use of 2 l-cm glass fiber filters in a membrane filter holder was investigated in an attempt to TABLE IV COMPARISON CF SUSPENDED SOLIDS DETERMINATION TECHNIQUES Number Sample Mean SS Cone, Percent of Standard Test of Size Gooch-Glass Deviation Series Technique Samples ml mg/1 Method mg/1 I Gooch-Glass 5 15 2109 100 34 I Membrane Filter 5 15 2094 99 37 II Gooch-Glass 5 15 1741 100 19 II Alundum 5 15 1672 96 22 II Glass in Membrane Holder 2 15 1620 93 ™ avoid the previously-described weight variations caused by the hygroscopic Gooch crucibles o The method proved unsatisfactory because of the difficulty of removing all solids from the sides of the filtration device „ It was concluded that the use of glass fiber filters in Gooch crucibles was comparable or superior to the other methods studied in accu= racy, reliability 9 and convenience s and that 9 because of its low cost, the technique was best suited for the present study "Type RA98 9 manufactured by Norton Refractories , Worcester 9 Mass, 92 Reliability^ It was necessary to investigate more thoroughly the reliability of the suspended solids determination procedure to estab- lish the required number and size of samples The information was used in subsequent experiments to distinguish random variations from significant differences in solids concentrations „ The general range of variation to be expected in suspended solids determinations was established by studying the distribution within groups of suspended solids determinations employing various sample sizes and con- centrations o Activated sludge from the Urbana-Champaign plant, adjusted to various concentrations by withdrawing clarified liquor, was placed in a 4-liter beaker „ The sludge was then stirred on a magnetic stirrer and, simultaneously, aerated vigorously,, Nine samples of the desired volume were then removed for determination of suspended solids. Figure 31 illus- trates the general relationship obtained between the coefficient of varia- tion of the group of nine samples and the sample volume and concentration „ The values necessarily include any variation caused by failure to obtain completely uniform distribution of solids in the beaker from which samples were withdrawn„ The maximum coefficient of variation obtained for any sample size and concentration compares favorably with the value indicated in Standard Methods (1960) for the filter paper Buchner funnel method and with the value obtained by Wyckoff (1964), who used glass fiber filters „ The coefficients of variation of four groups of suspended solids determinations on the Lake Park Subdivision activated sludge were 1„3 to lo8 times higher than those shown in Figure 31„ This could be caused by the fact that the plant does not employ preliminary or primary treatment and thus the waste contains randomly-distributed, heavy, gross solids which broadens the base of the frequency distribution curve for suspended 93 (/) « w UJ Ul liJ _l -I -I Q. Q. Q. < < < in (T> if) o u"> "^ — — C\J i i | a < o 8 o 00 o o o o o o to o o o If) o o o o o o o o o CM E < UJ o z o o (O Q _l o (/> Q UJ Q. z o < cc UJ \- UJ Q CO Q _J o en Q UJ a z UJ Q_ CO o o o CD < _l Ui or m CM O CM If) 6 jU90J9d 'NOIlVldVA dO !N3IDIdd300 ro UJ or 94 solids determinations o Reliability of suspended solids determinations using Mattoon and Tuscola, Illinois, activated sludges was in agreement with Figure 31 „ The number and size of samples for determination of suspended solids in particular experiments was established by assessing the impor- tance of the determination and consulting Figure 31 . In instances where reliability better than that given by samples of sizes shown in Figure 31 was required, the improvement in reliability was obtained by means of multiple samples rather than by using larger samples which required exces- sive filtration times c Temporal Variation in Sludge Characteristics The characteristics of activated sludge are subject to change as the environment surrounding the microorganisms which comprise the sludge is changed. Thus sludge samples obtained at a single plant at different times may not be considered to be identical, and the properties of a single sample taken from an activated sludge plant and moved to a laboratory environment cannot be considered constant „ Only the latter type of varia- tion is of interest here Individual experiments were completed utilizing single samples of activated sludge „ While the general properties of activated sludges obtained from individual plants from time to time were comparable, no quantitative comparison of sludge samples obtained at dif- ferent times from a particular plant was necessary in the experiments „ Upon collection of a sample, sludge was removed from its normal feeding schedule and maintained under endogenous conditions during the duration of the experiments Following transit to the laboratory, the sludge was stored under aerobic conditions, although from time to time, 95 portions of the sample were removed from the aerated environment and placed in settling columns „ Under these conditions, it was to be expected that characteristics of the sludge would change as experiments progressed,, Yet, somewhat contrary to the popular concept that the "energy level" of sludge controls its settling characteristics (McKinney, 1956), gross changes in settling behavior did not occur when samples were retained under endogenous conditions,, A sludge which was "bulking" at the time of its collection from a waste treatment plant was still basically a "bulking" sludge after several days of aeration in the laboratory. Figure 32 shows the change in initial settling velocities of several activated sludges with time under endogenous conditions,, In each case, sludges were brought to laboratory temperature before tests were conducted , The change in suspended solids concentration during the period due to auto-oxidation was not compensated for Note that continued aeration of the Sullivan sludge, which settled slower at a 1110 mg/1 concentration than did Tuscola sludge at 3620 mg/1 or the Urbana-Champaign sludge at 2480 mg/1, did not improve its settling characteristics . Note also that the change in settling characteristics of the Urbana-Champaign sludge was not appreciably different when the sample was held under anaerobic, rather than aerobic, conditions „ The following procedures were employed to minimize the error in experimental results due to temporal change in sludge characteristics: avoidance of initial periods of appreciable change in sludge characteris- tics, rapid performance of experiments once they were initiated, randomiza- tion of experimental observations, and application of temporal correction factors o The procedures can be best explained by means of an example. The problem of temporal change in sludge properties was most challenging in the long experiments of the second phase of the study involving a comparison of 96 o oo O o -~- CD y o cd or o LlI or £ fc O O 9 0) CM c\j «a* o» — 2 S < < CL 0. o ^ ^ 5 00 < _l CO CO CO _l 3 or or 3 H => => CO o o 10 o o UJ o ro O CM D O • < in o o m O b UJ o Q 2 or Q CO UJ H- or ui o. o cr Q_ e> _l I- Ul CO UJ Q ID _J CO Q UI \- % < UI £ e> - 2 cl < co X ui o or cvi ro UJ or ww/W 'Al 10013 A 0NI1113S u. 97 Theological and settling properties „ These experiments required the determination of settling velocity in various depths of columns for several different concentrations of the sludge sample and determination of the yield strength at several different concentrations. Performance of the experiments required about 48 hr. The paragraphs which follow describe the procedures used to minimize the effect of biological change of the sample in these experiments , Because the most rapid rate of change in sludge settling velocity normally occurred during the first hours after collection of the sample (Figure 32), samples were collected about 12 hr prior to the beginning of the experiment o The time for completion of the experiments was minimized by working out the experimental design and preparing the laboratory apparatus in advance 9 and then working as rapidly and continuously as possible Collection of data in a random pattern was an effective method of ascertaining that the observed trends in the data did not merely reflect biological change. The various concentrations were examined at random rather than in order of increasing or decreasing dilutions. Similarly, the depth of the settling column in successive tests was varied randomly and the speed of rotation of the viscometer was altered randomly between successive observations. Finally J a control was maintained to monitor the temporal change in the sample, A portion of the sludge sample was reserved for this pur- pose, and its settling velocity was determined at intervals throughout the experiment. In addition, a second control was used to monitor changes in the rheological properties. Trends in the change of rheological proper- ties could rarely be established, however. While the major value of the 98 controls was to ascertain that major changes in the sample had not occurred during the experiment, the data were used to normalize all experimental observations to a single point in time,, The time of each experimental observation was recorded, and the value of the observation was divided by the ratio of the value of the appropriate control at that time to the value of the control at the normalized time 99 III. DEVIATIONS FROM PRESENT THEORIES OF THICKENING PURPOSE OF INVESTIGATION The basic hypothesis provoking this research was that prevailing theories might inadequately describe the thickening of activated sludge, and that any deviations from the present theory might advantageously be described in terms of rheological properties of the sludge „ Before embark- ing on the rheological studies, it was desirable to establish that depar- tures from accepted theory do, indeed, exist „ The purpose of this phase of the study was to detect instances in which the present concepts inade- quately described thickening of activated sludge. As discussed in Chapter I, the basis of the design procedure for determining the required area of a thickener is the theory that the velocity at which a given suspension subsides is a function only of its concentration, Accordingly, experiments were designed to detect instances in which settling velocity was influenced by factors other than concentration The experi- ments investigated the effect of depth, effect of stirring underlying sludge $ and effect of a large lower column. Activated sludges from waste treatment plants at Urbana-Champaign, Tuscola, and Sullivan, Illinois, were employed. The Urbana-Champaign sludge was studied at the mixed liquor suspended solids concentration found in the plant (2400 mg/1), and at two greater concentrations (4210 and 6280 mg/1). The Tuscola sludge was observed at the concentration found in the plant (5010 mg/1) and at lesser and greater concentrations (4020 and 7260 mg/l)„ Sullivan activated sludge was tested only at 1020 mg/1. With the possible exception of the 6280 mg/1 Urbana-Champaign sludge and the 100 7260 mg/'l Tuscola sludge, all sludges displayed the characteristic constant rate settling curves attributed to zone settling Representative settling curves for the activated sludges are shown in Figure 33 „ The two concen- trated sludges displayed the erratic behavior concomitant with high con- centrations (see Chapter II )„ EFFECT OF DEPTH According to the Kynch theory, identical suspensions of equal concentration should subside at the same rate regardless of depth „ On the other hand, if a portion of the weight of particles at the top of the sus- pension is supported by underlying particles, as was postulated here, then the depth of the suspension should influence its settling rate A deep suspension would be expected to settle faster than a shallow one because the greater weight of the suspension would more readily cause the under- lying supporting structure to fail Coulson and Richardson (19 55) summarized the commonly accepted views, stating that if the interface position vs„ time curve for one initial depth of a suspension is known, the curves for all other depths can be determined from ito Mancini (1962) found that the depth of suspen- sions of pulped news print did not influence the initial settling rates , Clifford and Windridge (1932), who worked with activated sludge, found that the settling velocity was directly proportional to depth, but investi- gated only depths less than 10 in Gaudin, Fuerstenau, and Mitchell (1959) found that depth Influenced the settling velocity of concentrated kaolin suspensions, but that the settling velocity of dilute suspensions was substantially independent of depth „ The initial settling velocity of the three activated sludges at 101 V | ""i — / r ' I / / ' -^ 6 / / z E / / i < > O / * - _i _i 3 O 1 1 i * If/ - 2 CO • V / / < / / * > J /' _J _J r - => — if) Q 2 ^^ /// \ N v. < < E E E < _J o o 10 O O CM _l o CO O o f Jjf O CO N- iT> ^-^ a 1 JP "*- * 1 i i _ in _ O - m c E Ld _ o — m CO LU > cr 3 O o LU CO LU > LU CO LU q: cl LU ro ro LU tr O U 'NOIllSOd 30Vdd3±NI 102 various concentrations was observed in 3 5-in diameter columns at initial depths ranging from 0„5 to 7„5 ft„ The devices and procedures described in Chapter II were employed to assure uniform initial distribution of suspended solids „ In every case, an increase in depth of the suspension was accompanied by an increase in the initial settling velocity,, As might be expected, the depth dependence for a given sludge was more pronounced at higher concentrations,, It was observed that the data became quite orderly when the ratio of the initial depth of the suspension to the initial settling velocity was plotted as a function of the initial depth. Such curves are illustrated in Figure 34 The curves take the form D — = R + SD 32 v o o where D = initial suspension depth v = initial settling velocity R = — at D Q = S = slope of curve Equation 32 may be written as D o o R + SD o 33 The nature of the relationship between settling velocity and depth is illustrated in Figures 35 and 36 „ 103 *>*>* O* o> E E O O (\J < o o _l ID ^ o 1 1 o o <1 (/> 3 -o < E E < X o I < < m a: 3 - LxJ C/5 < O X I- CL UJ Q UJ o Q 3 _) \- O UJ u. u. UJ ro UJ Z> o o o o o o o o 00 N (0 lO T lO <\J ww 4 A1I0013A 9NI1113S / H±d3Q 39amS 1 1 V \ \ \ \ \ - \o \ ° \ ^ E X \ 1 1 (d) SULLIVAN o - 1020 \ \ \° \ \ o \ 1 1 1 1 l\ 1 \ 00 104 - (O — X e> 0_ z LU Q LU O Q \- LU CO Z> _l < H in o in O in O *- i- to K) CM CVJ ww 'A1I3CTI3A 9NH113S / H±d3Q 39amS **s* \ 1 1 o \ 1 1 1 \< OD \ i -< E \ _ r- _l < \ o _l O \ o o \ _co Z> o en 3 CJ 1 < \ ° \< 10 o — *\ -z in < _\ z ~c?\ °\ -C5 t\ vp\ _ T 2 oil < O o\ f-\ Q_ 2 O \ ^ 2 ^ X \ X < CP E o « \ ro o 1 o 1 O \ -< < 00 CM < \ CM z < < 1 o \ \ 00 cr O X \ -or 3 \ \ — — z> \ \ ^. \ o \ < O \ \ *■*' i i . 1 1 1 \ 1 III r> O O o O o O O o o in o m O in o m o in _l 3 CO h- 2 O CJ sr ro LU QT Z) o Ll 105 ■♦- O E c o a. >- CJ o _l UJ > LlI FIGURE 35. EXTENT OF RETARDATION URBANA- CHAMPAIGN ACTIVATED SLUDGE. 106 100 CD ■»- D £ c <1> O t- _l I- I- LlI in 2 3 4 5 6 SLUDGE DEPTH, ft FIGURE 36. EXTENT OF RETARDATION TUSCOLA AND SULLIVAN ACTIVATED SLUDGES. 107 It may be seen that when R is zero, the settling velocity is independent of the depth of the suspension., Such a situation is illus- trated in Figure 34d but was not observed with the activated sludges testedo Whenever R has some finite value, the rate of subsidence is de- pendent on the depth of the suspension „ The magnitude of R is a measure of the extent of retardation, and accordingly, it was termed the retarda- tion factor o In harmony with the basic postulate of this research, the retardation factor was interpreted to be a measure of the support which the sludge at the interface received from the sludge below it» It may be seen that as the sludge depth approaches infinity, retardation becomes insignificant and the settling velocity approaches a constant value . The value of the settling velocity at infinite sludge depth is given by the reciprocal of S and was termed the ultimate settling velocity, v „ v = i 34 u S The ultimate settling velocity was interpreted to represent the zone settling velocity at which the interface would subside if it received no support from underlying sludge The curves shown in Figure 34 were fitted by the method of least squares to determine the characteristic constants R and S for the various sludges o These values together with the ultimate settling velocities are shown in Table V The values of R and S were used to compute the relation- ship between settling velocity and sludge depth given by Equation 33, and the resulting velocities, expressed as percent of the ultimate settling velocity 5 are shown in Figures 35 and 36 „ Experimental points are included for comparison,, Settling velocities for 2-ft sludge depths expressed as 108 w >-4 P4 < CO W o Cm- ID J CO Q W < > M H O < < Cm- Cm 1 > w CO 'Cm O o M E-< < Q Pi < Cm O o CO (— 1 Pi < Cm 2 o o cm m H Ol (O (N 44 ■H ft +-» Mm Mm II O CM o\° 4-> w tti > CO CD _t 3 SI en to .d- > *V. H ^H O ■P Mm o o o CO Pi w bO >, X) C o) •H ■H T4 H X) o rd & to o a) ►J a, 0) bfl o n xi H o 3 C 04 H its M b0 44 fc H 44 O H e M bO > ^ CO H e o ^ C H O "v. O bO B CO v-< CO o o <-\ o o J" o o en en cm cm en j- MHO rH H rH O O O CO o o to to o o CO 4-> Mm en cm en o in CO \ H O tO m it to co C O O O O o a >H in to cm t~- CO en CO B CM co co en CO CM CO C o o o o o c H o to to o H r» r- B to r- CM O O to o o O O o o o en — 1 CO CM H to CM CO CM CM O o CM o CM _t to d- Ln r- H c c c bO M bo =H tH -H rO rd tU ft a a e b e rd rd rd 44 xi 44 o o o (4 1) II rd m rd rd rd rd rd H H H > C (4 C O o O •H rd rd rd O o o H 44 44 43 03 w HI H l- o o -I 1 2 UJ > e> UJ CO Q. UJ Q ,-t; o.6 2 g CO z UJ CL CO CO I 08 4 2 12 3 4 SUSPENSION DEPTH, ft FIGURE 37. SETTLING BEHAVIOR OF SAND SUSPENSIONS. Ill settling velocity was not influenced by the initial depth of the suspension,, Thus s sand conforms to the Kynch theory — settling velocity is a function only of the local particle concentration „* The prevailing thickening theories would work very well to determine the area of a "sand thickener," but they are not strictly applicable to the design of an activated sludge thickener because of their failure to consider the differences between activated sludge and the ideal suspension considered in the Kynch analysis „ It is interesting to note that, while retardation was found in all of the activated sludges examined, it became increasingly significant as the concentration of a given sludge was increased. At shallow depths, retardation was of more significance in reducing the settleability of con- centrated sludges than was hindered settling „ It is also noteworthy that the data tabulated in Table V can readily be interpreted in terms of the general nature of the sludges (see Appendix C for descriptions of the activated sludge plants sampled) „ At comparable concentrations, the Urbana-Champaign sludge had a higher retardation factor than the Tuscola sludge o This might be expected since the Tuscola plant operates as a con- ventional activated sludge process with an exceptionally low organic loading^ while the Urbana=Champaign plant is loaded more heavily, and samples were taken from the contact tank effluent „ The Sullivan sludge provides a more extreme example The Sullivan sample had a sludge volume index of 600 and would be considered a bulking sludge „ Although the sludge had a high ultimate settling velocity, it was highly retardedo Its retard- ation factor at a concentration of only 1020 mg/1 exceeded the retardation factor of Urbana-Champaign sludge at 4210 mg/1, or of Tuscola sludge at 5010 mg/1. "Shannon et_ al, (1964) have also confirmed that the Kynch analysis is an accurate description of the behavior of certain ideal suspensions They used glass beads „ 112 EFFECT OF STIRRING UNDERLYING SLUDGE This group of experiments was suggested by the work of Mancini (1962), who reported that the rate of subsidence of the interface in a column of activated sludge could be hastened by mixing only the lower part of the column,, This is contradictory to the prevailing theory which maintains that the rate of subsidence of the interface is a function only of the particle concentration there o The implication of Mancini ' s observations is that the mixer aided in destroying the structure of the flocculent material at the bottom of the column, permitting the sludge which it supported to subside more rapidly „ It was felt that Mancini *s findings could not be accepted unequivocally s since the shaft on his stirring mechanism passed through the overlying sludge and could have altered the flocculent characteristics of the suspension or created additional wall effects „ Accordingly, a mixer was designed which did not disturb the sludge at the top,, A sketch of the device is shown in Figure 38 „ The mixing paddle consisted of a section of o 25~in o diameter copper tubing to which blades were attached at l<,5-in„ intervalso The blades were o 5 by 3<,l-in„ pieces of sheet metal with o 25-in o holes drilled in the center to fit on the tubing „ They were attached in horizontal positions, and adjacent blades were at 90° angles to one another o Two mixers 9 one with a 9-in length and one with a 2-ft length, were employed,, Half an old pump casing was used to provide the bearing and seal at the bottom of the column, and the shaft was connected by a pulley to a variable speed drive which permitted continuous variation of the mixer speed from 3 5 to 110 rpm„ Vanes fabricated from o 125-in o Plexiglas were situated immediately above the mixer to prevent propagation of turbulent eddies into the upper part of the column, The vanes were made of two 3,5 by 9„0-in„ pieces of Plexiglas fitted together in the form of a cross o When the sludge-water interface was situated at the top of the 113 NORMAL 3.5 in. DIAM. COLUMN VANES MIXER \ \. VARIABLE SPEED DRIVE FIGURE 38. DEVICE FOR STIRRING BOTTOM OF SETTLING COLUMN . 114 vanes j the mixer could be operated at top speed without disturbing the inter face o All mixing experiments were conducted in 3., 5-in columns with 3o5-ft sludge depths o Results from experiments employing the 2 -ft mixer were dismissed because the interface approached the mixer before a settling velocity could definitely be ascertained , and it was possible that the observed increase in settling velocity was caused by alteration in floe particles due to turbulence from the mixer,, Of the experiments employing the 9-in mixer , those with Sullivan sludge at a solids concentration of 1C20 mg/1 best illustraxed the effect of mixing the bottom of the column „ Some of these results are shown in Figure 39 „ While an increase in initial settling velocity could readily be shown in the stirring experiments , the technique did not lend itself to quantitative description as did the experiments on the effect of sludge depth o Surprisingly j the mere presence of the mixer in a settling column increased the initial settling velocity In Figure 39 s the curve labeled "0 rpm" shows the subsidence of the interface in a column outfitted with the mixing apparatus but with the motor turned off. The curve labeled "control" shows the subsidence rate in a similar column with no mixing equipment. When the mixer paddle was placed in the bottom of the control columns, the same increase in settling velocity occurred^ demonstrating that the increase was not due to any peculiarities of the column equipped for mixing o Presence of only the vanes could not be shown to influence the subsidence velocity „ It is speculated that mixing , induced as solids sub- sided past the stationary mixer blades i was sufficient to disrupt the structure of the sludge and hasten the rate of subsidence of the interface,, The increased wall effect could also have been a factor 115 E o o E o Q_ LlI Q FIGURE 39. EFFECT OF STIRRING UNDERLYING SLUDGE. 116 No relationship between the speed of mixing and the interface subsidence rate could be discerned,, In the series of tests depicted by Figure 3 9 , five different stirring speeds were employed , ranging from to 60 rpm Ail stirring speeds produced an increase in the initial settling velocity c The mean initial settling velocity in the stirred columns was o 197 ft/min as compared to 0=135 ft/min in the control columns o The ultimate settling velocity of the sludge as determined by investigation of the effect of depth was C 300 ft/min. A hypothetical settling curve illustrating the ultimate velocity is included in Figure 39 for comparison o EFFECT OF LARGE LOWER COLUMN It was envisioned that s if a column of comparatively small diameter were placed above a larger column, the volume of clarified liquid in the lower column would exceed the volume of solids settling from the smaller overlying column „ This would remove any underlying support from the top column and permit the interface to subside at a higher velocity,, A 3o5-in diameter column was used for the upper portion, and a 7 5-in diameter column for the lower „ The apparatus is illustrated in Figure 4-0 „ In every case s the interface in the upper column subsided at a faster rate than in 3 5=in o diameter control columns „ However, density currents were created in which clarified liquid from the lower column was transported into the upper column, resulting in a reduction of the sus- pended solids concentration there Because of this, no conclusions were drawn from this series of experiments Results for Urbana-Champaign sludge at 6700 mg/I are shown in Figure 41„ 117 3.5 in. DIAMETER COLUMN — \ V ,i >s **- m • ' 7.5 in. DIAMETER ll COLUMN — \ H— if) C\j ' FIGURE 40. APPARATUS FOR OBSERVING EFFECT OF LARGE LOWER COLUMN. CO o Q. UJ O fi en LU 40 60 TIME , min. FIGURE 41. EFFECT OF LARGE LOWER COLUMN. 118 OTHER EVIDENCE OF NON-IDEAL BEHAVIOR In a few instances with sludge exhibiting extremely poor settling properties, it was noted that sludge in the lower part of columns did not appear to flocculate „ Analysis of the suspended solids profile of such columns revealed that the lower portion did not compact, but remained at the initial concentration while compaction occurred in the upper floccu- lated portion, Such a profile is shown in Figure 42 „ The data are for Sullivan sludge It is postulated that sludge in the lower portion formed a gel which had greater compressive strength than that of the overlying solo The cause of the localized gel formation is not understoodo The suspended solids profile in Figure 42 is not representative of the normal mode of compaction of activated sludge „ It is presented merely as further evidence of the danger of applying ideal thickening theories to activated sludge without inquiring as to the properties of the suspension and the nature of the forces which control its consolidation „ SIGNIFICANCE OF RESULTS The experiments on the effect of depth and the effect of stirring underlying sludge were successful in confirming the basic hypothesis -- that the behavior of activated sludge deviates from that of the ideal sus- pensions considered in thickening theories „ In both series of experiments the rate of subsidence of the interface was found not to be solely a function of the local particle concentration „ In both cases, support from underlying sludge appeared to be an additional factor controlling the subsidence rate The experiments concerning the effect of sludge depth were valuable in providing a measure of the extent to which underlying sludge retarded the subsidence of the interface „ Analysis of the data afforded a 119 E o o -Q E o O g 1000 2000 3000 SUSPENDED SOLIDS CONCENTRATION, mg/A FIGURE 42. ABNORMAL SUSPENDED SOLIDS PROFILE DURING THICKENING. 120 measure of the settling velocity of sludge in the absence of retardation, This permitted an evaluation of the relative roles of retardation and other properties of the sludge in establishing the settling velocity of activated sludge ; 121 IV 8 RELATIONSHIP BETWEEN RHEOLOGICAL AND SETTLING BEHAVIOR INTRODUCTION The relationship between the Theological properties of sludge and its thickening characteristics was explored theoretically and experi- mentally,, An idealized mathematical model describing the hypothesized mechanism of thickening was developed, and the predictions of the model were compared to the deviations from the prevailing thickening theory reported in Chapter III, In the experimental portion of this phase of the study 9 rheological and thickening properties of activated sludge from several sources were determined, and the relationship between the two properties was established „ The mathematical model of thickening served as a guide to interpretation of the experimental data MATHEMATICAL MODEL OP THICKENING Development of Model A mathematical description of the postulated process of thickening of activated sludge was developed to assist in describing the basic hypothe- sis of this investigation and to serve as a basis of comparison for observed thickening behavior „ As is commonly the case with mathematical models, the one presented here is somewhat idealized, and possibly emphasizes the mechanism of interest (that is, the resistance to thickening offered by the structural rigidity of sludge) to the exclusion of other factors influencing the process o Such limitations must be borne in mind in application of the model 9 but do not detract from its usefulness in studying the influence of the variables considered,, The mathematical model is based on an analysis 122 of the forces acting on a column of subsiding sludge, and predicts the influence of the depth and structural characteristics of the suspension upon the velocity at which it settles „ Figure ^3 shows the forces acting on a column of sludge of depth, Do The column is of unit cross sectional area. The free-body diagram shows the sludge at the onset of sedimentation when the solids are uniformly distributedo The sludge is considered to settle en masse with floe par- ticles maintaining their relative positions one to another,, As sedimentation occurs 9 the flocculent structure is envisioned to collapse against the bottom of the container„ Steady motion of the entire sludge column is considered to occur so that the net force on the column is zero, or F W = F B + F D + F S 35 where F„ = downward force due to dry weight of sludge solids, w F = upward force due to buoyancy of sludge solids, F = drag force resisting downward movement of sludge, and F = resistance to subsidence of sludge due to the compressive strength of the structure of flocculent particles, The forces due to the weight and buoyancy of the sludge may be combined in a force, F , representing the effective weight of the suspension „ This force may be written as F E = F W - F B 36 F E = P s gV - P w gV 37 F E = (p s - p w } S V 38 123 w " F, UNIT AREA FIGURE 43. DEFINITION SKETCH FOR MATHEMATICAL MODEL OF THICKENING. 124 where p = mass density of dry solids , p = mass density of liquid^ g = gravity constant s and V = total volume of dry solids „ V may be expressed as a constants K , per unit gravimetric concentration per unit depth; V = K cD 39 Incorporating the other parameters in Equation 38 which have constant values for a particular sludge gives F £ = K 2 cD 40 where K_ = K, (p - p )g 41 K 2 * K l (p S - "w>8 The constant s K represents the effective weight of sludge solids in a unit cross sectional area of settling basin per unit depth and unit concen- tration,, It is constant for a given sludge regardless of its total depth or concentration,, The drag force acting on the descending sludge , or, its equivalent, the resistance offered by the sludge particles to the escape of the dis- placed fluid s is dependent upon the nature of the flow regime which exists „ When flow is laminar (fluid moves in layers with only molecular interchange of momentum) 9 resistance is related to the viscous properties of the fluid When turbulent motion (eddy formation with more violent interchange of momentum) occurs s the rate of energy dissipation is increased, and resistance 125 also becomes a function of the momentum transferred in the fluid as a result of the relative movement between the fluid and the solid Intuitively s one would predict that flow about the slowly descending mass of activated sludge would be laminar Flow through porous media at comparable face velocities (for example , in rapid sand filters) is commonly considered to be laminar „ Indeed, Camp (1936) assumed that the flow regime about normal activated sludge in settling basins was lami- nar,, Yet visual inspection of a subsiding sludge mass shows a tendency for formation of channels through which the displaced fluid escapes at high velocities o Sometimes "volcanoes" can be observed at the sludge interface where newly formed channels "erupt" at the surface a This suggests that channel formation in activated sludge is not restricted to the visible area at the wall of laboratory settling columns s but occurs throughout the masSo It should be pointed out that the existence of a finite yield strength facilitates the formation of channels in activated sludge Cer- tainly, the ability of a material to behave as a solid should enhance its capacity to maintain channels Mathematical models were developed to predict behavior for both laminar and turbulent conditions „ The laminar model visualizes flow to occur uniformly throughout all interstices of the sludge. The turbulent model considers the fluid displaced during sedimentation to collect into small channels through which it is transported up to the sludge-water interface o The actual mechanism by which displaced fluid escapes is probably a combination of the two models „ It will be seen that the funda- mental predictions of both models with regard to the effect of rheological properties are basically the same 126 Darcy's law describing the percolation of fluid through a homogeneous porous medium, Q = K ±A 42 provides a convenient method of expressing the drag force, F , under con- ditions of laminar flow„ The coefficient of permeability, K„, reflects the viscosity and density of the fluid and the size, geometry, and distri- bution of pores in the medium It may be considered constant only for a particular sludge at a particular concentration and temperature „ In Equation 42, i is the slope of the energy grade line and A is the cross sectional area of the column,, Dividing by A, and expressing i as the head loss, H , per unit depth, D, gives H L " - K 3 - " where v is the face velocity and equals the rate of subsidence of the sludge mass Solving Equation 43 for H and multiplying by the collective area of the pores s A s the mass density of the fluid, p , and the gravity constant, W g, permits Equation 43 to be expressed in terms of the drag force Ap w g p = _____ n v 44 D K 3 Combining the constant parameters in Equation 44 gives F D = K 4 Dv 45 127 Ap w S where K., = — — — ■ 46 4 K 3 The value of the constant,, K s like the value of K_ , depends on the character and concentration of the sludge „ Should one prefer to visualize F as the summation of drag forces on the individual floe particles which comprise the sludge mass s he may arrive at Equation 45 through application of the general expression for the drag resisting movement of a body through a liquid, 2 p v^ w F = C A 47 The coefficient of drag, C n , is a function of Reynolds number, M , and in laminar flow, C D = E = p vd 48 w The constant K has some dependence on particle shape, and to that extent would be dependent on the source and concentration of the sludge „ The value of K c for spheres of diameter, d, is 24 In Equation 48, d is taken as a representative linear dimension characterizing the size of the inter- stitial pores through which water displaced by the subsiding solids escapes „ As before , v is the subsidence velocity of the sludge, p the w mass density of the liquid, and jj the viscosity of the fluid. The term. A, in Equation 47 is taken as the collective projected area of the flocculated particles in the sludge mass. It is expedient to express A as a function of depth, D„ 128 A - K r D 49 b The constant c K r , represents the collective effective area per unit depth $ b and could be expected to be constant only for a particular sludge at a particular concentration,. Substitution of Equations 48 and 49 into Equation 47 yields -. ■ m «•■• F) Simplifying and combining all parameters except those of interest in the mathematical model gives F Q = K y Dv 51 which is the same as Equation 45 „ As before, the constant reflects physical properties of the fluid and parameters related to the flocculent nature of the sludge j and could be taken as a constant only for a particular sludge at a single concentration and temperature The drag force for the turbulent version of the mathematical model s which considers displaced flow to escape by turbulent flow in chan- nels through the sludge s can best be approximated by analogy to turbulent flow in pipes Such a force may be expressed as P v ^ F = f L A W 5? which will be recognized as the general expression for drag (Equation 47) 129 adapted to pipe flow nomenclature „ The term, f , in Equation 52 is the Darcy-Weisbach friction factor and depends upon the relative roughness of the channel and Reynolds number,, In pipe flow, it is found that when ]R becomes large and/or the relative roughness of the boundary becomes great, f becomes independent of IR and the resistance to flow becomes dependent on the second power of velocity „ In Equation 52, d is the conduit diameter, A its cross sectional area, L its length, and v is the mean velocity of flowo Equation 52 may be adapted to the present case of flow through channels within the subsiding sludge mass by writing 2 F D = V T A "V 53 Here, F is the drag force per unit area of a column of sludge of depth, D„ The mean effective diameter of the channels is characterized by d, and the length of channels is related to D„ The velocity term, v, is the sub- sidence velocity of the sludge mass, since for a given value of d, the velocity in the channels will be related to the amount of fluid displaced and hence to the settling rate The collective area of the channels is represented by A The constant K ft is included to represent the geometric difference between the parameters in Equation 53 and their counterparts in Equation 52 „ Turbulence is considered to be developed to the extent that f is constant, and the drag force depends on the second power of velocity,, Consolidating all parameters except those of interest in the mathematical model gives F D = K g Dv 2 54 130 As was the case with the laminar model 9 the constant depends upon fluid density as well as physical properties of the sludge and may be presumed to be constant only for one sludge at one concent rat ion „ Characteristics of the force representing the resistance to deformation of the sludge structure will be considered later The force will be represented here as merely F The mathematical models may now be completed by combining the expressions for the various forces „ Combination of Equations 35, 36, 40, and 45 (or 51) s gives K^ Dv = K 2 cD - F g 55 which is the mathematical thickening model in which motion is considered to be laminar,, Similarly 9 the model for turbulent motion is obtained by replacing Equation 45 with Equation 54 to give K g Dv 2 = K 2 cD - F s 57 / K 2 F S It will be noted that both versions of the model predict that settling velocity is dependent upon the depth of the sludge mass and the magnitude of the structural support force The relationship between the models and experimental data will be shown subsequently,, In both versions of the model, the second term becomes negligible when F is small and/or 131 the total depth is great. Under these conditions, settling velocity becomes a function only of concentration -- in accordance with Kynch's analysis o Assumptions of Mathematical Model of Thickening It is by now apparent that numerous assumptions are necessary to permit formulation of the complex process of thickening , Inasmuch as it is the author's basic argument that the assumptions in the prevailing model of thickening have not been adequately appreciated, it is appropriate that the limitations of the model presented here be discussed,, The model is used to inquire as to the settling velocity of a uniformly dispersed column of sludge at the onset of sedimentation „ No relative movement is considered to occur between the flocculent sludge particles except at the bottom of the column where the structure of the sludge must deform to permit subsidence. The initial period of accelera- tion is ignored with consideration only of established motion so that the summation of static forces on the entire sludge mass is zero. The characteristics of a particular sludge at a particular concentration are presumed to be independent of the depth to which sludge is placed in a settling column „ The gravimetric and volumetric distribution of solids, floe particle size and effective area, permeability, and channel diameter for a given concentration of a given sludge are not considered to be influenced by the depth at the onset of compaction. Limitations of small laboratory columns such as extensive channelization at the wall or possible bridging from wall to wall are ignored. The assumption that the extent of channel formation is not affected by the depth to which sludge is placed in a column seems reasonable, 132 inasmuch as the rate of upward displacement of water is independent of depth per se It should be noted , however, that Shannon and Tory (196 5) have suggested that channeling is more pronounced in columns of greater depths „ The most severe limitation of the mathematical models is the assumption that the velocity of displaced fluid in the channels in the turbulent model bears a direct relationship to the settling velocity of the suspension„ In fact, the channel velocity is related to the total cross sectional area of channels as well» This limitation makes it diffi- cult to compare predictions of the turbulent model for two different concentrations of the same sludge „ Grossly different degrees of channeling could exist, and channel velocities would then bear little relationship to the corresponding interface subsidence velocities Unfortunately, any alternate assumption which might be made regarding the relationship between the drag force in turbulent motion and the sludge settling velocity would be similarly arbitrary, and subject the model to the same limitations „ The turbulent model is still of value as a basis for comparison, but the severe restriction discussed here must be recognized,, Predictions of the Mathemat ical Model Genera l Form of Model 3 For purposes of discussing the predictions of the mathematical model and for convenience in subsequent manipulation of the equations, it is helpful to express the laminar model (Equation 56) as a L " - 59 and the turbulent model (Equation 58) as 133 b T a T - ~ 60 In these expressions K~ K~ a T = ~- c and a_ = rr- c 61 L K 4 1 K g F F S S and b T = — and b„ = -rr- 62 L \ l K g Figure 44 shows the general form of Equation 59 and Figure 4 5 shows the general form of the parameter D/v as a function of D„ It may be seen that, with appropriate values for a and b, Figures 44 and 45 could also be presented as the general form of the predictions of the turbulent version of the modelo The discussion in the paragraphs which follow, then, applies to both versions of the mathematical modelo Figure 44 illustrates that the model predicts a relationship between v and D similar to that observed with activated sludge and reported in Chapter III„ It may be seen that as b goes to zero, the curve of v vs„ D becomes a straight horizontal line, and the suspension behaves in accord- ance with the prevailing theories of thickening „ Since b equals F /K (or, in the turbulent version, F„/K q ) s the model states that the cause of devia- tions from the "ideal" behavior of suspensions (where v is independent of D) is the existence of a finite value of T„ a That is, settling velocity is a function of the suspension depth only when the suspension possesses structure, and a force to collapse the structure is required to permit subsidence The model also shows that the extent of retardation caused by a given value of F is dependent upon the magnitude of K (or K in the turbulent version) „ A suspension which, in the absence of retardation due 134 > >- O O _J Ll) > DEPTH, D FIGURE 44. GENERAL FORM OF MATHEMATICAL MODEL. Q > DEPTH, D FIGURE 45. - vs D PLOTS PREDICTED BY MODEL v 135 to F , settles slowly (that is, K or K is large, so that a drag force equal to the effective weight of the suspension is attained at low velo- cities) will be relatively less affected by structural retardation than one which settles rapidly when unretarded,, Defect in Model „ Inspection of Figure 44 reveals that the mathematical model is defective in that it predicts that, at some small depth, sludge will stand without settling,, That is, the v vs„ D curve intercepts the D axis,, Based on the limitations described in developing the model, the conclusion that shallow sludge layers will not settle is inevitable o When the depth becomes so small that the effective weight of the sludge equals the structural support force, the drag force — ■ and hence the settling velocity — must become equal to zero. Experimental determination of settling velocities of shallow depths of activated sludge was difficult,, The period of subsidence between the end of the flocculation period and the time that higher concentrations reached the interface was too short to permit reliable determination of settling velocities o No settling velocity determinations were conducted with initial sludge depths less than 6 in„ However, it was observed that, in time s a zone of clear water developed at the top of the shallowest of sludge depths , and s on this basis, curves of experimentally determined settling velocity vs„ depth were drawn through the origin (see Figure 35 )„ Similarly the nature of the experimentally determined — vs„ D curves at low values of D was not closely investigated and the observed data was extrapolated back to its intercept with the —axis (see Figure 34 ) Figure 4 5 shows the discrepancy at low values of D in the latter type of plot caused by the defect in the model „ 136 The defect In the model can be explained by more thorough con- sideration of the rheological properties of activated sludge „ Consolidation of the structure within activated sludge is a viscoelastic process involving the deformation of floe particles and the sliding of adjacent particles over one another to effect a more compact arrangement of particles „ The process continues at low loadings (i e , shallow depths) by the phenomenon known variously as creep or plastic flow (Scott, 1963 )„ All molecules which form the "bonds" which give sludge its structural characteristics are in a constant rate of thermal agitation „ From time to time molecules acquire sufficient energy to release them from their neighbor and cause them to move to a new position „ In this way con- nections between adjacent floe particles may, from time to time, break and reform in an unstressed position,, This results In a redistribution of interparticle stresses and contributes to subsequent failures of other connections o The time-dependent failure of the structure of activated sludge might also be viewed with reference to its lyophilic nature „ Heukelekian and Weisburg (19 56) found activated sludges to have a high bound-water content o Bound-water contents equal to 50 percent of the weight of dry solids were common, with much higher values in bulking sludges „ It is likely, then, that solid particles in activated sludges -- at least at normal gravity thickening concentrations — are not in actual contact, but are separated by liquid films „ The deformation characteristics of sludge must be related to the nature of the interparticle films The rate of deformation depends not on the mechanical properties of the particles s but on the viscosity of liquid films between them (Cottrell, 1964), Frank and Evans (1945) introduced the atomistic approach to the study of characteristics 137 of bound-water „ They argued that such water had a higher degree of orien- tation and existed in a quasi=solid state,, The idea is frequently referred to as the iceberg concept — referring to the "frozen patches" or "micro- scopic icebergs" which exist about iyophilic substances „ Weyl and Ormsby (1960) explained that the extreme fluidity of normal water is attributed to the ease with which protons can move about — submerging in the electron clouds of the adjacent negatively charged oxygen atoms „ The proton arrange- ment in the microscopic layer of water surrounding a molecule s ion, particle or surface is altered „ The protons in the iceberg must overcome an energy barrier to move about „ The viscosity of the bound-water is thus greatly increased and s hence, the terms "quasi-solid" and "iceberg," The thickness of the adhering film of water is not well defined , Its rigidity decreases with distance away from the attracting particle In a simpler fashion. Grim (1962) explained that liquid water has little cohesive power, but oriented water has considerable „ Thus it is seen that deformation of activated sludge is an extremely complex process involving intraparticle and interparticle defor- mations resulting from viscous flow of the quasi-solid film separating particles s with periodic failure of individual connections and subsequent redistribution of stress , The structural support offered by the rigidity of the sludge cannot be likened to that of a box which will support all loads up to its structural capacity and then abruptly collapse upon addition of the "last straw." Instead , the sludge deforms under all loads „ It might be expected that deformation would continue until fluid films are displaced and solid particles come into actual contact „ Stresses could then be transmitted elastically between particles and a structure could develop 138 which, like the box^ would not deform inelastically until an excessive load was applied „ The nature of the structural support force s F , will be considered in more detail in a later discussion „ At the moments suffice it to say that structural failure of the type proposed in the preceding paragraphs has not been successfully formulated „ Representation of the force which resists deformation of the sludge structure as simply F„ without attempting to further describe its characteristics is an expedient which permits the otherwise impossible development of the mathematical thickening model „ This expedient use of F q also leads to the defect in the model „ As long as the cause of the Imperfection is understood s the imperfect model can be beneficially employed In the study of the mechanism of thickening „ Fitting of Ob served Data to the Ma thematical Model Direct determination of the constants a and b in the formulas for the mathematical thickening models was not possible , for F and the constants K and K could not be readily determined experimentally It thus became necessary to devise an alternate means of determining a and b from experimental observations o Two experimentally determinable parameters discussed in Chapter III — the retardation factor, R, and the slope, S 9 of the - vs. D plot ~ were found to be useful for this purpose „ The slope at any point of the curve shown in Figure 45 is "h® Substitution of the laminar version of the value of v (Equation 59) gives s l = 3d (^^'^(s^:) Differentiation leads to 139 S L = a L D ' 2b T D (a L D - V 65 which is the expression for the graphical slope, S, in the laminar model,, The retardation factor, R, is the intercept on the — axis of the back extrapolate of the tangent to any point on the curve in Figure 4 5, Thus, v DS 66 Substitution of Equation 59 for v and Equation 65 for S gives R D 3 ? a T D - 2b D Lj Lr L a_D - b T , _ , .2 L L (a D - b ) 67 which reduces to R L = b L D (a L D - b L )' 68 The turbulent version of Equation 64 is obtained by substituting Equation 60 in Equation 63 S T " dD — D I b \l/2 Lb --) J 69 140 Differentiation yields b T l/2 x b T / b^-1/2 \ a T - D~/ " 2 D~ V a T " D / T D which reduces to 2a T D - 3b T S T / b T \3/2 2D V a T ~ D" and is the expression for the graphical slope in the turbulent model. Similarly, R in the turbulent version is obtained by substitution of Equation 60 and 71 in Equation 66: p 2a T D * 3b T R T = / b T \l/2 " 7 b T \ 3/2 If T " D7 2 ifT " D-J Equation 72 may be expressed more simply as b T R T = / b T \3/2 2 (fT "- Thus a means of experimental determination of a and b, which are constants for a given sludge at a given concentration, was affordedo Repetitive settling tests were conducted at various initial sludge depths to develop the plot of — vs„ D Then, the slope, S, of the tangent at some point, D, was determined along with its back extrapolate, R„ With these known values of D, S, and R, simultaneous solution of Equations 65 and 68 for the laminar version and Equations 71 and 73 for the turbulent version yielded values of the two unknowns a and b„ In both the laminar and turbulent versions of the mathematical 141 thickening model , the expression for — is, asymptotically, a straight line„ A question arises as to whether the experimentally observed slope of — vs„ D can be treated as the ultimate slope of the mathematical model (at D = °°) , or whether it corresponds to a finite value of D„ If the slope can be considered to correspond to the slope of the asymptote, simultaneous solution of the equations in the preceding paragraphs can be greatly facilitated by taking the following limits; lim S r = — 74 L a L D -> lim R T = -=- 75 L 2 D -*■ °° lim S T = — — 76 a T D -> °° b T lim R = — -— - 11 2a T d/2 D ^ 00 Values of a and b for the experimental data reported in Chapter III were computed by considering the observed slope to correspond to the slope of the mathematical model at D = 4 ft, 6 ft , 8 ft and °° The results for the three different concentrations of Urbana-Champaign sludge were representative, and covered the range of observed degrees of retardation,, These curves together with the model predictions are shown in Figures 46, 47, and 48 142 X I- Q_ UJ Q a: o > < UJ CD UJ Q O O en < Q_ o o CO UJ or (0 E Q UJ > or o uj o co *■ m oj °K Q < Z < UJ is! O Q Q UJ or < 0_ ^ < 2 < X o < CO 0T Z> u|UJ/u 'A1I0013A 9NH113S 143 UJ Q O UJ _l 3 CD or ID I- _l UJ Q O ■ < < _1 Q UJ > or UJ CO CD o sr ao * n M n O O O h- I- I- < < < CO CO CO UJ UJ UJ Q Q Q O O O sr oo Q Q Q < < < Q CO CO CO UJ > - r r cc — i — ' — ' qj UJ UJ UJ Q O <£> X H Q_ UJ Q vD ^ OJ O CO u> ft c\. — ~ : — o o O O O O O o o 6 b 6 or o > < x UJ CD CO £ Q UJ CO OJ oo «■ o . UJ Q 3 2Z h- O Q Q UJ or < a. r: H -I O UJ < Q ■si co 7 or < o_ o o 1^- ui or < CD or 3 WW/4J 'A1I0013A 9NI1113S 144 oo Ul Q O UJ _l CD 3 UJ Q O 0T ■ < ^j- cO oo o ii ii n H Q Q Q Q I- I- \~ H- [Jj uj UJ UJ UJ o Q O Q Q O O UJ _l < o I to u. u. o Q UJ > or stf- 00 ° II II II II O O O O < < < < CO CO CO CO _ — I — > t Uj UJ UJ UJ UJ CO o Q Q Q Q O O O O I m ro O 6 o o UJ Q m o 8 o o o or o > < x LjJ . 00^ UJ E > cr o uj oo O . < UJ H O Q Q UJ or < Q. ri -J O UJ < o o GO or < o_ o o 00 UJ or < x o I < z < 00 or 3 u|UJ/u 'AllOCTGA 9NH113S 145 The figures demonstrate the basic agreement of the model predictions and the experimental data. At low degrees of retardation (Figure 46, R = 0,8 min) the differences between the experimental and pre- dicted curves due to the defect in the model are minimal. At moderate degrees of retardation (Figure 47, R = 6,3 min) the differences become more pronounced, and under conditions of severe retardation (Figure 48, R = 166 min) the differences are considerable,, Fortunately, most experimental data corresponded with curves 46 and 47, Values of the retardation factor as high as shown in Figure 48 were rare. In Figure 46, it is seen that the value of S was nearly fully developed at 4 ft. That is, the predicted relationship for v vs, D was essentially the same whether Equations 65 and 68 or Equations 74 and 75 (laminar model) were used to solve for a and b„ In Figure 47 differences between the curves predicted from use of the various values of D became significant. In other words, the slope of the — vs. D curve of the mathe- matical model was not constant over the range of depths considered. In Figure 48, the differences were more severe. It was concluded that the experimentally observed value of S could not be considered as the ultimate slope of the mathematical model, but rather that the observed slope must be considered to correspond to a finite value of D, The 4-ft depth, which was near the mean of the range of depths employed in experiments, was selected as the depth to which the observed slope was considered to correspond. In all subsequent discussions, S, in either the laminar or turbulent versions is understood to represent the slope of the tangent to the — vs, D plot of the mathematical model at D = 4 ft. 146 EXPERIMENTAL RELATIONSHIP BETWEEN THICKENING BEHAVIOR AND RHEOLOGICAL PROPERTIES Introduction Having shown that observed deviations from prevailing thickening theories could be explained by a mathematical model which was derived by envisioning a structural support force to resist subsidence, it remained to show that activated sludge does, indeed, display a structural rigidity, and that the magnitude of this rheological property can be related to the extent of the observed deviations,, It should be noted that others have considered the relationship between sedimentation and rheological properties of suspensions, Michaels and Bolger employed the same model to investigate both the sedimentation (1962a) and rheological (1962b) properties of flocculated kaolin suspensions, The model was conceived by envisioning solids as existing as aggregate particles, and by considering the effect of shear rate on the flocculated mass, Kearsey and Gill (1963) were able to show reasonable agreement between the yield stress of flocculated thoria slurries determined in a viscometer and the yield stress determined from considering the forces acting on a bed in compaction „ Their formulation would, however, appear questionable inasmuch as they likened the relationship between yield strength in shear and the compressive strength of the bed to that of an elastic body in unconfined compression,, Determination of Structural Support Characteristics from Sedimentation Behavior The nature of the structural support force, F , was revealed by the mathematical thickening model. Expression of the mathematical model 147 in terms of experimentally determinable parameters permitted quantitative solution of the relative magnitude of F for a particular sludge at a given concentration o In the case of the laminar version of the model, the equality of the denominators in Equations 6 5 and 68 permits one to write . a T D 2 - 2b D b D 2 ( * lD . ^ = s = -^- or R(a T D - 2b. ) = b T DS 79 h Li Li Hence b T (SD + 2R) = a. DR 80 Substitution of the expressions for a and b (Equations 61 and 62) gives F SL K 2 -r^ (SD + 2R) = ~ cDR 81 The constant K , which relates the drag force per unit depth to the subsi- dence velocity, cancels, giving F - K cDR «2 F SL " K 2 SD t 2R 82 All values in Equation 82 may be experimentally determined. Values of K 9 (the effective weight of solids per unit depth per unit concentration) will not be reported here inasmuch as K is constant for a given sludge and, as will be seen, only the relative value of F q is of interest. The expression for the structural support force in the turbulent 148 model, F qT , is determined in a similar fashion,, Combination of Equations 71 and 73 gives b \3/2 2a D - 3b b D la i - irj = s = — 83 or R(2a T D - 3b T ) = Sb T D 84 Hence b T (SD + 3R) = a T (2DR) 85 Substituting for a and b yields ST 9 - — (SD + 3R) = 2^ cDR 86 Kg K g Simplifying gives F - K 2cDR q 7 ST K 2 SD + 3R which is the turbulent equivalent of Equation 82 Nature of Structural Sup port Force The general characteristics of the structural support force were considered in the discussion of the defect in the mathematical model „ It was pointed out that the mechanism of collapse of the structure within sludge was extremely complex, and involved viscous flow between particles with periodic failure and reformation of individual "connections" within the sludge mass 149 One looks to the field of soil mechanics for a means of analyzing such a failure mechanism The same type of failure is involved in the consolidation of clays „ The problem has been given considerable study because of its importance in considering the settlement of structures „ Historically s soil consolidation has been considered to occur in two phases. Primary consolidation is considered to be governed by the rate at which pore water is able to escape, and secondary consolidation is considered to be governed by the rate at which soil particles are able to move over one another and arrange themselves into a more compact mass. Yet the two processes cannot occur independently as they are normally considered,, As noted by Olson (1960), secondary compression is due to shear stresses between particles, and must occur whenever soil undergoes volume change „ Unfortunately, the process of secondary compression has not been analyzed on the basis of fundamental principles „ As stated by Scott (1963), "To date, no completely satisfactory stress theories have been developed by means of which the history of the deformation of the soil underneath the structural loading can be traced,," Leonards (1962) noted that ",..the compressibility of the mineral skeleton is time dependent „ Therefore additional retardations exist s to a greater or lesser degree, during the entire consolidation periodo A satisfactory treatment of this phenomenon has not been formulated „" Engineering designs involving soil consolidation are based on the Terzaghi consolidation theory,, This theory states that the rate at which a soil consolidates is governed by the rate at which pore water can escape according to Darcy's law„ The theory is known to be in error because of its failure to consider the plastic resistance to consolidation caused by the relative movement of soil particles (Taylor, 1948 )„ Because no satisfactory 150 means of expressing the plastic resistance has been devised, and because the error arising from omitting plastic lag is a conservative one, the resistance caused by rearrangement of the soil mass is commonly ignored in engineering practice In the case of activated sludge, consolidation is desirable -- not undesirable as in the case of soils Thus, failure to consider the plastic resistance to compression is not an error on the conservative side„ Furthermore, in the thickening model, the pore water which is displaced upon collapse of the sludge structure passes up through the entire bed„ This hydrodynamic resistance (or "primary compression") has been adequately dealt with in the drag force, F „ The structural support force, F q , would be primarily concerned with the plastic resistance or the resistance offered to rearrangement of the sludge particles ("secondary compression" ) „ As has been seen, this is the type of resistance which escaped formulation in the field of soil mechanics,, Thus we are left with no fundamental means of describing the structural support f orce s and must resort to some experimentally measurable property of the sludge which might be related to the relative magnitude of F_o Yield strength determinations in a viscometer were used for this pur- pose o The difference between conditions in the viscometer and those at the bottom of the settling column must be emphasized,, In the viscometer, the entire body of sludge is subjected to shear -- each layer of sludge moves with relation to its neighbors,, In contrast s collapse of a structure during sedimentation is characterized by periodic failure at individual points rather than complete shear of .the entire specimen,, It is reasonable, however j to expect that the same properties which determine the yield strength of a suspension are related to the structural support force, F q0 151 Proceeding on this basis we may write F Q = f( T ) 88 b y where t is the yield strength as determined in the viscometer and f denotes some unknown function,, If a direct linear relationship is presumed, F_ = K t 89 S 10 y where K is an unknown constant „ It must be emphasized that there is no firm basis for presuming a direct relationship,, It is merely an expedient, The expected relationship between thickening and rheological behavior can now be obtained by combining Equation 89 with the expressions for F deduced from the mathematical model „ Combining with Equation 82 gives cDR T y = K ll 5FT2R 1 as the expected relationship in the laminar model „ Use of Equation 87 gives 2cDR T y - K ll STT"3R ' as the expected relationship in the turbulent model <. The value of K is K 2 /K 1QO 152 Experimental Results Activated Sludges Examined ,, Three municipal activated sludge plants of widely varying characteristics — Urbana-Champaign, Tuscola, and Sullivan $ Illinois — were used as sources of activated sludge. The plants are described in Appendix C, A sufficient quantity of sludge was collected at one time to conduct all sedimentation and rheological experi- ments „ Experiments were conducted within as short a time as possible, and the technique discussed in Chapter II for monitoring temporal change in sludge characteristics was employed to normalize all results to one common time,, Rheological and thickening experiments were conducted over the range of suspended solids concentrations which might occur in the final settling tank in the plant from which the sludge was collected,, That is, experiments were conducted at various concentrations between the concentra- tion in the aeration tanks and the concentration of the return sludge. The various concentrations employed in the rheological and in the thickening studies were not identical. Thus, in comparisons between rheological and settling properties at a particular concentration, values of the various parameters were obtained from fitted curves of the parameters as a function of concentration. Table VI shows the suspended solids concentration in the mixed liquor and the return sludge together with the sludge volume index at the mixed liquor concentration, and the organic loading as estimated from plant operational records. If one takes the sludge volume index as some measure of the settling characteristics of a sludge, it is seen that the Sullivan sludge was grossly different than the other two, and would normally be classed as a "bulking" sludge. 153 TABLE VI PROPERTIES OF ACTIVATED SLUDGES EMPLOYED Organic Loading Source of Sludge SS Conc (mg/1) SVI / lb BOD per day \ Mixed Liquor Ret urn Sludge (ml/gm) V l b sludge so! .ds/ Urbana-Champaign 2280 8230 75 o 14 Tuscola 4350 7420 55 o 06 Sullivan 1225 2820 300 1 35 Sedimentation Properties „ It was necessary to determine retarda- tion factors and slopes of — vs. D curves for various concentrations of 1 v each sludge in order to obtain the information necessary for comparing sedi- mentation and rheological properties „ Initial settling velocities at various initial depths were determined using the procedures reported in Chapter II Because of the erratic nature of such data, large numbers of determinations are required to adequately define the relationship between depth and settling velocity (Figure 35 ) „ To minimize the time required to establish the relationship (and hence to minimize the change in sludge characteristics during tests) and to improve the reliability of the data, all settling data from one sludge were analyzed as a family of curves with data from one concentration fortifying that of another„ Such curves for the Urbana-Champaign s Tuscola and Sullivan sludges are shown as Figures 49, 51, and 53, respectively,, The corresponding - vs, D plots from the fitted v vs. D curves are shown in Figures 50 , 52, and 54 „ With each sludge, it was found that the retardation factors varied with the suspended solids concentration within the range investigated according to the relationship c E o _J UJ > _l I- h- W CO 0.20 I 3-""* i - I ■ i a" 1 1 3175 mg/* 5440 >i_ 5910 6435 I 1 0.15 0.10 A 05 T ■ n 6635 i 1 164 DEPTH, ft FIGURE 49. SETTLING PROPERTIES OF URBANA - CHAMPAIGN ACTIVATED SLUDGE. c 'i Q > DEPTH, ft FIGURE 50. D/v VERSUS D CURVES FOR URBANA- CHAMPAIGN ACTIVATED SLUDGE. c >■ o o _l LU > o _J I- h- LU CO 1 1 1 1 1 4310 mg/f 1 1 020 u _ • 4615 *n?0 A • A 0.15 A a" Rtfi5 ^ 0.10 ▲ 6785_ ^ D 0.05 □ 7735 . n V ■ V i ■ 1 1 ""I"" I 1 ■ I 1 155 FIGURE 51, DEPTH, ft SETTLING PROPERTIES OF TUSCOLA ACTIVATED SLUDGE. 100 c E Q > 50 — FIGURE 52 DEPTH, ft D/v VERSUS D CURVES FOR TUSCOLA ACTIVATED SLUDGE. 0.14 1 1 1 1 \\\0j£S^ 1 1 2— — — — — 1 o " ~ c "e 0.12 0.10 "G — ° >- o 0.08 Oy \32^ •""" • o -J LU > 0.06 — < \730 - (3 0.04 0.02 /* A *™ — 2070 A □ LrJ D — n 1 1 D 1 1 1 1 1 156 DEPTH, ft FIGURE 53. SETTLING PROPERTIES OF SULLIVAN ACTIVATED SLUDGE. 300 — c *E Q > too 200 — FIGURE 54. DEPTH, ft D/v VERSUS D CURVES FOR SULLIVAN ACTIVATED SLUDGE. 157 t, he nn R = ee 92 where g and h are constants for a particular sludge and e is the base of the Naperian system of logarithms. Calculated values of the constants are shown in Table VII „ The suspended solids concentration, c, is expressed in mg/l 9 and R is in min„ TABLE VII CONSTANTS IN EXPRESSION RELATING RETARDATION FACTORS TO CONCENTRATION Source of Sludge Urbana-Champaign 0„065 0.00090 Tuscola 0o020 0.00094 Sullivan 0.13 0.0033 Figure 55 demonstrates the conformance of the data to exponential form of Equation 92. While the present study was not concerned with the biological variables which influence the settling behavior of sludges , it would seem that determination of the factors which influence the magnitude of g and h would contribute to the understanding of the fundamental factors influencing sludge settleability. Rheological Properties . From a priori consideration of the fact that activated sludge is a two-phase system in which the dispersed phase is 158 cr. o 2 < a UJ a: 1000 700 500 300 100 70 50 30 10 3 - URBANA- CHAMPAIGN A TUSCOLA □ SULLIVAN 2000 4000 6000 SUSPENDED SOLIDS CONIC, mg/A 8000 FIGURE 55. VARIATION OF RETARDATION FACTOR WITH SOLIDS CONCENTRATION. 159 very flocculent and has a high volumetric concentration, it is reasonable to predict that it would display non-Newtonian behavior and that it would possess a yield strength,, While several investigators (Hatfield, 1938; Wolfs, 1950; and Geinopolos and Katz, 1964) have reported activated sludge to display the non-Newtonian property of thixotropy 9 apparently no one has previously measured its yield strength „ Babbitt and Caldwell (1939) could not detect a yield strength of activated sludge in a 0„375-in o pipe vis- cometer o Hatfield's data suggest a yield strength, but lack of information on his modified Stormer viscometer prevents an absolute confirmation „ The fact that activated sludge has been shown to be thixotropic indicates it must be either plastic or pseudoplastic also (see Appendix A). The fact that the literature yields little information on the rheology of activated sludge is understandable inasmuch as most previous rheological investigations of sanitary engineering sludges have been related to pumping problems „ Activated sludge is rarely concentrated to the extent that it causes pumping difficulties. In reviewing previous work on sludge pumping, Behn (1960) concluded that activated sludge is apparently much more Newtonian than other sludges encountered in waste treatment o However, Hatfield (1938) showed, by severe extrapolation of his data, that activated sludge was potentially more of a problem than other types of sludge „ He estimated that activated sludge composed of 10 percent solids by weight would have an apparent viscosity of 21,000 centipoise,, This value was 10 to 100 times as great as his estimates for digested sludges at the same concentration,, The development of a viscometer suitable for investigating the rheological properties of activated sludge was described in Chapter II „ The procedures described there were used to obtain the relationship between 160 rotational speed and the resulting torque at various suspended solids con- centrations o Data of this type for various concentrations of Tuscola activated sludge are shown in Figure 56 „ The extrapolated values of torque at zero rotation were used to compute the yield strength of the sludge (Equation 116, Appendix B)„ The dotted portion of the curves in Figure 56 indicates that the torque was less than the torque produced by a shearing stress at the outer cylinder equal to the yield stress „ Therefore the viscometer contents were not sheared across the entire gap between cylinders, A finite yield strength was observed at every concentration of each sludge investigated,, Figure 57 shows the observed relationship between suspended solids concentration and yield strength It is seen that the equation relating yield strength to concentration has the same form as Equation 92 • kc t = ie 93 y where j and k are constant for a particular sludge „ Calculated values of the constants are shown in Table VIII „ The yield strength is measured in dynes per sq cm and c is expressed in mg/l TABLE VIII CONSTANTS IN EXPRESSION RELATING YIELD STRENGTH TO CONCENTRATION Source of Sludge j k Urbana-Champaign 0„0091 0„ 00060 Tuscola 0„0077 0,00056 Sullivan 0„0038 0„0019 1G1 E a. Q LJ UJ CL < o cr TORQUE, Brookfield Units FIGURE 56. TYPICAL VISCOMETER DATA 162 E o o- 00 \ (/> c >» CD z UJ q: i- co O _I LlJ >- 1.00 0.70 0.50 0.30 0.10 0.07 005 0.03 0.01 O URBANA- CHAMPAIGN A TUSCOLA D SULLIVAN 2000 4 000 6000 SUSPENDED SOLIDS CONC, mg/ X 8000 FIGURE 57. VARIATION OF YIELD STRENGTH WITH SOLIDS CONCENTRATION. 163 It is reasonable to expect that j and k are influenced by the same factors which influence g and h in Equation 92 „ As mentioned pre- viously , disclosure of the relationship between biological variables and j and k would be instructive „ Comparison of Rheological and Sedimentation Data ,, Figure 58 shows the relationship between the yield strength, as determined from vis- cometer studies, and the retardation factor, as determined by observation of the behavior of sludge in settling columns „ The relationship is of the form R = m(x ) n 94 y where m and n are constants for a particular sludge,, Values of the constants are listed in Table IX„ R is measured in minutes, and t in dynes per sq cm The similarity of the values of n for the vastly different sludges is note- worthy. TABLE IX CONSTANTS IN EXPRESSION RELATING RETARDATION FACTOR TO YIELD STRENGTH Source of Sludge m n Urbana-Champaign 70 l o 50 Tuscola 70 1„67 Sullivan 2100 1.75 While a relationship between the retardation factor and yield strength is reasonable and is in support of hypothesis being considered c *e O I- o o < a < \- UJ 1000 700 500 300 1004— 70 50 30+- — 5- — 3 — 01 1 1 1 — I I I! I — TTT O URBANA-CHAMPAIGN A TUSCOLA D SULLIVAN 164 1 — I I I I I I III 0.03 0.05 0.07 0.1 0.3 YIELD STRENGTH, dynes/sq cm 0.5 07 1.0 FIGURE 58. RELATIONSHIP BETWEEN RETARDATION FACTOR AND YIELD STRENGTH . 165 here, a word of caution is in order „ Equation 94 cannot be related to fundamental principles , It is possible that the excellent correlation between the experimentally determined values of R and t reflects their mutual dependence on the suspended solids concentration rather than a cause-and-eff ect relationship,: * A more convincing indication of the relationship between observed settling behavior and the rheological properties of sludge results from application of Equations 90 and 91 „ These expressions indicate the rela- tionship between yield strength and thickening properties as predicted by the mathematical model of thickening „ The agreement of the experimental data with these equations is illustrated in Figures 59 and 60 In view of the assumptions contained in the mathematical model and the complications created by the defect in the model, the agreement between the measured yield strength and yield strength deduced from observ- ing thickening properties is convincing „ The absolute magnitude of the values of the ordinates are irrelevant here since, it will be recalled, the magnitude of the constant relating them, K.. , , cannot be directly deter- mined,, It should also be recalled that the justification for calling K. , a constant was weak The fact remains that the relative magnitude of the structural support force computed from observed settling data is in basic agreement with the measured yield strength „ •'Since, for a given sludge , both the retardation factor (Equation 92) and the yield strength (Equation 93) are a function only of concentration, it is inevitable that a relationship between the two should exist „ From com- parison of Equations 92, 93, and 94, it may be shown that m = exp (In g - r- In j) 95 and n = r 96 k 166 to 6 < a. S < x < -J < Z O > < a _i CD (/) _l (TDD 3 \- (/) I I o < a a: <1- 6 + a \ to b cc Q o CVJ d LU CO LU • >- -J LU a a LU O > 2 cn lu en co < OQ Z o ^ LU LU LU CO GO O z o a. h ES2 CO Q Z LU o tr < LU Z q: < If) LU ir ujo bs/sauAp 'H19N3dlS Q13IA CD 167 X I- Ld q: i- co o -j • Ld -I — Ld >- Q O Ld > h- cr 2 Ld Ld CO d m o CD or 3 Ld Ld Li_ £0 Ld W 00 1 CL H X CO o Q Ld cr -J Q luo bs/sauAp 'HlONaUlS CH3IA Ld cr o CD Ld cr CD 168 The curves in Figures 59 and 60 describe neither exponential nor simple power functions,, The lower portions of the curves are linear, with deviations occurring in the upper portion (which corresponds to higher suspended solids concentrations) „ It will be recalled that the defect in the mathematical model caused negligible deviation from observed behavior at low degrees of retardation, but that the defect manifested itself more severely at high degrees of retardation (Figure 48)„ The effect of arbi- trarily considering the observed slope of the - vs„ D curve to be the slope of the mathematical model at 4 ft rather than at infinity is to reduce the predicted structural support force at high suspended solids concentrations, but to leave it unaffected at low concentrations „ Thus the defect in the model could be the cause of the deviations at high concentrations from linear behavior in Figures 59 and 60 „ It will be recalled that the defect in the model was of more consequence in the turbulent version than in the laminar version (Figures 46 through 48 )„ The variation from linear behavior is also of more consequence in Figure 60 than in Figure 59 „ Figures 59 and 60 tend to unify the data from the three sludges „ In previous comparisons of their behavior, the differences in sludge charac- teristics ~ particularly those of the Sullivan sludge — were evident » Figures 59 and 60 show that The structural support force manifested by a sludge depends only on the rheological nature of the particular sample, and is quite independent of factors such as concentration and the settling characteristics of the sludge in the absence of retardation,, To clarify this point, it is noted that the range of concentrations represented by the points in Figures 59 and 60 is 3000 to 5750 mg/1 for the Urbana-Champaign sludge, 4250 to "775^ mg/1 for the Tuscola sludge, and only 1000 to 2125 mg/1 for the Sullivan sludge. Yet the three curves are essentially the sane. This 169 is because,, as indicated by Figure 57 s the yield strength of the Sullivan sludge at j for example 9 1750 rag/1 is equivalent to that of the Urbana- Champaign sludge at 4000 mg/1 or the Tuscola sludge at 4600 mg/l„ The biological factors which cause this great difference in rheological behavior are the cause of the structural support which the Sullivan sludge displays at low concentrations,, If operation of the Sullivan process could be modified to reduce the yield strength, settling properties would be im- proved It has been shown that the mathematical model predicts that the amount of retardation which a given sludge displays is dependent not only on the structural support force, but also on the settling characteristics of the sludge in the absence of structural support. The excellent corre- lation between yield strength and retardation factor (Figure 58) suggests that the same factors which affect yield strength also influence the settling characteristics of the sludge in the absence of structural sup- port o Thus operational changes which minimize the structural support force will have a compound effect in improving settleability„ It will be recalled that the postulated mode of sedimentation was something intermediate between the two versions of the mathematical models Expelled water probably travels by laminar flow to channels through which it flows turbulently at a velocity determined both by the subsidence velocity of the sludge and its channel forming characteristics „ The basic correlation between yield strength and observed settling characteristics seems to hold for both the laminar (Figure 59) and turbulent (Figure 60) models o This is not to imply that both models are correct, for the values of K (the slope of the curves) shown by the two sets of curves are not the same The actual value of K is probably something different than that predicted by either version of the model „ 170 SIGNIFICANCE OF RESULTS In this chapter the deviations from prevailing theory described in Chapter III have been Interpreted in terms of the rheological charac- teristics of sludge o A mathematical model was developed to show that observed settling behavior could be explained by the existence of a struc- tural support force within the sludge Then, it was shown that activated sludge does 9 indeed, possess such structural characteristics „ Finally, the magnitude of the yield strength of sludge as determined from viscometric analysis was related to the structural characteristics as determined from experimental settling tests and predictions of the mathematical model. Development of a mathematical description of thickening was beset with difficulties in formulating the drag force on particles and the structural support force , Two versions of the model were developed by considering different flow characteristics of the displaced water. Neither of the versions was felt to truly describe the actual flow pattern „ The model was also defective because of the impossibility of accurately describ- ing the complex nature of the structural support force. These limitations of the model had to be considered in contemplating the inferences of the model and in attempting quantitative comparisons of model predictions and observed behavior. The work has confirmed the basic hypothesis of this investigations that the "ideal thickening theories which have been advocated for use in design of gravity sedimentation devices for activated sludge are not strictly applicable. The observed settling velocity of activated sludge is not merely a function of the local particle concentration as the theory supposes, but also depends upon the support which the sludge receives because of the resistance of the sludge structure to collapse. The magnitude 171 of the deviations from the prevailing theory depend on the characteristics of a particular sludge, and may be appreciable even at the relatively low suspended solids concentrations found in final settling tanks „ It is felt that an attempt to quantitatively relate the implica- tions of this research to design practice is premature „ The laboratory techniques used here are too laborious to gain ready acceptance by design engineers, and the relationship between laboratory settling tests and plant scale performance needs to be more adequately explored. However, several important suggestions applicable to design can be made The prevailing concept that the area of a thickener is inalterably determined by the subsidence velocity of some limiting concentration of sludge is in error. The area requirement can be reduced by adequate manip- ulation of the sludge to destroy its structure and prevent the structural support force from retarding subsidence. Settling tests must be conducted at depths and under mixing conditions representative of plant operation. The practice of relating expected return sludge concentrations to results of sludge volume index determinations appears to be highly questionable. While no study of plant-scale thickening was conducted to permit a direct evaluation of the effect of retardation on thickener performance, laboratory data permitted an assessment of the effect of retardation on the solids handling capacity as it is ordinarily determined. The capacity of the three suspensions studied to be thickened to 1 percent solids was computed according to the procedures outlined in Chapter I. In the case of the Urbana-Champaign sludge , the solids handling capacity at a 1-ft sludge depth (63 lb per sq ft per day) was slightly less than 80 percent of the unretarded solids handling capacity of the suspen- sion (as determined by using the ultimate settling velocity in computing 172 the solids handling capacity) , The solids handling capacity of the Urbana- Champaign sludge could be increased 14 percent by operating at a 4 -ft sludge depth rather than at 1 ft. The solids handling capacity of the Tuscola sludge at 1-ft depth (113 lb per sq ft per day) was about 73 percent of the ultimate solids handling capacity, and the ability to transmit solids could also be increased 14 percent by increasing the sludge depth to 4 ft„ The effect of retardation was more severe with the Sullivan activated sludge. While there was some question as to whether the concentration range studied included the rate-limiting concentration, the estimated solids handling capacity at 1-ft depth (3,9 lb per sq ft per day) was 35 percent of the ultimate capacity, and an 87 percent increase in solids handling capacity could be realized by increasing the operating depth to 4 ft. To summarize, if the area required for thickening of the activated sludges considered here were based on observed behavior in laboratory settling columns, the diameter of the thickeners would be 125 to 285 percent larger than if activated sludge behaved according to the Kynch theory. The required area could be reduced by proper manipulation of the sludge — for instance, merely increasing the depth of sludge from 1 to 4 ft would reduce the required area by 14 to 87 percent , Application of the thickening theories currently being applied to activated sludge would suggest that neither depth nor manipulation of underlying sludge could influence the required area of a thickener „ Use of increased sludge depths to reduce retardation would require longer retention of solids in final settling tanks. Although common prac- tice calls for return of activated sludge from final settling tanks as quickly as possible to minimize anaerobiosis , the literature }rields little data to support the merit of this practice. Indeed, Wuhrmann (1960) and 173 the Water Pollution Research Board (1962) have reported that the properties of activated sludge are not influenced by exposure to an anaerobic environ- ment for extremely long periods. The work suggests the value of rheological determinations as a guide for activated sludge plant operation „ "uch remains to be learned about the effect of biological variables upon the rheology of sludge. 174 V. CONCLUSIONS lo The Kynch theory is valid for the ideal suspensions which were considered in derivation of the theory. If the characteristics of real suspensions do not deviate too far from the ideal, their behavior is accurately described by the theory. For example, the behavior of sand suspensions was found to be in agreement with the Kynch theory, 2, The settling behavior of activated sludge cannot be predicted by the Kynch theory. Hence the prevailing theories of thickening are not strictly applicable to the design of final settling tanks and gravity thickeners for activated sludge, 3, In addition to being dependent upon concentration (in accord- ance with the Kynch theory) the rate of subsidence of activated sludge is dependent upon sludge depth and the mixing of underlying layers. This is true even at concentrations less than that of the "compression point," 4, The area of thickeners, as determined from quiescent batch settling tests with the three activated sludges investigated, would be 125 to 285 percent greater than the size of thickeners which could be used if the Kynch theory applied unconditionally to activated sludge. Proper control of sludge depth and mixing conditions should permit a reduction in the required area. With destruction of underlying support, the thickener area could be reduced to that which would result if the Kynch theory were applicable, 5, Analysis of the relationship between the initial depth of an activated sludge suspension and its initial settling velocity provides quantitative measures of the extent of the deviation from ideal behavior 175 (the retardation factor) and the ultimate settling velocity of the sus- pension,, 6 The retardation factor can be related to the general nature of activated sludge „ It appears that, at comparable concentrations, low retardation factors are associated with sludges of good settleability , while bulking sludges have high retardation factors „ 7 The observed deviations of activated sludge from ideal thickening behavior can be interpreted in terms of a mathematical model in which activated sludge is considered to possess internal structure „ In the model, sludge subsidence is resisted by the force required to collapse the structure The conclusions reached from study of the model are the same whether displaced water escapes by laminar or turbulent flow. Probably a combination of the two regimes actually occurs „ 80 The extent of retardation caused by a given structural support force is dependent upon the settling properties of the sludge in the absence of retardation,, A rapidly settling sludge will be more seriously retarded by a given structural support force,, 9„ Activated sludge at concentrations found in normal activated sludge plants possesses a yield strength „ Thus the structural support force considered in formulating the model truly exists . The yield strength depends upon the characteristics and concentration of activated sludge „ Yield strength values from o 03 to o 6 dynes per sq cm were measured „ 10 o The retardation factor of a sludge can be related to its yield strength „ The relationship is a power function„ 11 „ The relative magnitude of the structural support force computed from observed settling data with the aid of the mathematical model can be shown to correspond to the yield strength of activated sludge 176 computed from viscometer data This is true whether displaced water escapes by laminar or turbulent flow 12 o The area required to accomplish thickening in a settling tank is not fixed by the observed settling velocity of the rate-limiting concentration of sludge „ The thickener area may be reduced by adequate manipulation of the sludge to avoid retardance due to structural support, 13 „ Within the concentration ranges investigated, the retardation factor of activated sludges studied varies exponentially with sludge concen- tration o 14 o Within the concentration ranges investigated, the yield strength of activated sludges studied varies exponentially with sludge con- centration , 15 „ Viscometer surfaces must be roughened to prevent slippage if reliable rheological information on activated sludge is to be obtained, 16, Activated sludge exhibits thixotropic properties, 17, In situ observation of the rheological properties of sub- siding activated sludge is complicated by the extremely small magnitude of forces involved, and by limitations encountered in the use of laboratory columns such as wall shear and bridging. The most promise for future work in this area should be in the development of a sensitive instrument for measurement of minute differences in excess hydrostatic pressure, 18, Determination of the biological variables which establish the relationship between the concentration of activated sludge and its yield strength and retardation factor would contribute to an understanding of fundamental factors influencing sludge settleability „ 19, Rheological observations show potential as guides for activated sludge plant operation. 177 20 o The effect of the wall in laboratory settling columns is to increase the rate of subsidence of activated sludge„ The effect is most severe with container diameters smaller than about 2 5 in 21 The initial dispersion of solids in batch settling tests must be accomplished in a manner which minimizes turbulence so that exces- sive sedimentation does not occur during the period of decay of turbulent eddies and reformation of floe Aeration in settling columns is not a satisfactory means of dispersing solids Uniform distribution of solids at the end of the flocculation period can be obtained by pumping solids into the bottom of columns at a controlled rate 22 o Reliable settling data cannot be obtained from the normal batch settling test in small graduated cylinders „ While such tests may be of value in routine plant operation, they should not be used as a source of design data or as a basis for estimating the expected return sludge con- centration o 23,, Settling tests for determining design data must be collected at depths and mixing conditions comparable to plant operating conditions « 24 o The glass fiber filter-Gooch crucible technique for deter- mining suspended solids concentrations is convenient and economical „ The reliability of the method is comparable with the membrane filter technique „ 25 o While biological change of sludge with time is troublesome in sedimentation studies, difficulties may be minimized by avoiding periods of most rapid change, performing experimental work expeditiously, random- izing experimental observations, and monitoring the temporal change 178 VI. REFERENCES Aldertorij, J, L, 1963, Discussion of Analysis of Thickener Operation, by Behn, V. C„ 1963c J, Sanit, Eng„ DJVo An Soc Civil Engrs - 89jSA6, 57-59, Alves, Go E, 1951c Non-Newtonian Flow Fluid and Particle Mechanics , (Lapple, Cc C„ 9 Ed ) University of Delaware, Newark, Delaware, 115-134= Aronson, M„ H, , and Nelson, R, C 1964c Viscosity Measurements and Control , Instruments Publishing Co„ s Inc „ Pittsburg, Pa 134 p. 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Yoshioka, N , Hotta, Y„ s and Tanaka, S 1955, Batch Settling of Homogeneous Flocculated Slurries, Chem, Eng, (Tokyo), 19;616-626 Yoshioka, N„, Hotta, Y, , Tanaka s , S„, Naito, S,, and Tsugami, S„ 1957, Continuous Thickening of Homogeneous Flocculated Slurries, Chem , Engo (Tokyo) , 2i?66=7^, 184 VII, APPENDICES 185 APPENDIX A A REVIEW OF RHEOLOGY THE FIELD OF RHEOLOGY Rheology is the science of deformation and flow of matter „ The study of two specialized areas of rheology -- Newtonian fluids and per- fectly elastic solids — was developed independently from the field of rheology and is highly advanced „ However, rheology as a science is in its infancy o Many date its birth to Bingham's work with paint in 1919 (Reiner, 1959 ) Bingham observed that paint must behave as a viscous liquid to be uniformly spread over a surface without leaving brush marks „ But he also noted that if it were merely a viscous liquid, it would flow off vertical surfaces before it had an opportunity to dry„ His work lead to the descrip- tion of materials now known as Bingham plastics and precipitated the study of other materials which display properties conforming to neither purely elastic nor purely Newtonian behavior „ Unfortunately, a good deal of the work which has been done in the field of rheology has been directed at defining properties of particular substances such as blood, dough 9 and synthetic polymers, and not toward development of rheology as a science „ Hence, predictions of rheological behavior are based more on inferences from the behavior of similar systems than from the application of fundamental principles „ TYPES OF NON-NEWTONIAN BEHAVIOR Introduction Pure, single-phase liquids characteristically demonstrate Newtonian behavior — that is, the shearing stress, t, is directly 186 dv . proportional to the rate of shear, —— , in wholly viscous motion x = y £. 97 dx The constant of proportionality, y, which for a given liquid at a given temperature is a characteristic physical constant, is the absolute vis- cosity. The characteristics of such a liquid are shown as curve A in Figure 61, A fluid is said to have a viscosity of 1 poise when a force of 1 dyne per sq cm is required to move two plates separated by 1 cm of fluid at a relative velocity of 1 cm/sec, Hence, 1 poise equals 1 dyne sec per sq cm. Viscosity is caused by molecular friction, and, thus, is determined by the molecular characteristics of a substance „ Fundamental approaches to the study of viscosity have employed the kinetic theory with modifications to account for molecular interactions and the Eyring model which considers a liquid to be an imperfect molecular lattice in which vacancies are filled by flow and molecular diffusion (Van Wazer et al, , 1963), The viscosity of a substance is dependent upon temperature , While the effect of temperature on the viscosity of a fluid varies widely, liquid viscosity normally decreases with an increase in temperature, A gas, in contrast, becomes more viscous at higher temperatures. Within normal pressure ranges, the viscosity of a liquid is not influenced by pressure, although viscosity increases under extreme pressures. Addition of a second phase to the system makes possible particle interactions, interactions of particles with the fluid, and particle deforma- tion. The resulting behavior of the system may be Newtonian with altered viscosity, viscoelastic, one of the time-independent types of behavior 187 shown in Figure 61 9 or one of the time-dependent types shown in Figure 62 „ Combinations of the various types of behavior are also possible. For example, a system may be pseudoplastic, have a yield strength, and display thixotropic behavior „ Altered Newtonian Behavior Addition of particles may increase the viscosity of a fluid without imparting non-Newtonian behavior,, This type of behavior is found in suspen- sions of non-attracting particles — for example, in suspensions of sand„ Such a situation is illustrated in curve B, Figure 61. If the fluid between two plates moving with different velocities is considered to contain a sphere, it may be seen that the presence of the sphere will disrupt stream- lines in the fluid and produce a higher viscous force on the planes. Einstein (1906) derived the following equation for the viscosity of the suspension; u = y T (1 + [y]c ) 98 o ij V where y = viscosity of suspension (Poises), \i, - viscosity of liquid (Poises), [y] = intrinsic viscosity (dimensionless) , and c = volumetric concentration (dimensionless). The intrinsic viscosity (Van Wazer et al„, 1963) may be expressed as [y] = lim 99 c -0 U L C v v 188 CO CO UJ QC \- CO O < UJ E c/ 6/ yS I./ yS C/ // // X A /X A - NEWTONIAN B - ALTERED NEWTONIAN C - PSEUDOPLASTIC It AS D - DILATANT ItjtA^ E - PLASTIC FIGURE 61 RATE OF SHEAR TYPES OF TIME-INDEPENDENT RHEOLOGICAL BEHAVIOR. CO CO UJ or i- co q: < ui x CO F-THIXOTROPIC G- RHEOPECTIC NOTE : SHEAR RATE CONSTANT TIME FIGURE 62. TYPES OF TIME -DEPENDENT RHEOLOGICAL BEHAVIOR . 189 and represents the effect of the solute at infinite dilution The value of [y] for rigid spheres has been reported as 2,5 (Einstein, 1911) , While the relationship is accepted as being theoretically correct (Roscoe, 1953), it is applicable only when the disturbed regions of flow around particles do not overlap (Cottrell, 1964) and the concentrations term must be altered to compensate for any hydration of the particles (Mysels, 1959 )„ The intrinsic viscosity is unaffected by particle size other than as size affects concentration „ Vand (1948) has modified the expression to account for interparticle attractions „ Viscoelasticity An elastic solid undergoes strain which is proportional to stress, and which is recoverable upon removal of the applied stress „ In contrast, viscous liquids deform continuously under stress, and the deformation is not recoverable o It is not surprising, then, to find that some suspensions exhibit intermediate behavior,, Such materials are termed viscoelastic When viscoelastic liquids are suddenly sheared, they undergo elastic deforma- tion o If the strain is maintained, the stress will disappear with time as viscous flow takes place „ Such behavior is typical of suspensions of modern synthetic polymers (Lodge, 1964), The same phenomenon is involved in creep and relaxation of "rigid" solids, Pseudo plasticity Pseudoplastic materials are those which become increasingly less viscous as the rate of shear is increased. Shear-thinning is a descriptive term often applied to the phenomenon. Curve C in Figure 61 represents pseudoplastic behavior. The shear stress-rate of shear relationship for 190 such materials (Van Wazer et al„, 1963) is often found to approximate the power function, , = K ,§)" where t = shear stress (dynes/sq cm) 9 k = constant with dimensions of viscosity (Poise), •5— = velocity gradient (sec ), and n = constant (dimensionless) „ It is seen that for such a system, "viscosity," which for Newtonian systems is a constant, cannot be defined. The same is true of other non- Newtonian systems o Often this difficulty is circumvented by reporting "apparent viscosity" as represented by the slope of the line OC' in Figure 61o Obviously, such values are meaningless unless the shear rate or shear stress at C is also reported,, Pseudoplastic behavior is associated with systems containing aggregate particles which are broken up by shear,, In such systems, some equilibrium particle size is characteristic of each shear rate,, The nature of the particles may change as the loose particles will tend to break up while the dense particles are relatively unaffected. The apparent degree of hydration and hence the volumetric concentration may be altered as the result of the release of entrapped liquid (Mysels, 1959 )„ Pseudoplastic behavior has also been associated (Alves, 1951) with the alignment of asymetric particles in the flow. In suspensions of linear polymers, pseudoplastic behavior is caused by uncoiling and disentanglement of mole- cules (Van Wazer et al„ , 1963 )„ 191 Dilatancy Dilatancy was originally used to describe closely packed systems of low water content (such as moist sand) which, upon the application of stress 9 must temporarily expand before any deformation can occur Some authors (Roscoe, 1953) insist on adherence to this definition. Others (Van Wazer et al„ , 1963) consider dilatancy to be the opposite of pseudo- plasticity; that is, the apparent viscosity increases with increased rate of shear,, The phenomenon is not common and is associated with suspensions of repelling particles „ Curve D in Figure 61 represents a dilatant sub- stance o Dilatant behavior is frequently found in suspensions which have been deflocculated by addition of polyphosphates or organic polyelectrolytes, Plasticity Plastic materials, illustrated by curve E in Figure 61, behave as elastic solids until the applied stress exceeds the yield stress of the material o At higher stresses, they flow viscously „ Materials which show a linear shear stress vs. rate of shear relationship beyond the yield stress, such as shown in curve E, are sometimes called Bingham plastics to distinguish them from pseudoplastic or dilatant substances with a yield strength,, Because of the difficulty in establishing the limit of elastic behavior, the term "apparent yield value" is probably normally more exact than "yield value „" The shear stress-shear rate relationship for Bingham plastics is dv t = x y + n ^ ioi 192 where t = shear stress (dynes/sq cm), t = yield stress (dynes/sq cm), n = coefficient of rigidity or plastic viscosity (Poise), and -r- - shear rate (sec ), dx Plastic behavior occurs when the solid phase is in sufficient concentration to form a continuous structure. So long as the liquid phase is inert to the suspended particles, the behavior of the material below the yield stress is completely independent of the liquid. At shear stresses above the yield value s flow characteristics are dependent upon the liquid phase (although the coefficient of rigidity may be altered by the other rheological phenomenon discussed here) To illustrate, a tem- perature change does not alter the yield strength, but it does affect the coefficient of rigidity 3 because it changes the viscosity of the continuous phase (Bingham, 1922) „ While the yield stress is normally attributed to the formation of an internal structure due to bridging action between particles, Crowley and Kitzes (1957) have suggested that the yield stress in suspensions of fine lyophilic particles might be due to immobilization of all of the dispersing medium under conditions of no flow. That is, all liquid is bound to the lyophilic solids s leaving no interstitial fluid. Clay suspensions typically display plastic behavior. Beaten egg whites and foam are other examples, Thixotropy Strictly interpreted, thixotropy is the reversible transformation of a gel into a sol upon shaking (Cottrell, 1964); however, the term is generally used to describe systems which become more fluid with time when 193 subjected to shear (Mysels, 1959) „ Such a system is depicted by curve F in Figure 62 „ The behavior is typical of clay suspensions „ Thixotropic suspensions are considered to be those which possess structure s the breakdown of which is a function of time as well as of shear rate Thus, it is necessary that a thixotropic material also be plastic or pseudoplastic Plastic and pseudoplastic materials are not necessarily thixotropic, however „ If the equilibrium situation at a given shear rate is envisioned as being that at which the rate of breakdown of structure is equal to the rate of reformation of structure, then thixotropy may be thought to occur when the rate at which equilibrium is approached is observable o In other words s a thixotropic substance which is exposed to a constant shear rate is not able to repair "bonds" as rapidly as they are damaged,, Ultimately, the equilibrium condition will be reached,, Some rheologists (Roscoe, 1953) define another basic type of behavior; false body,, Others (Alves, 1951) consider it to be an extreme type of thixotropy s while most workers ignore it„ False-bodied suspensions show a finite yield stress immediately after being shearedo This indicates the persistence of some structure within the suspension. Apparently, such materials heal very rapidly „ Rheopexy Rheopexy is a rare phenomenon in which the apparent viscosity of a material increases with time when it is sheared at a constant rate c A rheopectic fluid is shown in curve G of Figure 62 It is seen to be the opposite of thixotropy o Presumably the behavior is due to the formation of structure under shear because of the increased opportunity for flocculation c Eliassaf, Siberberg and Katchalsky (1955) reported a 5 percent solution of polymethacrylic acid to be rheopectic „ 194 APPENDIX B THEORY OP ROTATIONAL VISCOMETRY GENERAL RELATIONSHIPS The two cylinders in coaxial cylinder rotational viscometers are separated by the material being analyzed, and are rotated relative to one another causing a viscous drag on the cylinders „ The rate of shear and shearing stress are deduced from the relative angular velocity of the cylinders and the resulting torque „ In the unmodified Brookfield Synchro- Lectric instrument the inner cylinder is rotated and the outer cylinder is stationary,, The viscous drag opposing movement of the inner cylinder is measured by observing the deflection of a calibrated spring through which the power is transferred,, A schematic diagram of a coaxial cylinder viscometer is shown in Figure 63 „ In the analysis which follows, flow between the cylinders will be considered steady and laminar , and end effects will be ignored „ Rela- tionships will be developed for the unmodified Brookfield viscometer in which the inner cylinder is rotated,. The relationships are the same when the outer cylinder is rotated inasmuch as the relative motion of the cylinders is unaltered,, The shearing stress at any point in the viscometer can be computed from the expression T T 2frhr since the torque of a couple is the same at any point „ In Equation 102, T - torque on inner cylinder as indicated by deflection of 195 C CD = 12 J v i h 1 1 i Ri i Ro ■ 1 FIGURE 63. SCHEMATIC REPRESENTATION OF COAXIAL CYLINDER VISCOMETER . 196 calibrated spring (dyne cm), A = area of cylinder of radius, r 5 and height, h (sq cm), r = radius (cm) , h = immersed height of inner cylinder (cm), and t = shearing stress (dynes/sq cm), Thus, shearing stress distribution is not a function of the fluid being examined, and may be readily computed by measurement of the torque on the inner cylinder. The other property needed to describe the rheological behavior of a substance — the rate of shear -- is not so easily determined. The distribution of shear rate depends not only on the geometry of the instru- ment, but also on the properties of the fluid. With Newtonian fluids, the rate of shear is directly related to the shear stress and hence, varies as the inverse square of the radius. With plastic substances, the rate of shear near the outer cylinder will be zero until shear stress throughout the instrument exceeds the yield stress, Pseudoplastic materials will be sheared at a higher rate near the inner cylinder than will Newtonian liquids. A general expression for rate of shear in a rotational viscometer may be developed as follows. The velocity, v, at a distance, r, from the center of the viscometer is v = rco 103 where w is the angular velocity at the point. Moving to a point dr further away from the axis, the velocity becomes 197 v = (r + dr)(w + dw) = rto + udr + rdw + drdw 104 Dropping the second order differential, subtracting Equation 103 from Equation 104 and dividing by the linear distance, dr, the velocity gradient is seen to be dv dw n . c -3— = a) + r -r- 105 dr dr The rate of internal shear is given by the second term of Equation 105, The first term merely represents whole body rotation of contents of the viscometer,, RELATIONSHIPS FOR SPECIFIC FLUIDS Newtonian Fluids With Newtonian liquids, the shear rate from Equation 105 may be inserted into the basic relationship between shear stress and shear rate to give t = M C-r §) 106 From Equation 102 s it follows that T = 27Tr Z hy (-r ~) 107 dr or -dco = ttt— ^T 108 2iThy 3 r 198 At the inner cylinder (r = R.) oj will be ft, the speed of the viscometer drive mechanism The outer cylinder is stationary, so co is at r = R , Integrating Equation 108 between these limits gives 109 All geometric characteristics of the viscometer may be combined in a single variable 9 K , and the viscosity of a Newtonian fluid may be found from the A expression T y = K A ft 110 Plastic Fluids A plastic material will not flow in a rotational viscometer until the shear stress exceeds its yield value. As the shear stress is increased, flow begins at the inner cup where the shear stress is highest , For a given speed of rotation, shearing will cease at some critical radius where the yield stress exceeds the shear stress„ The material outside of this criti- cal radius will behave as a solid. When the radius of the outer cup is less than the critical radius 9 all of the fluid in the viscometer is sheared, The basic equation for plastic flow is dv T - T = n -T— 111 y dx where x is the yield stress and n is the plastic viscosity. Substitution of the shear rate from Equation 105 and the shear stress from Equation 102 yields 199 T = d(£ 12 n u 2 T y ~ nr dr 2iThr Equation 112 may be written as .do, = T $L _ i ^L 113 2iThri 3 n r r If all of the material in the viscometer is considered to undergo shear (t at R > t ) then the angular velocity varies from 1] at R. to at R , oy i o' and integration of Equation 113 gives i \ T R This is the fundamental equation describing flow of a plastic material in a rotational viscometer, and is attributed to Reiner and Riwlin (1927), When the viscometer contents are not completely sheared, R must be replaced by the critical radius „ Figure 64 shows the relationship between torque and angular velocity obtained from plastic fluids in rotational viscometers „ The straight^iine portion of the curve is described by Equation 114 „ The curved portion results from the critical radius being less than the radius of the outer cup at low rates of shear „ Historically, the curve shown in Figure 64 has been a source of confusion in rheology because it resembles the flow curve of a pseudoplastic material (Green 5 1949 ) The extent of the curved region can be minimized by reducing the gap between the inner and outer cylinders (or, more correctly, by permitting the ratio of R to R. to approach one) Unfortunately, a small gap cannot be employed when suspen- sions of large particles are to be studiedo 200 o o _l UJ > < _J O TORQUE, T FIGURE 64. BEHAVIOR OF PLASTIC MATERIAL IN A ROTATIONAL VISCOMETER. 201 The yield strength of the suspension corresponds to the torque at zero angular velocity, T^ , and may be calculated from the expression T v ■ -V y 2tjt h However, the extrapolate of the straight line portion of the curve, T , may be obtained more readily than T , and, from Equation 114, the yield stress may be determined from T, by the following relationship: "(" " ~) 115 T , X R , o In ~ * i A more informative representation of Figure 64 would be obtained by plotting shear rate vs, shear stress , Equation 102 could be used to convert torque to shear stress. The rate of shear is a function of both the instrument and the fluid being examined, and may be obtained by elimi- nating n between Equations 111 and 114 „ The expression for shear rate at the inner cylinder becomes 117 dv doj dr (t. - t ) Q i y dx T 4irh fer^W 1 ^ where t. is the shear stress at the inner cylinder, and other symbols are as previously defined. The plastic viscosity could be obtained from the slope of the straight line portion of the shear rate vs, shear stress curve. 202 Pseudoplastic and Dilatant £luids_ Flow relationships for pseudoplastic materials in rotational viscometers may be obtained in a manner similar to that employed for Newtonian and plastic substances „ Their behavior is frequently described by the exponential expression <-(§) 118 where the exponent, n, is less than 1„ Substituting the appropriate values for shear stress and shear rate gives V-*(-£ 2irr h 119 or (-dto) dr 2irhk n t 2 r 120 Taking the nth root of both sides of Equation 120 and integrating between the limits of w = fi at R. and to = o at R yields 1 o J Q - T n 1 1 | R 2/n R 2/n, 121 By expressing T in terms of the shear stress at the inner cup, t . , as given by Equation 102, Equation 121 becomes and 122 123 203 This equation demonstrates how rotational viscometer data from pseudo- plastic materials can be handled, A double logarithmic plot of fl vs. t. yields n as the inverse of the slope, and k may be computed from the intercept,, It should be noted that when n = 1, the fluid is Newtonian and Equation 121 reduces to Equation 109 with k being the equivalent of u- Also, when n is greater than 1, Equation 118 describes a dilatant fluid. Hence, these relationships apply to dilatant as well as pseudoplastic substances. 204 APPENDIX C SOURCES OF ACTIVATED SLUDGE INTRODUCTION The activated sludges used in this study were obtained from municipal water pollution control plants in Central Illinois, The plants were selected to give a wide variation in organic loading intensities so as to be representative of the spectrum of activated sludges employed in waste treatment „ Brief descriptions of the plants are included in this Appendixo URBANA-CHAMPAIGN SANITARY DISTRICT The main treatment plant of the Urbana-Champaign Sanitary District was the major source of activated sludge for the study and is referred to as the Urbana-Champaign plant throughout this thesis. The activated sludge portion of the plant employs the Kraus and contact stabilization modifica- tions to the conventional activated sludge process „ The population contributory to the plant is nearly 100, 000 „ In addition to domestic sewage, waste treated by the plant contains an appre- ciable amount of organic material from food processing industries. On an organic basis , the population equivalent of the waste is about 130, 000 „ Following preliminary treatment, the waste is divided, and a portion is treated by the activated sludge process and the remainder by trickling filters. About 3,2 mgd of waste is normally treated in the activated sludge portion, A sufficient volume of trickling filter effluent is added to the waste entering the aeration tanks to maintain a relatively constant hydraulic load of about 4,5 mgdo 205 The mixed liquor suspended solids concentration is maintained at about 2000 mg/1 and the sludge is about 7 5 percent volatile „ The rate of sludge return including the nitrified sludge is about 50 percent of the waste flow and suspended solids concentrations of from 5000 to 8000 mg/1 are ordinary in the stabilization tanks „ The retention times are somewhat less than 2 hr in the contact tanks, about 5 hr in the stabi- lization tanks, and about 24 hr in the nitrification tanks „ The average sludge volume index is about 100 „ Average organic loading on the plant is about 0„14 lb BOD per lb of sludge solids or about 33 lb per 1000 cu ft of aeration tank volume . Samples were normally taken from the contact tanks at their point of discharge into the secondary settling basin When more concen- trated sludge was desired, it was taken at the influent end of the stabi- lization basins , TUSCOLA The Tuscola, Illinois, activated sludge plant receives domestic wastes from about one-half of this community of 3800 people „ Although the flow diagram of the plant is that of the conventional activated sludge process, the loading and operation of the plant resemble that of the extended aeration modification to the conventional process „ Flow to the planx averages about 0»15 mgd. Mixed liquor solids concentrations of about 5500 mg/1 are common, and the sludge volume index is ordinarily about ~ib a The sludge has a relatively high content of non- volatile material (about 68 percent volatile), reflecting the high degree of oxidation which occurs, The aeration tank volume is sufficient to provide over 12 hr 206 retention., Organic loading on the plant is about 8 lb per 1000 cu ft or o 025 lb BOD per lb of sludge solids „ Occasionally one of the two aeration tanks is taken out of service, and these loadings are doubled „ Samples were collected from the effluent end of the aeration tanks o When more concentrated samples were needed, they were obtained from the return sludge channelo SULLIVAN The Sullivan, Illinois, waste treatment plant serves a community of about 4000 „ In addition to domestic wastes, the plant receives consid- erable organic wastes — often in shock proportions -- from industries. One notable industry is a candy factory which contributes a waste high in carbohydrates o The average population equivalent of the waste treated by the plant is about 11, 000 „ The plant utilizes the contact stabilization modification to the activated sludge process „ About 2 hr of contact and 5 hr of stabilization are provided „ During the period of this study, mixed liquor suspended solids concentrations averaged slightly less than 1000 mg/1 and the average concentration of suspended solids in the stabilization tanks was about 2500 mg/lo Volatile solids comprised about 82 percent of the sludge,, The sludge volume index of the sludge averaged somewhat over 300 and values two to three times this high were not uncommon „ The average organic leading on the plant was about 54- lb per 1000 cu ft of aeration tank volume or 0„5 lb BOD per lb of sludge solids „ Samples were collected from the effluent end of the contact tank and from the influent end of the stabilization tank 207 LAKE PARK SUBDIVISION The Lake Park plant serves a subdivision near Champaign, Illinois, It is a prefabricated* extended aeration plant with a rated capacity of 30,000 gpd and receives domestic sewage from 21 homes „ Compartments in the unit include a contact tank, stabilization basin, aerobic digester, and settling tanko Aside from screening, no preliminary or primary treatment is provided. Suspended solids entering the settling tank from the contact area were typically too dilute (800-1200 mg/1) to display zone settling. Samples were collected from the beginning of the stabilization basin and, occasionally, from the aerobic digester. The sludge contained considerable inert material. The percentage of volatile suspended solids was commonly 60 to 65, The plant served as a convenient source of sludge for developmental work but was not used as a source of sludge for any of the major experiments. ■••'Manufactured by Walker Process Equipment Company, Aurora, Illinois, APPENDIX D SYMBOLS 208 Symbol L/T 2 2 L /T Quantity Dimensions Settling velocity of suspension as depth approaches infinity (laminar model) Square of settling velocity of suspension as depth approaches infinity (turbulent model) Gross cross sectional area of settling column, collective projected area of flocculated sludge particles, area of pipe, area of channels in sludge, or area of viscometer cylinder Unit area Structural support force per unit drag, depth, and velocity (laminar model) Structural support force per unit drag, depth, and velocity squared (turbulent model) Suspended solids concentration Initial suspended solids concentration Concentration with limiting solids handling capacity Suspended solids concentration at beginning of settling test TL 2 /F 2 L/T L 3 /T 2 F/L 3 T/V F/L v Final s or ' underflow , suspended solids concentration Volumetric concentration Solids handling capacity Coefficient of drag Limiting solids handling capacity Differential operator Representative diameter of interstitial pores, or of channels through pores Depth Dilution factor F/L F/L 3 Dimensionless F/L 2 T Dimensionless 2 F/L T L L Dimensionless D u Quantity Dilution factor at onset of compaction Initial dilution factor- Initial suspension depth Dilution factor at time s T Dilution factor at underflow concentration Ultimate dilution factor Base of Naperian system of logarithms Darcy-Weisbach friction factor Function Derivative of function Force Filling time Buoyant force of sludge solids Drag force on subsiding sludge Effective weight of sludge solids Structural support force Structural support force in laminar model Structural support force m turbulent model Force due to weight of sludge solids Gravity constant Constant relating retardation factor to an exponential function of concentration h Slope of plot of logarithm of retardation factor vs„ concentration h Immersion of inner viscometer cylinder h End effect in terms of apparent immersion of inner viscometer cylinder D (X e f f f* F F F B D SL ST 209 Dimensions Dimensionless Dimensionless L Dimensionless Dimensionless Dimensionless Dimensionless Dimensionless F T F F F F F F F L/1' L 3 /T Depth of column of sludge 210 Symbol H b k k k k j K A K B Quantity Back extrapolate of tangent to settling curve Interface position at end of apparent flocculation time Interface height at time 8 T. Head loss Height of top of compression zone in laboratory thickener Initial depth of sludge column Height of compression zone in plant scale thickener Depth of sludge at underflow concentration Interface position before lowering interface Interface position after lowering interface Slope of energy grade line Constant relating yield strength to an exponential function of concentration Constant in power law defining pseudoplasticity Slope of plot of logarithm of yield strength vs. concentration Rate constant in compression zone Modified rate constant in compression zone Instrument constant for Newtonian fluid Instrument constant for determining yield strength Instrument constant for determining plastic viscosity Volume of dry solids per unit concentration and depth Effective weight of sludge solids In a cross sectional area of settling basin per unit depth and concentration Coefficient of permeability Drag per unit depth and unit velocity in laminar flow Product of drag coefficient and Reynolds number Collective projected area of flocculated sludge particles per unit depth Dimensions L L L L L L L L L L Dimensionless F/L . 2 FT/L L 3 /F m -l L 5 /T L L/T FT/L 2 Dimensionless 211 10 11 m IR R R R R. l R L R Quantity Drag per unit depth and unit velocity in laminar flow Dimensions FT/L' Quotient of Darcy-Weisbach expression for drag force from flow in sludge channels and equivalent expression for flow in pipes Dimensionless FT 2 /L 3 Drag force per unit depth and per unit velocity squared in turbulent model Constant relating structural support force and yield strength Constant relating yield strength to settling parameters Dimensionless Distance between bottoms of inner and outer viscometer cylinders Length, or length of conduit Constant relating the retardation factor to a power of yield strength Exponent in power function relating retardation factor and yield strength Exponent in power law defining pseudoplasticity Volumetric rate of waste sludge flow Volumetric rate of flow Volumetric rate of flow into thickener Volumetric rate of underflow withdrawal Radius Reynolds number Retardation factor- Volumetric rate of returning activated sludge Gravimetric rate at which solids enter thickener Radius of inner viscometer cylinder Retardation factor in laminar model Radius of outer viscometer cylinder Retardation factor in turbulent model L L 2 TL /F Dimensionless Dimensionless L 3 /T L 3 /T L /T L 3 /T Dimensionless T L 3 /T F/T L T L T 212 Quantity Slope of — vso D curve Br Br Solids flux Solids flux in batch settling test Solids flux in continuous thickener Slope of — vs D curve in laminar model Slope of - vs D curve in turbulent model Back extrapolate of tangent to flux curve Torque Elapsed time 9 or detention time Torque in Brookfield units Time of beginning of compaction Apparent flocculation time Time required for layer of concentration, c. to be propagated to the surface Time required for sludge to settle to depth, H Back extrapolate of viscometer flow curve Back extrapolate of viscometer flow curve in Brookfield units Torque at zero angular velocity Time of lowering of sludge-water interface Rate of upward propagation of layer in batch settling test 5 , or bulk downward velocity of sludge in continuous thickener Rate of upward propagation of layer with concentration, c. Settling velocity of sludge, or face velocity of water Linear velocity of inner viscometer cylinder, or settling velocity of sludge of concentration, c. Initial settling velocity Ultimate settling velocity Dimensions T/L 2 F/L T 2 F/L T 2 F/L T T/L T/L 2 F/L T FL T FL T T T T FL FL FL T L/T L/T L/T L/T L/T L/T 213 w Y y t \ n y y L Cm] p P s p w T . 1 rpm Quantity Relative volumetric capacity , total volume for compaction 9 or total volume of dry solids Volume of liquid Volume of solids Weight Weight of solids before lowering interface Weight of solids after lowering interface Linear distance Unit weight Unit weight of suspension Unit weight of water Plastic viscosity Coefficient of viscosity Viscosity of liquid Viscosity of suspension Intrinsic viscosity Mass density Mass density of dry solids Mass density of liquid Shearing stress Shearing stress at inner cylinder Yield stress Angular velocity Rotative speed of viscometer cylinder Rotative speed of viscometer cylinder in rpm Dimensions L F F F L F/L 3 F/L 3 F/L 3 FT/L/ FT/I/ r FT/L' f FT/l/ Dimensionless 2 4 FT/L 2 4 FT/L 2 4 FT/L F/L' F/L : F/L^ -1 T -1 -1 214 VITA Richard I„ Dick was born July 18 s 1935 , in Sanborn, Iowa, and received his high school diploma in 1953 at Sibley, Iowa. He received his B„ S, degree in Civil Engineering from Iowa State University in 1957 9 and his M„ S„ degree in Sanitary Engineering from the State University of Iowa in 1958 , From 1958 to 1960, he was a Commissioned Officer in the U S 8 Public Health Service and was assigned to the Division of Water Supply and Pollution Control in the Kansas City Regional Office „ He was employed as a sanitary engineer with the consulting engineering firm of Clark, Daily, Dietz, and Associates in Urbana, Illinois, from 1960 to 1962 , During the 1962-1963 academic year, he was an Instructor of Sanitary Engineering at the University of Illinois „ He was a Public Health Service Research Fellow from 1963 to 1965, and will become an Assistant Professor of Sanitary Engineering at the University of Illinois in September, 1965 „ He is a member of the American Society of Civil Engineers, the Water Pollution Control Federation , the American Water Works Association, the Royal Society of Healthy Chi Epsilon, Tau Beta Pi s Sigma Xi, and Phi Kappa Phi , and is a Registered Professional Engineer in Iowa„