m m 1 I E> R.AFLY OF THE UN IVERSITY OF ILLINOIS 'miun M yS^fl DESTABILIZATION-AGGREGATION OF DILUTE COLLOIDAL SUSPENSIONS BY POLYELECTROLYTES Roger Miles Jorden s Ph D, Department of Civil Engineering University of Illinois 9 1968 An empirical equation for the aggregation of destabilized colloidal suspensions has been developed,, It has been found that the rate of decrease of supernatant turbidity of mildly agitated , dilute colloidal suspensions undergoing aggregation is approximately second- order with respect to supernatant turbidity 6 This has been found to be true for a wide range of conditions and for a number of types of systems where destabilization is accomplished by different types of mechanisms , The second-order rate constant for the decrease of turbidity qualita- tively shows the same response to a change of variables as does the rate of aggregation which is suggested by theory for relatively simple cases „ The linear form of the empirical equation which is thought to describe aggregation of dilute colloidal suspensions for a batch reac- tion is TTtT = tToT + K app (where T(0) represents initial supernatant turbidity^ T(t) represents the supernatant turbidity at aggregation time t, and K is the apparent second-order rate constant ) For aggregation induced by mild agitation (G=10 to 80 sec ) and by polyelectrolytes the variables which have been investigated and have been shown to affect K are grouped under two app ° c major independent variables as follows; (1) particle collision opportunity - particle radius, particle number concentration , and mixing intensity, (2) degree of destabilization - destabilant chemical, colloid surface, and milieu The latter three items are further subdivided into six variables which interact in a complex fashion to determine the degree of destabilization: destabilant concentration, destabilant physical-chemical properties, colloid surface concentration, colloid physical-chemical properties, pH, and other solute molecules, especially ionic species o Through application of knowledge of physical-chemical phenomena it has been possible to explain qualitatively the effect of the interactions of these variables upon K „ app The phenomenon of turbidity values first increasing and thence decreasing during the course of aggregating particles whose initial diameter is less than the wavelength of light has been investigated,, It has been found that this phenomenon presents no apparent problem for estimating aggregation rates of the magnitude encountered here I I I ACKNOWLEDGEMENTS The author wishes to express his sincere appreciation to his major Professor, Dr. Ben B. Ewing, for his suggestions during this investigation and for his guidance in the preparation of this manuscript. Sincere appreciation is extended to the Federal Water Pollution Control Administration, U.S. Department of the Interior, for the research grant, WP00801 , which financed this research. Also the author wishes to thank the Grants Division of the U.S. Public Health Service, the agency which originally awarded the grant, for allowing the grant to be trans- ferred between institutions and for their generous extension of time for execution of this research. Sincere appreciation is extended by the author to the Travelers Research Center, Inc., Hartford, Connecticut, and to Doctors Glen R. Hi 1st and Paul Bock for allowing this grant to be transferred to the University of Illinois. Appreciation is extended to Professors Richard S. Engelbrecht and Ben B. Ewing for accepting the transferred grant on behalf of the University. The author also wishes to acknowledge the U.S. Department of the Interior for providing the Fellowship which supported the author during a portion of this work. Finally, the author wishes to thank his fellow students for their helpful discussions during the course of this investigation. IV TABLE OF CONTENTS Page AOlxr* UW Lihi JJoJLjMijJN 1 j o o g o o o o a o o o o o o o o o o o o o o o o o 1 11 Jj-L J 1 Ui 1 A-D-UlJO OOOOOOOOOOOOOOOOOOOOOOOOOOO VI Lib i Ur i 1 oUi>Xj O q o o o o o o o 6 O O O O v 11 X c -LW 1 .KUDU Lf 1 J- UlN ooooooooooooooooooooooooo J- II„' LITERATURE REVIEW AND THEORY,, „ . . . „ . . . , o . . o o » . 7 &ol 111 t2?OCLUC L lOli oooooooooooooooooooooo ' Z. o 1 o -1 J- ©X^nilllOlOgy ooooooooooooooooooo / 2 lo2 Experimental Quantification o o o o 9 2 2 Aggregation Kinetics o » o o « „ <■ o o « o o o 15 2 201 Perikinetic Aggregation » o o <> o o o » o o 16 2 202 Orthokinetic Aggregation o « o o o o o » 18 202 3 Experimental Results for Orthokinetic Aggregaxxon ooooooooooooooooooo £o 2 2 4 Features of Systems of Practical Interest „ o o 28 A- (_, ^L o w LCUC 1US lUlJo ooooooooooooooooooo <£ »3 £ q o U6S LdDl il^idl lOn ooooooooooooooooooooo O U 2 3 1 Polymer-Bridging Model o o o o » o 33 h k i j I / iiiXxenoeQ oegmenxs oooooooooooooooo om* 2 3o3 Adsorption Isotherms cooooooooooooo 36 2 3oM- Adsorption Kinetics o o o » o o „ o o o o 38 ^- o O o i. JlllcU LrrSCLSo o o o o o o o o o o o o o o o o o O »? *£ l O o D UOTlC J-liS lOTlS ooooooooooooooooooo 44 2 4 Turbidity as a Measure of Aggregation Rate ° o o o o o 44 IIIo MATERIALS AND METHODS <, o o „ o o , . „ o » o o o o „ . 51 wo 1 lia. LcFldlS oooooooooooooooooooooooo Ol Oo^ iipP'QX^a LLIS oooooooooooooooooooooooo D ii O o *^ ilcX^IlOCJ. ooooooooooooooooooooooooo *J' 3 4 Plotting of Experimental Data c o » » o o o » a o o 59 IVo RESULTS AND DISCUSSION„ ooooooooooooooooooo 63 4 1 Qualitative Confirmation of Light Scattering Theory Prediction for Particle Growth o o o o o <, 63 4 2 Comparison of Aggregation Rates Depicted by Turbidity and Numbers of Particles „ » « o o 68 Page 4 3 Generality of Assumed Kinetics „ „ , <> o o o » o o o 69 4 4 K Dependence on Mixing Intensity „ « « ° o o o o o o 73 4 U 5 K Dependence on Colloid Concentration „ o o o o o o 77 app 4 6 K Dependence on Settling Time c o o o o o o o o o 82 app M-o 7 K Dependence on Destabilization <, o o o o ■> o o 87 app 4 7 1 K Dependence on Destabilant Concentration „ „ 87 app 4 7 2 K Dependence on pH„ „ „ „ o „ o <, o <> « o 92 app 4 7 3 K Dependence on Type of Destabilant at P Q 104 4 8 Rapid Mixingo oooo'oooooooooooooooco 106 4„9 Optimum Dose and the Colloid Surface „ „ <, o o o o 113 4 10 Suspension Aging o o o « o o o « o o 118 4011 Qualitative Description of Aggregation by Polyelectrolytes <. o o <. - o o o o o 128 M- 12 Engineering Application o » o o o o o ° o 130 V o L-U1N LJjUbl L/1N Ooqooooooooooooqoooooooooo^-^O I\£j r .LjI\XjlN \^XJ O o CJ OOOOOOOO OOOOOO.OOOOOOOOOOOOO-L' - '*-' VJLl/io O O O O O O O o o-LHO VI LIST OF TABLES Table Page 1 TABULATION OF THE VARIOUS USAGES OF THE TERMS COAGULATION AND FLOCCULATION, . . „ , „ . 8 . . « . o 10 2 EXPERIMENTALLY DETERMINED PROPERTIES USED FOR QUANTIFYING DESTABILIZATION-AGGREGATION , . . , . . . . « . 12 3 FACTOR RELATING TOTAL SCATTERED LIGHT TO PARTICLE SIZE FOR EQUAL TOTAL MASS „ . . . „ „ « „ c a „ . . . « . a 47 M* COLLOIDAL MA 1LK1 ALo ooooooocooooooooooooo O-L D .rUL 1 III IjILi L- 1 i\vJJ-J I liliOo ooocooooooooocooofioooo Oo 6 K DEPENDENCE ON MIXING INTENSITY FOR LUDOX „ „ „ . . 76 app 7 K DEPENDENCE ON MIXING INTENSITY FOR MONTMORILLONITE e . „ 76 app 8 K DEPENDENCE ON COLLOID CONCENTRATION FOR MIN=U=SIL. . „ . 80 app 9 K DEPENDENCE ON COLLOID CONCENTRATION FOR LUDOX 00000 80 app 10 K DEPENDENCE ON DESTABILANT CONCENTRATION „ 00000000 92 app 11 K DEPENDENCE ON pH, MONTMORILLONITE-C7 0000000000 99 app 12 K DEPENDENCE ON pH. MONTMORILLONITE-PEIM . , . „ 99 app 13 K DEPENDENCE ON pH e MONTMORILLONITE-PL . . 99 app 14 OPTIMUM DOSE AS A FUNCTION OF SURFACE AREA CONCENTRATION „ 115 15 K AS A FUNCTION OF SUSPENSION AGE . M0NTM0RILL0NITE-A22 a 126 app 9 16 K AS A FUNCTION OF SUSPENSION AGE, MONTMORILLONITE-PAA , „ 127 app 8 17 K AS A FUNCTION OF SUSPENSION AGE 9 MONTMORILLONITE=PAC „ „ 127 app » Vll LIST OF FIGURES Figure Page 1 GROUPING OF THE VARIABLES AFFECTING AGGREGATION KINETICS. . . 4 2 AGGREGATION OF LATEX SUSPENSIONS 25 3 AGGREGATION OF DETROIT RIVER WATER WITH ALUM 27 4 GENERALIZED DEGREE OF AGGREGATION VERSUS POLYMER DOSE CURVE . 35 5 TOTAL PARTICLE CONCENTRATION VERSUS OPTICAL DENSITY 48 6 GENERALIZED RELATIONSHIP OF TURBIDITY-PARTICLE RADIUS FOR CONSTANT TOTAL MASS 49 7 SCALE DRAWING OF REACTION VESSEL 56 8 SCHEMATIC DRAWING OF APPARATUS 58 9 SUPERNATANT TURBIDITY VERSUS TIME FOR AGGREGATING LUDOX ... 64 10 SUPERNATANT TURBIDITY VERSUS TIME FOR AGGREGATING PSL .088. . 65 11 SUPERNATANT TURBIDITY VERSUS TIME FOR AGGREGATING PSL .557. . 66 12 SUPERNATANT TURBIDITY VERSUS TIME FOR AGGREGATING MIN-U-SIL . 67 13 COMPARISON OF AGGREGATION RATE DEPICTED BY TURBIDITY AND NUMBERS OF PARTICLES 70 14 AGGREGATION KINETICS FOR POLYELECTROLYTE , ALUM AND NaCl DESTABILIZATION 72 15 K DEPENDENCE ON MIXING INTENSITY FOR LUDOX 74 app 16 K DEPENDENCE ON MIXING INTENSITY FOR MONTMORILLONITE ... 75 app 17 K DEPENDENCE ON COLLOID CONCENTRATION FOR MIN-U-SIL. ... 78 app 18 K DEPENDENCE ON COLLOID CONCENTRATION FOR LUDOX 79 app 19 K AS A FUNCTION OF SETTLING TIME FOR PSL .796 84 app 20 K AS A FUNCTION OF SETTLING TIME FOR PSL .557 85 app 21 K AS A FUNCTION OF SETTLING TIME FOR PSL .088 86 app 22 K AS A FUNCTION OF DESTABILANT CONCENTRATION 88 app Vlll Figure Page 23 AGGREGATION OF MONTMORILLONITE WITH PURIFLOC C-31 pH 8„2o , . 89 24 AGGREGATION OF MONTMORILLONITE WITH PURIFLOC C-31 pH 7. „ „ „ 90 25 AGGREGATION OF MONTMORILLONITE WITH PURIFLOC C-31 pH 6, a „ .91 26 3-D SCHEMATIC DIAGRAM OF DEGREE-OF-AGGREGATION 9 REACTION TIME AND DESTABILANT CONCENTRATION . a . „ „ . . . . 93 27 K DEPENDENCE ON pH FOR MONTMORILLONITE-PURIFLOC C-31 . „ . 95 app F 28 AGGREGATION OF MONTMORILLONITE-PRIMAFLOC C-7„ a a „ „ „ . . 96 29 AGGREGATION OF MONTMORILLONITE~POLYETHYLENEIMINE„ . . „ . „ a 97 30 AGGREGATION OF MONTMORILLONITE-POLYLYSINE „ „ „ . • . , . „ o 98 31 TITRATION OF PURIFLOC C-31„ . . „ „ , . „ o « . » . . « <, 101 32 TITRATION OF PRIMAFLOC C~7 „ „ „ „ „ „ . „ „ a „ „ „ o 103 33 EFFECT OF RAPID MIX TIME ON AGGREGATION RATE, G = 47 sec"^ o 107 34 EFFECT OF RAPID MIX TIME ON AGGREGATION RATE t G = 18 sec'^'o 108 35 EFFECT OF RAPID MIX ON AGGREGATION RATE FOR ALUM„ a , . „ 110 36 OPTIMUM POLYETHYLENE IMINE CONCENTRATION VERSUS COLLOID SURFACE CONCENTRATION a „ „ „ „ „ „ a a a a „ a 114 37 OPTIMUM POLYETHYLENEIMINE DOSE AS A FUNCTION OF LUDOX SUSPENSION AGE a a a „ „ „ „ „ a a a a a „ 120 38 INITIAL SUSPENSION TURBIDITY AND K AS A FUNCTION OF LUDOX SUSPENSION AGE a o . . f P ? „ a a a „ a . o . . « . 122 39 AGGREGATION OF LUDOX FOR VARIOUS SUSPENSION AGES a „ a a a a 123 40 K AS A FUNCTION OF MONTMORILLONITE SUSPENSION app AGE FOR AGGREGATION WITH ANIONIC POLYMER. „ a , a „ a a a a a 125 41 DIFFERENTIAL SIZE DISTRIBUTION SPECTRA DURING AGGREGATION a 131 I, INTRODUCTION It is the purpose of this thesis to establish a rate equation for the aggregation of dilute colloidal suspensions under the influence of mild agitation and in addition 9 to show how physical and chemical variables affect the rate of aggregation Since the rate of aggregation is a function of an extremely large number of variables, many of which are interrelated in a complex fashion, an attempt is made to group the variables into a realistic framework which reduces this complex problem to a comprehensible and yet meaningful level The reason for undertaking this work was that there is no appropriate 8 sufficiently meaningful equation for aggregation kinetics Such an equation is needed for purposes of optimal design and operation of aggregation reactors, i e„, flocculatorsc Reactors of this type are employed as part of the treatment for over fifty percent of the water used for industrial and domestic purposes in this country (Durfor and Becker, 1964) Reactors have been designed by "the rule of thumb" without expressed consideration of aggregation kinetics In practice, attempts to optimize operation have been accomplished by trial and error c Conceivably, economies of design, construction and operation could be realized through the availability and application of a rate equation for aggregation The reason no appropriate rate equation has been offered to date is largely due to the extreme complexity of the phenomenon There are mathematical formulations which deal with special cases of only the physical aspects of the aggregation process c There are no known analytical solutions to these equations which approximate what is encountered in a water-treatment plant Furthermore, the equations do not treat the highly significant group of variables which are related to the chemical additives needed to achieve acceptable efficiencies of aggregation,, Finally, we do not have a practical and sufficiently flexible technique for collecting the data that the theoretical equa- tions (for which we have no analytical solutions) call for, i c e , par- tide number concentrations over the size range of 10 to 1 cm diameter In an effort to circumvent these problems and also to establish an equation, an empirical approach was taken „ The approach involves the use of supernatant turbidity to estimate the rate of aggregation,, Briefly, it has been established in this study that the rate of decrease of supernatant turbidity of destabilized, mildly agitated dilute col- loidal suspensions undergoing aggregation is reasonably approximated by second-order kinetics, with respect to supernatant turbidity „ This has been found to be true for a wide variety of types of systems The second-order rate constant for the decrease of turbidity during aggre- gation is interpreted as a measure of the relative or apparent rate of aggregation - the justification for assuming this is presented later,, By varying, one at a time, the variables which are thought to affect the rate of aggregation, it has been possible to determine their indi- vidual influence in terms of their effect upon the experimentally determined apparent second-order rate constant c Experimental design and interpretation of experimental results has been facilitated by a grouping of the variables which affect aggre- gation rate This grouping is based in part upon the theoretical equations of aggregation kinetics and in part upon our qualitative knowledge of the phenomenon of destabilization Since this grouping of variables is thought to enhance comprehension of the overall complex picture of destabilization-aggregation it will be presented at this point o In Figure 1 the differential form of the empirical equation of aggregation kinetics is presented along with a block diagram showing the variable groupings The rate of decrease of supernatant turbidity , -dT/dt, where T represents turbidity is assumed to reflect aggregation rate. K is then the apparent second=order rate constant, with units app of the reciprocal of both time and turbidity „ The block diagram shows the interrelationships of the variables affecting aggregation rate, as reflected in K The two major groups of independent variables are degree of destabilization, D, and particle collision opportunity, PC0 6 PCO is a grouping of two independent variables, particle transport, and particle concentration „ The latter is a grouping of two more independent variables, average particle concentration, N(0), and average particle radius, r(0) 9 initially or at time zeroc Particle transport is considered to be a function of the mean velocity gradient, G, which is an expression of mixing intensity The other two mechanisms of particle transport, Brownian diffusion, d , and diffusion (or rather transport) arising from the large size of particles, d , are neglected in this study They are discussed further in Section 2 2 The other major group of variables, D, is a function of the complex interactions among the destabilant s colloid surface and milieu c The cross lines are included to indicate the interdependencies among all three of them The two variables for each one of these three blocks are indicated as being independent of one another, e g c , the destabilant (or polymer) concentration and its physical and chemical properties can co to en w X E- U. c CD 55 M Cn O CD o CD M be varied independently of one another „ Hydrogen ion concentration, pH, is indicated as affecting the physical and chemical properties of both colloid surface and destabilant,, A dashed line has been drawn between destabilant concentration and colloid surface concentration to emphasize the fact that the optimum polymer (destabilant) concentration 9 P , is proportional to the colloid surface concentration „ Also it should be noted that while the destabilant and destabilant physical and chemical properties can be varied independently, the optimum destabilant concen- tration is related to the physical and chemical properties of the de- stabilant molecules as well as all the other four variables,. Recogni- tion of this fact is indicated by the grouping together of these two variables in the block titled destabilant The nine variables shown in the lower group of blocks of Figure 1 are thought to be the minimum number of variables necessary for specifying the conditions of an aggregation reaction „ In order to further specify and in turn understand the finer aspects of a particular reaction one needs to know all of the pertinent details (or further variables) of 4, 6, and 8, as well as the attendant interactions „ An additional fact conveyed by Figure 1 should be mentioned „ The two major groups of variables, D and PCO, are indicated as being independent variables This distinction is important and should be noted It arises because, for polyelectrolyte destabilants, the opti- mum dose, P , is proportional to colloid surface concentration (Black, Birkner and Morgan, 1965 )„ It is possible to adjust particle number concentration and particle radius and yet maintain the same colloid surface area concentration, thus theoretically not affecting D when all other variables remain constant Exceptions to the independence of D and PCO are considered later „ The discussion thus far should serve to illustrate the basic meaning of Figure 1 and to show how it should be interpreted „ It is obvious also from the discussion that the interactions among the group of variables comprising the degree of destabilization are complex indeed o When it is realized, for example, that there is a very large number of possible combinations of physical and chemical properties of the destabilant, the number of permutations upon this group of variables alone is seen to be extremely high The ideas conveyed by, and summarized in, Figure 1 are thought to be of considerable importance First of all it shows all of the essential variables and variable interactions affecting aggregation,, This is basic for achieving a clear understanding of an aggregation reaction This includes recognition of the fact that both destabiliza- tion and particle collision opportunity are essential (independent) contributions to aggregation,, An appropriate, clearly understandable terminology for describing the three aspects of the phenomenon of aggre- gation must allow for this overall distinction „ This clearly emphasizes the fact the terms coagulation and flocculation (for which there is a very serious semantic problem) are inadequate „ Secondly, the figure provides a ready reference for assessment of the possible ramifications of a particular variable and thus has utility in experimental design and interpretation For these reasons and purposes of clarity of pre- sentation Figure 1 will be referred to frequently hereafter and should be kept clearly in mindo II. LITERATURE REVIEW AND THEORY 2.1 Introduction The general subject of coagulation-flocculation (or as referred to in this thesis, destabilization-aggregation) is understood only in qualitative terms. The primary reasons for our lack of a complete under- standing of this phenomenon are felt to be (l) the diversity of the physical and chemical properties of the systems encountered in practice and worked with experimentally - and the accompanying difficulty of being able to explain a variety of experimental results with one theory, (2) an apparent preoccupation with the physiochemical aspects of the mechanism of destabilization to the exclusion of, or without regard to, the kinetics of aggregation, (3) the extreme confusion over terminology, and (4) the diverse experimentally-measured physical properties which have been used for quantifying, ad hoo t coagulation-flocculation. Terminology will be discussed first. This is followed by experimental quantification. The remainder of this chapter will deal with the three major topics of interest; namely, kinetics of aggrega- tion, destabilization, and turbidity, in that order. 2.1.1 Terminology Recently there has been shown an awareness of the long existing general confusion in our literature over the meaning of the terms coagulation" and flocculation* and efforts have been made to :: In the Random House Dictionary of the English Language , Random House, New York, 1966, a subtle distinction, if any, is made between the two terms, viz., Coagulate "to flocculate or cause to flocculate by adding an electrolyte." Flocculate "to form into flocculent masses . . . from aggregated or compound masses of particles." correct this by stipulating definitions (La Mer 1964, Robinson 1964, Hudson 1966, O'Melia 1966, Stumm 1966, O'Melia and Stumm 1967)„ This subject is so confusing that some basic concepts should be examined before attempting a discussion of meaningo What is going to be said borders on the trivial but it seems to be necessary if some degree of order is to be established First of all it should be recognized that in the overall process of coagulation-flocculation there is a cause-and-effect rela- tionship „ For reactions of the type which are encountered in water- treatment practice, destabilization and particle collision opportunity can be viewed as "causes " Aggregation of the destabilized t colliding particles is then an "effect „" Destabilization and (particle transport induced) particle collisions are independent variables Aggregation is thus the dependent variable „ In order for a conventional water- treatment plant to operate effectively both destabilization (accomplished by chemical addition) and particle collisions (accomplished primarily by mixing) must be provided Herein, destabilization is viewed as the physiochemical change which accompanies the addition of the chemical additives „ It is the action which allows particles to adhere , upon collision, with a tendency over and above that tendency in the absence of the additive Different types of mechanisms have been proposed for different types of systems to qualitatively explain how destabilization occurs In this thesis the concern is not primarily with the mechanism, but rather with the tend- ency to adhere when particle contact occurs „ Particle collisions, or rather particle collision opportuni- ties, occur as the result of relative particle transport „ This can be accomplished in a number of ways, as will be discussed below The overall collision opportunity is a function of particle transport, size, and concentration o Aggregation is the action of forming the destabilized par- ticles into larger particles or aggregates as a result of particle collisions „ Just how do these terms, as defined, relate to the past and present usage of the terms coagulation and flocculation? An attempt has been made to summarize this relationship in Table l c The first five authors listed have stated their definitions c The definitions attributed to the remainder of the authors were arrived at by deduction of usage from context „ Any misrepresentation is thus this author' s The table does indicate that there is no general agreement on the meaning of the two terms In fact if a clear understanding of just what various authors are saying is to be obtained the reader must go through rigorous mental gymnastics Re-definition here would only con- fuse the issue further „ Therefore, usage of the two ambiguous terms will be avoidedo The alternative terms, viz , destabilization 8 aggre- gation and particle collision opportunity, as defined, will be employed hereafter,, 2olo2 Experimental Quantification Degree of destabilization is a variable affecting the rate of aggregation, see Figure 1„ Aggregation is a rate process wherein the total number of individual particles is continuously being decreased as the aggregation reaction proceeds D The extent of aggregation at any point, ice , time, during the course of the reaction can be specified in Table 1 TABULATION OF THE VARIOUS USAGES OF THE TERMS COAGULATION AND FLOCCULATION* 10 Cause Effect Reference Destabilization + Particle Collision Aggregation Opportunity La Mer s 1964 Coagulation Flocculation Stumm, 1966 Coagulation Flocculation O'Melia, 1966 Coagulation Flocculation Robinson, 1964 Coagulation Flocculation Harris S Kaufman Coagulation Flocculation 1966 Overbeek, 1952 Coagulation Flocculation Fair & Gemmell Coagulation 1964 Black , 1960 Coagulation Black j Birkner, & Coagulation Morgan, 1965 Flocculation Birkner & Morgan Coagulation In Press Flocculation Langelier & Ludwig Coagulation 1949 Flocculation { See body for definitions of terms in headings, 11 one of several ways For example, if N is the number concentration of particles initially, (0), and at reaction time, (t), the extent or degree of aggregation can be specified as ; *. , or as 1° y , y If N(0) is negligible, or if N(t) values are used for comparative purposes, the degree of aggregation can be specified simply as N(t) or H < ■, Destabilization or degree of destabilization is a variable of aggregation rate and is more difficult to specify because, in a practical sense, there is no reference point „ If there were an appropriate theory and one could measure N, as well as all of the other variables (particle radius and particle transport), the degree of destabilization might be deduced in one of two ways It could be inferred as the ratio of the theoretical rate constant to the experimental rate constant, thus assuming values <^ 1„ Also if we add chemicals to induce aggregation, destabilization could be inferred as the difference in aggregation rate with and without the destabilant chemical The number concentration of particles is difficult to measure „ For this reason other t more conveniently determined physical properties have been used for estimating the degree of aggregation and/or destabi- lization o Some of these experimentally measured properties are listed in Table 2 There is generally a problem in deciding just what a par- ticular author has inferred from what he has measured First of all the author does not tell the reader explicitly what Is being inferred from a measured quantity and secondly there is the problem of confusion over terminology o For example „ an author tells the reader he is study- ing "coagulation," but does not define the term He measures superna- tant turbidity and plots experimental values of turbidity as a function of, say, destabilant concentration and the plotted curve goes through 12 O Q) lo m ID CD >> in CD a> CD LO CD rd bO J3 O LO P rO C w co o o O C cd o CD CD ^<1 (D s C M a> -H o rr: ^l x: « CD us CO o H u m CD o -H ■H < CD co uD CD +i P O Mh H a!) 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CD to Pi p H CO rH CO E-h H Pi o CD w T3 CO rd co rd co cd co <-i Eh ■H Pi CD c-i CD U CD ^ ^ U o O w CD H CD O CD O CD O CD CD CD •H k" •H Q -H »H a o a o c o P P P to s •P Pm o •H Pi •H u •rl P-, cd rd cd cd cd Pa >- CO S PL, S P-, S P-, & 3: & PQ ^ o CD p o M P CD •^ p Pi »H c P CO !4-» H >! H o G O to Ph p »H °H rd >, Q to Pi X •H p bO >, P XJ p p P "JC r H CD H •4-* C >, C P C rd cd O rd »H 6 CM 4h c CD P »rl -H CD fc H > O C T5 3 ^^^ *i* CM CD (0 S °-H H O e cd C/3 C^ > o o CO E-« o Q !z:l s *f* 13 an optimum,, The optimum is then referred to as the optimum "coagula- tion" and is used to deduce something about the mechanism of "coagula- tion " Is this the optimum degree of destabilization or aggregation? Since destabilization (an independent variable) affects the rate of aggregation (the dependent variable) the two are obviously related, but technically speaking they are not the same thing Assuming that all other variables - for example, time and intensity of mixing and particle concentration - are held constant, it seems permissible to infer desta- bilization from aggregation,, However r to avoid confusion it seems that the inference should be explicitly stated The different experimental quantities listed in Table 2 emphasize different physical properties of the supernatant, sediment or aggregate These different measures have varying sensitivity and have been found to be useful at quite different particle concentrations „ This fact has led to ambiguity in correlating experimental results from the various quantifiers As indicated previously, the ideal measure of the degree of aggregation is particle number concentration or more precisely particle number concentration and size There are two common ways of arriving at particle size and concentration - by microscopic observation and by the electronic particle counter, e go, Coulter counter,, Microscopic observation for studies of aggregation kinetics has been accomplished by visible light (Gillespie 1960, Kudryavtsea and Deryagin 1963) and by electron microscopy (Turkevich^ 1959) „ This technique is rather time- consuming and has been applied only to the initial stages of Brownian motion -induced aggregation,, It is quite impractical for application to systems of interest in water-treatment practice „ 14 The electronic particle counter has been utilized by Higuchi et ale (1963), Swift and Friedlander (1964), and Birkner and Morgan (In Press K This technique is less cumbersome but the equipment is ex- pensive and there are limitations „ The principle of the instrument is that a non-conductive particle suspended in an electrical conductive medium 9 when flowing through a small orifice, causes a change in the conductivity across the orifice. The change in conductivity is propor= tional to the cross-sectional area of the particle 9 perpendicular to its flow path, and can be observed by a current pulse Thus 9 in prin- ciple one can determine the particle size distribution for a unit volume of liquid by counting the pulses and observing their height „ The limitations are the particle diameter range which can be counted, 1 to 1000 microns, and the uncertainty of further particle aggregation or breakup in sample preparation and counting Aggregation is possible since salt must be added to bring the solution conductivity up to a level equivalent to 10,000 rng/1 NaCl Breakup is possible due to shear 9 as the particles flow through the orifice This may tend to offset the salt aggregation effect 9 however „ The magnitude of these effects may be specific for individual systems Birkner and Morgan (In Press) stated that neither effect appeared to be significant for the system they worked with This technique has not been employed in this study because of the non-applicability of this technique to particle diameters of less than 1 micron, the necessity to evaluate the magnitude of the aggrega- tion and breakup effects for every system, and the desire to obtain a practically useful, rapid, and inexpensive technique for estimating aggregation kinetics 15 Herein, aggregation rate was estimated by rate of change of supernatant turbidity*, The degree of destabilization and particle collision opportunity were arrived at through their respective effects on the rate of aggregation The theory and the limitations with regard to the interpretation of the meaning of turbidity will be discussed in Section 2 4 The justification of using turbidity to estimate aggrega- tion rate is reserved for Section U c 2 2 Aggregation Kinetics In this section the rate of decrease in the number concentra= tion of particles in an aggregating system is consideredc There are basic mathematical formulations which have been proposed for describing this process c. There are analytical solutions to the basic formulations for relatively simple cases and experimental results which tend to assert the validity of the basic equations. For the more complex sys= terns g e^go, a water=treatment plant , no appropriate analytical solutions exist c A number of features of aggregating systems of practical interest make the required theoretical developments a formidable task. In the heading of Table 1 the statement f which is here reversed for convenience; Aggregation -«— Particle Collision + Destabilization Opportunity was presentedc This is analogous to the functional equation -dN/dt = f(P t ,N,r,D) (1) 16 where ~dN/dt is the rate of decrease of particle number concentration, P refers to particle transport, N is particle number concentration, r is particle radius and D refers to destabilization which from a practical viewpoint is related to the chemical additive and the interactions be- tween it, the milieu and the colloid surface Particle collision oppor- tunity is thus a function of P 9 N 8 and r Particle transport actually refers to the movement of particles relative to one another This is of interest since it promotes inter- particle collisions „ There, are a variety of ways by which differential particle movement can occur „ They are (1) Brownian motion, (2) fluid motion by (a) a laminar shear field and (b) a turbulent shear field, and (3) additional ways which become significant when large particles are present^ e g u , impaction? Aggregation induced by the first two causes has been shown to be additive (Swift and Friedlander 9 1964) Assuming that the last term is also additive, this can be expressed (dN/dt). . . = (dN/dt).. + (dN/dt)_, + (dN/dt) T (2) total Br Shear Large There are aggregation theories incorporating collision induce- ment by Brownian motion e laminar shear, and isotropic turbulence but not for the large particle effects „ The latter will be discussed below in connection with the complexities of systems of practical interest 2 2ol Perikinetic Aggregation Due to the random movement or Brownian motion of small sus- pended particles, random collision or near approaches of the particles occur Aggregation resulting from this phenomenon has been called 17 "perikinetic coagulation" and was first described by Smulochowski (1916) He derived an expression for the collision frequency 8 J, of particles with a mutual collision radius of R. . present at concentration n. and n. i] i 3 with a mutual Brownian motion or diffusion coefficient d„ , which can be written J . = 47Td. .R. .n.n. (3) 13 13 13 1 3 If it is assumed that all collisions result in aggregation, i o e , the suspension is completely destabilized and thus D = 1, Equation 1, and that the particles are of equal size, an apparently reasonable solution for the rate of change of the total number of particles has been shown" to be dN/dt = ~KN 2 (4) where K s the theoretical rate constant, is equal to 87rd 1 R In the parlance of chemical kinetics 8 the perikinetic aggregation rate is second-order with respect to particle concentration „ Numerous workers (Hiemenz and Void 1965, Higuchi et al 1963, Swift and Friedlander 1964, Turkevich 1959) have obtained experimental results which tend to verify Equation 4 for non-stirred suspensions „ Most, however, have found the experimental rate constant to be some fraction of the theoretical rate constant This discrepancy has gener- ally been attributed to the possibility of the suspension retaining some degree of stability,, *This derivation appears in numerous places, e go, Overbeek 1952, and will not be shown here 18 Goodeve (1939) reasoned that breakup may accompany aggrega- tion a He proposed that second-order aggregation is accompanied by first- order breakup „ Gillespie (1960) adopted this idea and obtained results which tended to support this simple kinetic picture Also Hiemenz and Void (1965) obtained results by optical density measurements which sup- ported thiso Since the magnitude of Brownian motion decreases as the particle radii increase, the rate of aggregation by this mechanism decreases as the particle size increases Order-of-magnitude calcula- tions (Harris and Kaufman 1966, Levich 1962, Overbeek 1952) indicate that in a mildly mixed suspension perikinetic aggregation becomes negligible - relative to aggregation due to shear , Equation 2 = for particle radii greater than about one micron From a practical view- point we are interested in producing "settleable" particles which have radii approaching millimeter size Thus, the perikinetic contribution to aggregation in water-treatment reactors can be neglected without serious error 2 2o2 Orthokinetic Aggregation In a stirred fluid , velocity gradients exist This relative movement of adjacent layers within the fluid gives rise to the collision of small particles contained therein Aggregation resulting from colli- sions induced in this fashion (or as the result of any systematic particle movement such as differential settling velocity of different size particles) has been termed "orthokinetic coagulation 6 " apparently by Wiegner (see Overbeek 1952, p 291) „ Smoluchowski (1917) derived an equation which accounts for the collision frequency for systematic 19 particle movement resulting from laminar shear. He assumed that there was no particle effect on flow. His expression, analogous to Equation 3, can be written J.. = (4/3)(du/dz)(r.+r.) 3 n.n. (5) where J is the number of particle collisions (per unit time and volume) between n. and n. particles (per unit volume) of size r. and r., and du/dz is the local laminar velocity gradient. Equation 5 as written predicts the collision frequency for two sizes of particles. With the assumption that all collisions result in aggregation, the simplest solution to this equation is for the case of initially uniform size particles and thus applies to the initial stages of aggregation of an initially monodispersed suspension, since polydispersity - many different sizes of particles - soon appears as aggregates develop. The rate expression in total particle numbers, N , for this case is dN /dt = - iili N (6) t TT t where G, the mean velocity gradient is taken as representative of du/dz, and , the solids volume fraction, is the volume of particles per unit volume of suspension. The orthokinetic aggregation rate is thus said to be first order with respect to particle number concentration. The more general case, however, is for the rate of change of k-fold particles which result from the collision of an i-fold and j-fold particle. Here the rate of formation of k-fold (i+j=k) minus the rate 20 of disappearance of k-fold particles due to collisions with other par- ticles must be considered. Thus dn k 1 r 4 tv ^ du V 4 fa \ 3 du ,_. ■tt— = tt ) -s- n.n.(R. .) -3 ) rs-n.n.CR.,) -3— (7) dt 2 . *•„ 3 l i in dz . L n 3 l k lk dz 1=0 J J i=0 j=k-i An analytical solution for this non-linear partial integro-differential equation is not known, however. Swift and Friedlander (1964) obtained a particular solution to this equation by introducing a simplification pertaining to particle size distribution. Their expression written in terms of the total number of particles is 3 1/3 2 dN t /dt = -(j-i) £ GN t A (8) where A expresses the effect due to particle size polydispersity. They predicted that the effect of increasing polydispersity of the initial suspension was to increase the rate of aggregation. Harris, Kaufman and Krone (1966) also obtained a particular solution to Equation 7 by introducing a size distribution term, which also must be determined experimentally. Their equation can be written 3 Ctrl dN/dt = - — - G<{>ND (9) where a is collision efficiency, a is the ratio of particle collision radius to its physical radius, and D relates to the particle size 21 distribution effect „ They, however, predicted that the Initial degree of dispersity does not affect the rate of aggregation Typically in the mixing of water with turbine paddles the internal flow is turbulent rather than laminar „ For example , in a typical "jar test" the Reynolds number , N , is approximately 5000 The N_ defining the upper limit for laminar flow for mechanical mixing is 10 to 20 (Sterbacek and Tausk 8 1965 ) c Reynolds number can be calculated 2 „ from the expression N R = nD /v where n is impeller speed, D is impeller diameter, and v is kinematic viscosity For a typical "jar test" 2 n = 50 rpm, D = 3 in and v = o 01 cm /sec, thus N - 5000 Thus the Smoluchowski equation for laminar flow- induced aggregation may not strictly apply „ Birkner and Morgan (In Press) broached this subject by intro- ducing an equation of Saffman and Turner (1956) for the collision fre- quency of particles under the influence of isotropic turbulence 9 e 1/2 3 u\. = 1 30 («) (r ± + r.) ni n. (10) where e is the energy dissipation per unit mass per unit time For this to apply it is assumed that the colliding particles are contained within the turbulent eddies and that r./r. = 1 to 2„ Following Camp and Stein e 1/2 (1943) 9 they assumed that G = (-0 This leads to the conclusion that the only difference in laminar and isotropic turbulence- induced aggrega- tion s at the same G, is a small difference in rate, i o e , (dN/dt) T = o 98 (dN/dt) , from equations 10 and 6 Li Recently, Argaman and Kaufman (1967) have given a preliminary report of a proposed equation for turbulent- flow induced aggregation 22 that appears to be more realistic because it may allow for a more appro- priate estimate of particle contact opportunity This is a new approach to the problem wherein the mutual diffusivity 8 d.., of N. and N. par- ticles per unit volume , of size R. and R, is considered as leading to particle collisions Mutual diffusivity is said to be a function of the spectrum of turbulence and particle size They suggest that the colli- sion rate Jo. is given by J. . = 4ttN.N.(R + R.)d. . (11) id 131 : 13 and that d can be estimated from the time variations of velocity fluc- tuations as measured by hot-wire anemometer and particle size* An alternative approach to identifying the manageable controls for aggregation as predicted by Equation 7 is to obtain numerical solu- tions by appropriate mathematical simulation applied to a digital com- puter 9 thus circumventing the problem of obtaining an analytical solution to the equation c Fair and Gemmell (1964) used this approach, and at= tempted to simulate reality by imposing an upper limit on aggregate size and a breakup routine for oversized aggregates The breakup rou- tine and the details of the reasons for it in real systems are unknown , so they imposed several different alternatives „ Their conclusions are of interest in that they depict the orthoklnetic aggregation process as being quite similar to the one found empirically in this study, even though the similarity is probably fortuitous Namely, they concluded that the process is reasonably approximated by second-order kinetics This is in contrast to the predicted results of first-order kinetics as shown in all the orthokinetic equation solutions above 23 2o2 3 Experimental Results for Orthokinetic Aggregation Two reports have appeared in the literature for orthokinetic aggregation of initially monodispersed rigid spheres where particle concentration was measured directly by electronic particle counter,, The agreement with theory is mixed Swift and Friedlander (1964) obtained results for Q<,871 y p diameter monodispersed polystyrene latex spheres for N(0) = 2(10) 3 particles/cm destabilized with 6% NaCl (l o 03 M) for laminar shearing over the range of G = 1 to 80 sec „ Their results for the initial rate of aggregation were in excellent agreement with theory , i e„, Equation 6 Specifically, they found; (1) the overall rate from Brownian and laminar shear contributions are additive , (2) dN/dt is first-order with respect to N, (3) the experimental rate constant, i„e s slope of log N vs time plot, was a linear function of G as predicted by theory (thus indicating that no breakup was apparent due to increas- ing G), (4) the experimental rate constant was 37„5% of the theoretical rate constant, 4G/ir, which was exactly the same result they obtained for Brownian aggregation, i e , K = 37„5% (4kT/3)„ °° ° exp More recently Birkner and Morgan (In Press) have studied essentially the same system as Swift and Friedlander They provided shear with a rotating paddle rather than the couette apparatus as used above o They interpreted their results in terms of Equation 10 „ 8 3 For 1 M NaCl destabilant, 1.8(10) particles/cm , 1,3 y diameter monodispersed polystyrene latex spheres, and shear rates (pos= sibly turbulent) of G = 11 to 120 sec' , they found in contrast to Swift and Friedlander that the experimental rate constant was not a linear function of G, but decreased with increasing G This indicated that 24 breakup, or a decreased rate of aggregation, occurred when the shear rate, G, was increased,, This is in contrast to the results of Swift and Friedlander for a similar system Birkner and Morgan also obtained results for polystyrene latex and a different destabilant chemical For a polymeric destabi- lant, polyethyleneimine ? they found the same trend as in the case of 1 M NaCl 9 but the decrease of the experimental rate constant with in-, creasing G was more pronounced They concluded from their experimental data for initial aggregation that the process can be represented by a first-order rate equation of the form of Equation 6„ In Figure 2 their published data are plotted in a form representative of both a first-order (Fig 2A) as well as a second-order (Fig„ 2B) rate process This suggests 8 as per the "rules" of chemical kinetics t that the agreement of data, for a limited range, with the form predicted by theory is not a sufficiently severe criterion for testing the validity of the theory Thus g conclu- sions cannot be drawn about the validity of Equation 10 for isotropic- shear induced aggregation „ The only experimental results for initially polydispersed suspensions where particle concentration was determined were for emul- sions o The processes of aggregating rigid spheres and emulsions are similar in that they both involve particle collisions but the latter also involved coalescence Coalescence involves breaking of the film at the point of contact for two particles and the formation of a single droplet o Particle collision rate is normally assumed to be the rate limiting step (Swift and Friedlander g 1964) Thus the only conceptual difference in the aggregation of rigid spheres and emulsions is in the 25 •0.1 b0 O ■0.3 - G = 120 sec" D G = 47 sec -1 Fig. 2A First-Order Kinetics Assumed 4 6 REACTION TIME (min) C 10 o 1.0 1 1 1 1 0.8 - - 0.6 0.4 Fig. 1 2B Second-Order Kinetics Assumed 1 1 1 U 6 REACTION TIME (min) 10 FIGURE 2. AGGREGATION OF LATEX SUSPENSIONS 2.1(10) particles/ml, 420 \ig/l polyethyleneimine Data after Birkner and Morgan (In Press) 26 packing efficiency of the aggregates f i e , a volumetric effect „ Also the aggregates probably differ in their response to shear e i e u 9 breakup „ Thus the comparability of conclusions from experimental results for the two different types of systems is uncertain The results are presented here because they were the only ones available for initially polydis- persed suspensions „ Swift and Friedlander (1964) studied the aggregation of poly= dispersed oil-in-water emulsions for laminar shear rates of G = o 25 to 8 sec o They concluded that their "self preservation" hypothesis ade= quately described the particle size distribution throughout the course of aggregation but that a kinetic law such as predicted by Equation 5 cannot describe aggregation over the range of shear studiedc The aggre- gation rate appeared to be greater than first order for low shear rates and increased to second order for the higher shear rates „ Two attempts have been made to verify or interpret experimental results in terms of first-border aggregation equations (incorporating particle numbers) using supernatant turbidity (Harris 9 Kaufman and Krone 1966 $ and Hudson 1965 ) The relationship of turbidity to particle con= centration for the particle size range of interest is only qualitatively known o Furthermore 9 the rate of change of turbidity (dT/dt) as a func= tion of reaction timej, t 9 or the dimensionless parameter 9 Gt 9 appears to be approximated better by second=order kinetics (with respect to tur- bidity) than by first=order kinetics 9 as shown for the results of Hudson in Figure 3 The reasons for this apparent second=order kinetics are not known Q Thus the verification of a theoretical equation in particle numbers with such data does not seem justified,, 27 Gt x 10" 3 12 Ol+J 30 24 20 16 12 — r H~ -- ^— . -i — • / /• \ Alum Cone. \ (mg/£) V O 6 \ • 15 \ • \ \ V • /• o — Jl — — -£-~~~ ' o ^v-2-— 1 Fig. 3B. 1 Assuming Second-Order Kinetics 12 16 20 Gt x 10 FIGURE 3. AGGREGATION OF DETROIT RIVER WATER WITH ALUM Data after Hudson (1965) 28 2o2 n 4 Features of Systems of Practical Interest There are a number of features of aggregating systems of practical interest which may make the theoretical development of an appropriate equation a formidable task An attempt will be made to generalize these features here One of the more obvious problems is the non-uniform distribu- tion of velocity gradients „ This arises because of the variation in the velocity of paddle elements at different distances out from a ro- tating shaft, and the commonly low ratio of fluid volume traversed by the moving paddle to the total volume of suspension,, Qualitatively it can be suggested that this non=uniformity may lead to low collision rates and thus low aggregation rates in the areas of low shear and a proportionate increase in one along with the other up to some point of higher shear where breakup becomes significant c Variations in paddle design may alter the magnitude of this effect o From the practical viewpoint we do not know at present If this non=uniformity effect is beneficial or not or if there is an optimum Also this effect is undoubtedly a function of aggregate strength as well as concentration and as such varies from system to system,, It is un= doubtedly a problem in correlating the results from various laboratories or water- treatment plants because G, as we presently estimate it 8 is not an adequate representation for the overall process Aggregate breakup in itself is a serious problem from a theoretical point of view There is no theory nor theoretical basis for predicting this Breakup is not only a function of localized shear g particle concentration and particle size but also the aggregate strength which in turn is related to colloid-destabilant-milieu interactions „ As 29 such the details of this problem are probably not solvable theoretically , and must be treated empirically,, Another serious theoretical problem which authors have already attempted to treat is that of particle size polydispersity e The treat- ment of this problem by Swift and Friedlander (1964) has not been veri- fied for the case of orthokinetic aggregation The matter of particle size or size distribution is indeed important in view of the fact that the rate of aggregation is dependent on particle radius to the third power o One aspect of the particle size distribution may prove to be a significant theoretical hurdle in itself, namely the existence of aggregates of millimeter size In terms of the total number of particles, the number of millimeter size aggregates is trivial, eogo, the total num= 4 10 ber of particles is of the order of 10 /ml to 10 /ml whereas the number of millimeter size aggregates is l/ml c From the standpoint of sedimenta- tion, it is only the collisions involving the larger particles, ioe , the settleable particles, which are fruitful In Equation 2 a contribu- tion to overall aggregation was designated as (dN/dt). This term && & & Large includes some effects arising from aggregates of larger mass (or size and density) that Levich (1962) has treated briefly These are effects which would tend to increase particle collisions and thus dN/dt j namely, inertial and diffusional impaction, acceleration, and wake precipitation,, 2o2 5 Conclusions It would be ideal to have a theoretically derived, experi- mentally verified equation that applies to aggregation kinetics in a water-treatment plant „ The foregoing review indicates that theoretical 30 developments fall far short of achieving that idealo There is the basic Smoluchowski formulation for laminar- shear- flow induced aggregation but no known analytical solution for the general case„ There is a solution for the special case of the initial rate of aggregation of initially monodispersed suspension, Equation 6 C . There is also a solution based upon a simplification pertaining to particle size distribution , Equa- tion 8 s and experimental results which tend to verify it for the special case of initially monodispersed suspensions Moving closer to the conditions in a water-treatment plant there is an equation, 10, for the special case of the initial rate of aggregation of initially monodispersed suspensions induced by isotropic turbulence o For this case the experimental results are inconclusive „ Moving still closer there is a proposed equation, 11, for (general) turbulent-flow- induced aggregation but no published experimental re- sults to date„ The solutions to the above equations predict first-order kinetics in particle numbers „ The experimental results indicate 8 in one case, first-order kinetics and in two other cases both first- and second- order kinetics o A digital computer solution to the Smoluchowski equa- tion indicates that second-order kinetics is the better approximation In a water-treatment plant there is non-uniform turbulent shear flow and, since it is a continuous flow system, particles ranging in size from 10 to 10 cm Thus the gap between the theoretical developments and what is of practical interest is considerable „ 2 3 Destabilization In Section 2 old it was proposed that the degree of destabili- zation can be viewed as the change which accompanies the addition of the 31 destabilant and manifests itself as the tendency of particles to aggre- gate when particle contact occurs, and is measurable by its effect on the rate of aggregation „ This viewpoint is plausible if the physio- chemical change occurs within a short time after addition of the desta- bilant and the aggregation which follows is only a function of time and intensity of mixing and the initial colloid concentration „ In this section how and why this change occurs , i e , the mechanism of destabil- ization, is discussedc The bulk of the literature on the general subject of "coagula- tion-flocculation" has dealt with the mechanisms of destabilization, i„e„, the interactions occurring within the destabilization group of blocks in Figure l r This literature deals with the qualitative elucidation of the interactions between the destabilant, colloid and solute molecules and the relative importance of such physical concepts as reduction of the repulsive potential of the electrical double layer and immeshment into a three-dimensional network as the result of bridging by polymers „ The majority of this material deals with the action of Fe(III) and Al(III) and their hydrolyzed and polymeric forms Here we are concerned with destabilization by organic macromolecules, principally those with ionizable groups on the side chains, i e , polyelectrolytes The general feeling seems to be that there is a spectrum of ways of accomplishing destabilization that grades between two (concep- tually) character! zable "types" of mechanisms „ One "type" is typified by the action of non-hydrolyzing salts, e.g., CaCl„ or NaCl, on hydro- phobic colloids such as gold sols where there is a decrease in suspension stability with increasing salt concentration that is accompanied by a decrease in electrostatic repulsion as indicated by a decrease in 32 electrokinetic potential. This "type" of mechanism of destabilization has been referred to as "coagulation" (La Mer 1964, Stumm 1966). The other "type" is referred to as "flocculation" (La Mer 1964, Stumm 1966). It is characterized by the action of organic polyelectro- lytes, presumably anionic, on a colloid whereby the polymer bridges between discrete particles uniting or immeshing them into a random, three-dimensional network. Generally, no specific mention of potential reduction is made for this case. The gradations arise because, for some systems, features applying to both of these "types" of mechanisms appear. For example, Black, Birkner and Morgan (1965) worked with a positive or cationic polyelectrolyte and montmorillonite , a negatively charged colloid. They estimated the degree of destabilization by the reduction of supernatant turbidity. They noted that the clay-polymer complex exhibited a de- creasing negative potential down to zero and thence increasing positive potential with increasing polymer dose. The electrokinetic potential versus polymer dose curve was similar to the destabilization versus polymer dose curve with the optimum destabilization occurring at a slightly negative potential. That is, in accomplishing destabilization in this case, both bridging by polymers (a feature of one "type") and potential reduction (a feature of the other "type") occurred. Thus they explained the destabilization as being assomplished by "coagulation- flocculation." O'Melia and Stumm (1967) have indicated that while the idea of these two "types" as mechanisms of destabilization may be useful for conceptual and descriptive purposes there are practical limitations to the idea. They used the term "coagulation" to apply to any case where 33 "particle aggregation was observed" since with the iron(III)-silica system, over a wide range of concentrations and pH values it was impos- sible to determine if destabilization was due to potential reduction or immeshment in a three-dimensional network „ That is s it was impossible to determine just what percentage of either "type" of mechanism was responsible for destabilization at any point In the system diagram Thus 8 no concerted effort will be made to invoke potential reduction to explain the mechanism of destabilization Rather, an attempt is made to qualitatively explain the role of chemical features as they affect destabilization by polymers „ In general the process of destabilization by polyelectrolytes involves (1) initial adsorption of polymer to the colloid which occurs at a relatively rapid rate, and (2) the formation of bridges between colliding particles as the result of polymer molecules having segments attached to two or more colloidal particles „ Thus adsorption and what affects it is of interest „ Also the factors which affect the ability of an adsorbed molecule to bridge when particle collisions occur is of interest o To begin with, let us consider the broader aspect of the overall phenomenon, namely the polymer=bridging model 2 3 1 Polymer-Bridging Model The polymer-bridging model was first proposed by Ruehrwein and Ward (1952), later given a mathematical treatment by La Mer and cc= workers (1963), and more recently was succinctly stated by Black, Birkner and Morgan (1965) According to this model, flexible polymer molecules adsorb onto a colloid surface with one or more of their segments being attached 34 while the remainder extend into the bulk phase as pendant loops or free endSo When extended segments adsorb onto another particle t a bridge is formed o Intensification of bridging may lead to the formation of packets of particles whose size is limited by the shear gradient and the inten- sity of adsorbed polymer When the intensity of adsorbed polymer is low j particle incorporation into packets is also low Likewise when the intensity of adsorbed polymer is high, available adsorption sites for bridging segments are limited in number and packet building is limited, i^e^, restabilization occurs « At some point between these two extremes 9 polymer adsorption is optimal and packet formation is like- wise o This model allows for an explanation of a typical degree-of- aggregation-versus-polymer-dose curve as generalized in Figure 4 2o3 2 Extended Segments Fundamental to this model is the extension of segments into the bulk phase o Numerous theoreticians (Bluestone and Cronan 1966 , Hoeve 1965 s Roe 1965 , Rubin 1965 , and Silbenberg 1962) taking dissimilar approaches for predicting the configuration of an isolated, unionized polymer adsorbed at a planar surface have generally provided qualita- tive support for the existence of extended segments All of these works are based on statistical-mechanical models for which a partition function was formulated and the polymer structure was calculated from a minimization of polymer free energy The diffi- culty has been that model simplifications were necessarily extreme in order to permit calculations „ The different assumptions employed by the different authors have led to vastly different results, e ge, every- thing ranging from a tightly bound two-dimensional polymer layer to a 35 C o •H ■P cti bO Q) bO bO < O (U bO Q) Q Low Polymer Adsorption to Colloid Optimum High Polymer Dose FIGURE 4. GENERALIZED DEGREE OF AGGREGATION VERSUS POLYMER DOSE CURVE 36 to a polymer with long free-ends c These results generally predict, however, polymer behavior which corresponds qualitatively to essentially all the observed facts concerning adsorption (Silbenberg, 1962) u Roe (1965) was able to show that conformation may be classed into three categories , depending upon what might be loosely interpreted as "affinity o" For a high "affinity" the polymer lies flat on the surface* This is the picture that many of the models predict, e g , Silbenberg (1962) „ For the intermediate "affinity" fewer of the polymer segments are adsorbed and most of the desorbed segments are free-ends rather than internal or pendant loops „ For the lower "affinity" fewer segments are adsorbed and there is negligible probability of loop forma- tion,, Thus, essentially all of the desorbed segments are in the free- ends „ As mentioned, all of these theoretical predictions are for an isolated, unionized polymer c When polymer adsorption intensity in- creases , interference effects should tend to increase the number of extended segments Also, since the ionization of polyelectrolytes tends to produce a restricted configuration in solution, this should tend to alter the extension of segments from that predicted for an unionized polymer In addition to this theoretical support for the assumption that segments may extend into the bulk solution there is considerable experimental evidence cited for a variety of systems that substantiate this (Black et al 1965, La Mer and Healy 1963a), 2o3 3 Adsorption Isotherms Experimentally it has been found that polymer adsorption 37 fits a Langmuir- type equation. = be (12) where 9 is the fraction of adsorption sites occupied 9 c is the equilib- rium polymer concentration and b is a constant „ No theoretical work had directly predicted this Generally it is reasoned that the experimental data are for a narrow region of surface coverage which approaches surface saturation and the theoretical equations reduce to the Langmuir form at higher surface coverage For example Silbenberg (1962) predicts an isotherm which agrees in form with that of Simha 8 Frisch and Eirich (1953) The SFE isotherm is presented below in a form analogous to the Langmuir equation -JL- y = b « c ( 13 ) (i-e) 1 where £ represents the number of attached segments For 8 equal to unity this equation reduces to the Langmuir equation Near surface saturation 8 where there is considerable segment interference % the Langmuir form is thought to be approached c Thus there is an essentially empirical equation that describes experimental data but no physical significance can be assigned to b % which in the original derivation represented a ratio of adsorption- desorption rate constants La Mer and Healy (1963a) have rationalized that b represents a summation of rate constants for several adsorption-desorption reac= tionSo They felt that for the, present stage of theory development it 38 could loosely be interpreted as suchc 2o3 4 Adsorption Kinetics There is a paucity of information on the kinetics of adsorp- tion of polymers onto colloids c The accepted hypothesis seems to be that the rate of adsorption is considerably faster than the rate of aggregation and therefore is not the rate limiting process (Birkner and Morgan In Press 9 and Black et al 1965 )„ Black, Birkner and Morgan (1965) concluded , from adsorption studies on a system consisting of polydiallyldimethylamonium and kao- linite, that near the optimum dose adsorption is 85% complete in 30 sec- onds o An additional 10% adsorbed after 30 min of continued agitation They also concluded that the rate and equilibrium amount of adsorption were not affected by the intensity of agitation 9 within the limits studied,, To the contrary Healy (1961) concluded equilibrium adsorption intensity was dependent on agitation intensity for his systerru Jankovics (1957 r 1965) working with yet a different system found that the rate of adsorption was a function of agitation intensity but that the equilibrium adsorption intensity was independent of agita- tion intensity o The adsorption rate and intensity and the effect of agitation intensity thereon probably varies from system to system and is dependent on such factors as polymer affinity for colloid surface, and the effect of milieu on this affinity as well as the configuration of the polymer molecule o At any rate it would appear that the details of these three factors are specific for a particular system and cannot be generalized 39 or predicted a priori,, 2 3„5 Milieu Effects The existence of ionizable groups on the side chains of polymers has numerous ramifications with regard to adsorption and destabilization Ionization of the side chains is the result of inter= actions with the milieu Milieu also interacts with a colloid surface Because of this double interactions, interpretation of experimental results for a polyelectrolyte=milieu-colloid system is difficult 8 e go 8 see Figure 1 There are additional problems concerning our present knowl- edge for milieu effects Mathematical theories are not available which treat all aspects of the subject Numerous variables are involved,, Materials s which are well characterized physically and chemically 8 are not available „ It is even difficult to obtain samples of materials with "constant" physical and chemical properties „ The physical and chemical properties of polyelectrolytes which may be used in water- treatment practice are closely guarded secrets which are kept by their purveyors a Finally 8 there is a paucity of experimental results for polyelectrolytes o Thus g what we do know about milieu effects on adsorption-destabilization is most qualitative indeed Milieu Effects on Adsorption Very few experimental studies have been made on the effects of pH and ionic strength 8 I 8 on polymer adsorption even though the importance of these variables has been emphasized (La Mer and Healy 1963a) 40 in general s it appears that an increase in ionic strength increases polymer adsorption onto most colloid surfaces c Various workers have attributed this enhancement to a reduction of electro- static repulsion whereas others have attributed this to specific chemical effects and others explain it on the basis of polymer- solvent interactions o For various polymers and adsorbents, pH increases have been found to decrease adsorption and in some cases to produce maxima „ Specifically Ruehrwein and Ward (1952) concluded that polyan- ions adsorb predominantly at the plat let edges of montmorillonite whereas polycations adsorb onto the (001) faces „ Mortensen (1960) concluded that HPAN-10 (10% hydrolized polyacrylonitrile 8 i,.e 08 10% carboxylic acid, 90% nitrile side chains) was adsorbed at the edges of kaolinite but may have adsorbed to a limited extent on the (001) faces in the presence of divalent cations Ruehrwein and Ward found that an increase in NaCl concentra=> tion increased polymethylacrylate adsorption to montmorillonite Mortensen likewise found that an increase in electrolyte concentration increased HPAN=10 adsorption to kaolinite More specifically 8 he found that cations increase adsorption in the same order as the lyotropic series Th >Ca >Ba >H >NH >K >Na , and transition metals increase adsorption in the same order as their complex stability constants to +2 +2 +2 +2 polyanions (Gregor et at, t 1955) Cu >Ni >Co >Mn „ For anions he found the following order for effecting an increase in adsorption - F = >0H~>H P0~>C1~>CH COCf >NCC Reduction of pH also increased HPAN=10 adsorptionf however, different buffering systems gave different specific adsorptions at the same pH and molarity Black et al a (1965) found e at pH 7, that an increase in CaCl 41 concentration from 25 to 250 mg/1 increased the adsorption of both HP AM- 4 and HP AM- 30 (4% and 30% hydrolized polyacrylamide) to kaolinite HPAM-30 adsorbed much more strongly than HPAM-4 at both CaCl 2 concen- trations t Michaels and Morelos (1955) observed that both NaPA (sodium polyacrylate) and HPAN=21 adsorbed to kaolinite to an increased extent below pH 6 C 5 and NaPA to a greater extent above pH 6 C 5 C They attempted to account for this difference by reasoning that adsorption is con- trolled by a balance between the magnitude of electrostatic repulsion and the magnitude of hydrogen=bonding to the clay surface Schmidt and Eirich (1962) reported that adsorption of both PMAA (polymethylacrylic acid) and PAA (polyacrylic acid) to anatase (TiO^) as a function of pH passed through maxima but at different pH values In apparent contrast to this g they found that for the same adsorbent and a series of vinyl acetate-crotonic acid copolymers, i e<, 8 =C00CH and =C00H side chains g for the pH range 5 C 5 to 7 5 adsorption decreased with increasing pH 9 and also decreased with an increasing number of crotonic acid monomers per molecule B at constant pH c They did not attempt to explain this difference nor did they give any de- tails for the PMAA and PAA anatase system This might be explained if the maxima were below pH 5 5 and if anatase had an isoelectric point below this pH They did explain the results for the vinyl acetate-crotonic acid copolymers 8 however They were able to obtain a linear plot of adsorption capacity (mg polymer/gm solid) versus l/ApH 9 where ApH is solution pH minus the pH of limiting solubility for that polymer. This was interpreted to mean that adsorption in this case was primarily 42 dependent on the ratio of the number of "adsorbing groups" (-RCtO, i c eo, insoluble groups t over the number of "repelling groups" (-RC00 ) 9 beyond those necessary to maintain solubility This interpretation suggests that another factor is important in determining adsorption B namely solubility,, No experimental data were found for the pH and I dependence of polycation adsorption,, Limited data have been published for aggregation=destabilization studies and will be discussed below Milieu Effects on Destabilization=Aggregation Rebhun and Wachs (1965) g Black et al (1965), and Ruehrwein and Ward (1952) all found that the addition of neutral salts increased the aggregating ability of polycarboxylic polymers on kaolinite, at or near neutral pH The first two observed this effect with CaCl and the last one observed it with NaCl Linke and Booth (1960) studied milieu effects on polymer- amorphous silica systems by measuring relative sediment volume „ They found that the optimum polymer dose decreased with increasing NaCl concentration This trend was noted up to 2 M NaCl 8 but the optimum dose then remained constant with continued increase of molarity Silica has an isoelectric point of ^3 5, its electrokinetic potential being positive at pH values below this value and negative above this value c For a silica=anionic polymer system Linke and Booth noted that the required optimum polymer dose increased with increasing pH up to slightly above the pi of silica and then decreased with con- tinued increase in pH For poly cat ions Posselt and Reidies (1964) found that as pH 43 was decreased from 9 to 5 the optimum dose of a polymer required to aggregate manganese dioxide hydrate suspensions decreasedc They also ++ reported that an increase in Ca concentration reduced the required polymer dose for optimal aggregation c Pressman (1967) also found that the optimum polymer dose of a polycation decreased with decreasing pH for natural river waters „ Conclusions regarding milieu effects that may be drawn from the literature cited are limited but they nevertheless are useful as an elaboration on the interactions depicted in Figure 1 First of all the milieu effects on adsorption appear to be qualitatively similar to milieu effects on destabilization, for polyanlons at least Note that exceptions to this generalization may occur when solubility effects are important o This is because, as the solubility of a polymer decreases, the tendency to adsorb increases However , the decrease in solubility of a polymer is accompanied by a decrease in spatial extension of the polymer o Probability considerations indicate that the ability to bridge, i e , destabilize, should decrease with a decrease in spatial extension of the polymer For polyanions, increases in ionic strength tend to increase destabilization ability It cannot be generalized whether this effect is due to effects on the polymer or colloid surface or bothn Near neutral pH the destabilizing ability of polycations appears to increase with decreasing pH u However 9 effects on the colloid surface may give rise to exceptions For polycations, the results are scarce D However, indications are that the destabilizing ability increases with a decrease In pH and with an increase in ionic strength „ 44 2o3 6 Conclusions The mechanism of destabilization by polyelectrolytes involves the formation of bridges by polymer molecules which are ad- sorbed to the surface of two or more colloidal particles u For cationic polyelectrolytes s reduction of electrostatic repulsion appears to accom- pany destabilization c Such an effect is apparently not significant for anionic polyelectrolytes , The existence of an optimum degree of aggregation as a func- tion of polyelectrolyte concentration is rationalized by the polymer- bridging modelo Polymer adsorption and extension of segments of the adsorbed polymer from the colloid surface are fundamental to the pro- posed mechanism of destabilization and the polymer-bridging modelo Experimental results and theoretical predictions qualitatively agree in support of adsorption and the extension of segments Limited experi- mental results indicate that adsorption kinetics are quite rapid and are not the rate limiting step in aggregation Milieu effects are specific for a particular system but in general appear to be signifi- cant variables in destabilization=aggregation In general both a decrease in pH and an increase in ionic strength appear to effect an increase in destabilizat ion-aggregation u 2 4 Turbidity as a Measure of Aggregation Rate The extinction of light passing through water has been a widely used method for estimating the concentration of various sub- stances in water because of the relative ease of measurement „ Since a variety of variables affect this extinction 8 considerable care and control must be taken in interpreting such measurements The total 45 extinction of light s E, is described by the equation E = I + A (14) where I is the intensity of total scattered light (turbidity, optical density or opalescence) , and A is the absorbed light „ There are two theories (Oster, 1948) which describe I for monodispersed-spherical- independent-scattering particles which have served as the basis for estimating such quantities as particle number concentration s particle size and molecular weights According to Timasheff (1966) the general equation I = K'Nr 2 (r/X) y (15) describes the intensity of scattered light for any value of r/X where r is the particle radius B A is the light wavelength in vacuum, N is the number of particles in the scattering volume 8 K' is a constant indepen- dent of X and r, but y is a constant which is a function of X and r and varies from 4 to -2 2 P This relationship has served as the basis for estimating the size and number of particles during the course of aggregation of par- ticles below the size of about one micron,, For example, Timasheff (1966) has shown theoretically and experimentally, for an essentially monodispersed system, that as aggre- gation proceeds through the approximate particle size range of my to y, 3 I changes from being directly proportional to r to an inverse relation- ship g i e , l/r„ 46 Recently, Hiemenz and Void (1966) have presented arguments which allowed an empirical interpretation of optical density for non- stirred aggregating suspensions of carbon black in hydrocarbons „ The crucial assumption in this treatment was that the "mean optical proper- ties" of a floe will remain constant B independent of its size, provided floe structure remains constant Optical density differences were deemed usable for deducing differences in relative floe size or concen- tration when the exponential dependence of O.D on X was identical for the suspensions being compared A second criteria was that the mean optical properties must be identical for comparison Mean optical property is an adjustable constant which is a function of floe refrac- tive index $ absorption coefficient, density and A dependence on C D They admitted that even so, totally unambiguous size comparisons were not possible o When one progresses through the micron to millimeter size of particles which are polydispersed fe non-spherical and settle rapidly, the available theories become useful in only a qualitative fashion Black and Hannah (1965) in an important paper on light scat- tering phenomenon and turbidity pointed out the qualitative generaliza- tions based on the theories and noted the major pitfalls in the path of interpretation o They also pointed out that additional difficulty may be introduced through instrument geometry and calibration procedure „ Thus individual turbidity values have no real quantitative meaning For example, Birkner and Morgan (In Press), in their study of the kinetics of aggregation of polystyrene latex particles by polyethyl- eneimine, have clearly shown the danger of attempting to use individual turbidity values as an estimate of the number concentration of particles 47 in suspension when aggregated under different conditions u They found no simple correlation of optical density, 0„D O8 to total particle con- centration (Figo 5K These data are for aggregated^ settled suspensions which have been reacted at different mixing intensities (G was varied from 11 to 120 sec ) and "some" D values were obtained by dilution,. They did not, however, show data of D versus particle concentration, at a constant G 9 for various times of mixingo However j from theory it is possible to predict in a very general way how turbidity changes in the course of aggregating a dilute suspension, i e 08 I as function of r, for total constant mass of sus- pended material, as shown in Table 3 and Figure 6 Table 3 FACTOR RELATING TOTAL SCATTERED LIGHT TO PARTICLE SIZE FOR EQUAL TOTAL MASS (After Black and Hannah, 1965) Particle _Size ^F^P??^ ^?! 1 ^ j-"^- _^_ -^ 2r « X r 3 M 4 2r ^ X r/X 2 2r > X 1/ r The theory is too unwieldy to calculate such a curve but it shows that the exact position and shape of the curve would depend on such variables as X (for 2r < 1 n), refractive index 8 particle size distribution ? and interference effects due to high particle concentra- tions o Figure 6 is instructive in that it shows that particle growth, from about 1 y size and upward 8 is characterized by a decrease in 48 1.8 Numbers Represent Mixing Intensity G (sec"-'-) at which samples were pre- pared. 1.6 1.4 1.2 — •H W C Q O ■H •p a 1.0 o 0.8 0.6 — 927 60 7 0.4 0.4 0.5 0.6 0.7 0.8 Total Particle Concentration (cm"3) x 10™' 0.9 FIGURE 5. TOTAL PARTICLE CONCENTRATION VERSUS OPTICAL DENSITY For destabilized, aggregated, settled samples of latex suspensions prepared_ by mixing at various mixing intensities. Data after Birkner and Morgan. 49 Particle Radius FIGURE 6. GENERALIZED RELATIONSHIP OF TURBIDITY-PARTICLE RADIUS FOR CONSTANT TOTAL MASS 50 scattered light Additional reductions of scattered light may occur when particles are removed from the scattering volume, e go 9 by sedi- mentation o The essential feature for this micron-and-above size range is that either an increase in particle size or the removal by sedimen- tations, as indicated by total scattered light, constitutes particle aggregation We cannot predict by theory just what the relationship is, however This remains to be proved experimentally by measuring tur- bidity and particle size and number The theory also qualitatively shows that the intensity of light scattered at 90°, i (90° with respect to the path of the inci- dent light) is less dependent on particle radius than is the total scattered light The important fact to be realized is that I or i nn , for y u different colloidal suspensions or for colloidal suspensions aggregated under different conditions, e^gog destabilant dose or G, do not neces- sarily bear any relationship to one another in terms of particle number, radius or mass However, the rates of reduction of I or i during the course y u of aggregation of particles, one micron and above in size, may be related If the rate of change of i n can be linearized and the same procedure y u yields linear data for a variety of types of aggregating systems under a variety of conditions, e g , initial particle concentration, G, and de- stabilant dose, then the rates of change should be related to the respec- tive rates of removal of the light scattering substances The correspond- ence of changes in rate, with all known physiochemical effects as predicted in the theory of aggregation, should serve as qualitative support of this method of estimating rates of aggregation of dilute suspensions 51 IIIo MATERIALS AND METHODS 3 1 Materials The colloidal materials used in this study are listed in Table 4 along with some physical properties of the materials The montmorillonite or Wyoming bentonite is a 9 8% Na saturated clay that was prepared by the suppliers by grinding Sj cation exchange and spray drying o This material was found to have a cation exchange capacity of 81 meq/100 gn by the ammonium acetate method ( Mackenzie , 1951) The clay was supplied by Baroid Division, National Lead Company, the Ludox Table 4 COLLOIDAL MATERIALS Specific Number of Particle Surface Specific Particles @ Name Diameter Area Gravity 100 mg/l (y) 2 (m /gm) (cm ) Montmor i iloni te ._ 80-400 2 65 _= Ludox=TM (Amorphous Silica) o 023 140 lc388 3(10) 13 MIN-U-SIL-5 3(10) 7 (Crystalline Silica) lolt 2 o 06 2 D 65 Polystyrene Latex 0o088 64 * lo05 11 3(10) X Polystyrene Latex o 557 10 * l o 05 Kio) 9 Polystyrene Latex 796 5 5* lc05 3(10) 8 tManufacturer's data for average size from mean surface area "Calculated from particle diameter by duPont 9 the MIN-U-SIL by Pennsylvania Glass Sand Corporation s and the polystyrene latex by Dow Chemical Company All of the materials were used as supplied by the manufactur- ers,, The clay was made up in 102 rng/A suspensions and aged from 1 to 250 hours' before use In preliminary experiments the Ludox was used as 52 an aged 102 mg/Jl suspension but dissolution of silica was shown to be important o Thereafter,, the suspensions were made from a concentrated stock solution and used within one hour For MIN~U=SIL 8 suspensions were made from dry powder and used immediately The polystyrene latex was diluted from stock solutions t as supplied by the manufacturer Montmorillonite was selected because it has been shown to be present in natural waters iPackham, 1962) Also this particular clay was found to form quite stable suspensions „ The other colloidal mater- ials were selected because they are essential monosized materials of known diameter This was required in order to make a judgment on the use of turbidity as an estimate of aggregation rate and also since it was desired to incorporate studies of particle contact opportunity „ The polyelectrolytes used in this study are listed in Table 5 The first four listed in Table 5 were selected because they were the only water-soluble polyelectrolytes which could be found in this country which were marketed by their chemical name. The proprietary materials were selected at random 3 2 Apparatus The turbidimeter (Model 1800j Hach Chemical Co 8 Ames a Iowa) used throughout this study measures the light scattered at 90° with respect to the path of the incident white light source There was no particular reason for selecting this instrument other than the fact that it was the only economical 8 proprietary instrument which gives reason- able sensitivity below a turbidity of one Jackson candle turbidity unit 9 JTUo This feature was absolutely necessary In order to perform the kinetic runs for many of the suspensions g e g , see Figure 16 for 53 montmorillonite-purifloc C-31 where turbidity < 1 unit after approxi= mately 3 minutes of reaction time However g this instrument has a feature which is felt to be undesirable - it measures the light scat- tered at 90°j, rather than at a small angle s e„g , 15°. Black and Table 5 POLYELECTROLYTES M ** Ionized Name Abbreviation (10) H lonogenic Group Polylysinet hydrobromide PL 51 ~ NH 3 Polyethyleneitninef PE1M 30-40 NH* Na Polyacrylatef NaPAC =coo~ Polyacrylic Acidf PACA -coo™ Primafloc C-7 1 C-7 high" amine- Purifloc C-31 2 C-31 high- amine- Purifloc A-22 2 A-22 high" anion* 1 * •Number average molecular weight „ },{ It is the practice of manufacturers to be vague about the physical and chemical properties of their commercial products o tPilot Chemical Company g Watertown g Mass ^Monomer Polymer Divisions, Borden Chemical Company g Phila- delphia iRohm and Haas g Philadelphia,, 2 Dow Chemical Company g Midland g Michigan Hannah (1965) showed that small angle scattering results for different suspensions correlate well with the results for the Jackson candle tur- bidimeter whereas results at 90° did not correlate well Since the instrument is not designed to measure the intensity of the incident light g suspension optical properties cannot be expressed as optical density Therefore g the readings must be referred to a "standard " The manufacturer provides a "turbidity rod" for 54 standardization o This is a formazin* colloid (Thome 1961, Bishop 1960) fixed in an acrylic resin „ The turbidity of the "rod" is expressed in Jackson candle turbidity units „ Freshly prepared formazin suspensions gave reproducible results and the turbidity, as determined directly by the Jackson candle turbidimeter (Standard Methods , 1965), checked well with instrument readings However, the turbidity of the colloidal sus- pensions used in the kinetic experiments as measured directly by the Jackson candle turbidimeter did not correlate with the instrument "JTU" readings o This was due to (1) the difference in particle size distri- bution of the colloidal suspensions and the formazin reference standard, and (2) differences in the instrument geometry of the Jackson candle and the 90° light scattering photometer as thoroughly discussed in the important paper on turbidity by Black and Hannah (1965) Thus the turbidity values shown in this work are for 90° scattered light and are based on the Jackson candle turbidity of a formazin colloidal suspension Turbidity values are expressed as "tur- bidity units" rather than as Jackson candle turbidity units since kaolin - as recommended in Standard Methods (1965) - was not used as the reference suspension This is done in an attempt to give the reader a "feel" for the order- of -magnitude of the turbidity values and at the same time give the second-order rate constant,, K s dimensions of s app ' reciprocal time and a quantity which is (conceptually) analogous to -1 -1 concentration , i„e , time TU „ It should be noted that the absolute turbidity values are not of importance since it is the relative values of K which is of interest here app "Recently Hannah's i~al~>~{ 196 7) have noted that formazin is a reproducible reference standard This is not true of "kaolin" of unspecified type (i e , known particle size distribution) as presently recommended by Standard Methods (1965), unless a small angle scattering photometer is usedo 55 All turbidity readings were taken after the samples had been in the instrument for two minutes. The turbidity values are reported as the numerical average of triplicate samples. Values of pH were determined in individual beakers before the addition of polymer and after the settling period. A Beckman Model 76 expanded scale pH meter was used. It was standardized daily using com- mercial buffer solutions of pH 4, 7, and 9. Conductivity was measured (Industrial Instruments Model RC 16B2) on the suspension for each kinetic run as a cross-check on the constancy of electrolyte concentration. Electrolyte was made up in 49 I batches in a covered polyethylene vat. The electrolyte for all kinetic runs, except where otherwise stated, was 150 mg/£ NaHC0«, and 40 mg/i CaCl^. This was prepared by adding the salts to demineralized water. Mixing was provided with a six-place multiple stirrer (Phipps and Byrd, Richmond, Va.). The tachometer readings were found to agree with paddle rpm values. Specially constructed paddles (Fig. 7), made from 1/4 in. stainless steel rod, were used in an attempt to provide more uniform velocity gradients than is thought to occur with the con- ventional 1 x 3 in. paddle. The reaction vessels, 1 I Pyrex beakers, were not baffled. For the experiments involving rapid mixing a magnetic stirring bar, Figure 7, rotating counter to the slow-mix paddles, was used. The stirring bar was rotated by a water-driven magnetic stirrer. The inten- sity of mixing was presumed to be constant since the flow of water (4 Jl/min) was kept constant. The angular velocity of the magnetic stir- ring bar was determined with a strobotachometer. The intensity of rapid mixing was estimated according to the method of Camp (1955), assuming 56 C0 2 -Air ^_J> L ».r L*L 1/4" Stainless Steel Rod SH -id 1 £ Pyrex Beaker Magnetic Stirring Bar 1 l/2"x3/8" Water- Driven Magnetic Stirrer FIGURE 7. SCALE DRAWING OF REACTION VESSEL Magnetic stirrer used only for rapid mix studies. 57 a ratio of blade velocity to fluid velocity of o 53 and a coefficient of drag of 1„2 The intensity of slow mixing was estimated in the same fashion as Birkner and Morgan (In Press) and Harris and Kaufman (1966) did, by measuring shaft torque This was accomplished by mounting a torqmeter (Power Instrument Company , Skokie, Ill ) in the shaft with the lower end of the shaft rotating on a centered bearing made from a watch jewel Control of pHg, over the range of 8 3 to 5, was obtained by introducing various mixtures of air and CO into the partially confined atmosphere above each beaker, see Figure 8„ The gas was not bubbled through the liquid since polymers would tend to be concentrated at the air=water interface By measuring the individual gas-flow rates prior to blending, various mixtures of the two gases could be obtained,, The blended gas was distributed from a central manifold to the individual beakers o Each kinetic run was begun when an equilibrium pH was achieved, 1/2 to 1 hr Samples for the turbidity measurement, 30 ml each, were taken with a 4 mm bore pipette, 1 1/2 in below the air=water interface and delivered to 50 ml beakers 3 3 Method The following method was used in performing a kinetic runs (1) six 980 ml aliquots of a suspension were placed in individual 1 liter beakers situated on the mixing apparatus, (2) the six beakers were mixed simultaneously as pH was adjusted, (3) polymer was added to the individual beakers at various times prior to simultaneous cessation of mixing for all beakers, and (4) samples were taken for turbidity 58 h 0) +j 0) S o .h u. CM fc C •H U) o < rH •H 0) rH (!) 2 as CO 0) Q) o rH ftf ^ rH •H I U X ' <1> 1) O O .d a) -t- 1 (X) rtj 4-> taO •-H (C -H +J > CO CO \ O <-\ 1 •rH 5 \ dt 1 / "e \ r4 A), turbidity first increases with an increase in par- ticle radius until the radius is approximately one-half of a micron (2r^X) and then decreases thereafter with an increase in particle radius „ This relationship is seen to be qualitatively confirmed by the results shown in Figures 9 through 12 That is, the suspensions of particles with an initial radius of less than about o 27 y show an in- crease of turbidity in the early stages of aggregation, whereas the suspension of larger initial size particles (r(0)=0 o 55 y, Figure 12) shows only a decrease in turbidity For these suspensions, values of the initial particle radii were furnished by the manufacturer,, Additional results are not included for montmorillonite nor for 796 y diameter polystyrene latex The results for montmorillonite aggregation are not included because the particle size distribution was not known nor determined „ However 8 all of the aggregating systems of montmorillonite observed corresponded to the results shown for MIN-U-SIL in Figure 12 «, That is, no increase in turbidity was observed for aggregation times as small as one minute, as compared with the initial turbidity The results for o 796 y diameter 64 3.0 n H M Q b 2.0 < W CO 100 mg/Jt Ludox 3.2 mg/£ PEIM = 18 sec" r(0) = 0.012 \i 1.0 pH 7 10 20 30 REACTION TIME (min) 40 FIGURE 9. SUPERNATANT TURBIDITY VERSUS TIME FOR AGGRE- GATING LUDOX 65 10 20 30 REACTION TIME (min) FIGURE 10. SUPERNATANT TURBIDITY VERSUS TIME FOR AGGREGATING PSL .088 66 120 100 — 20 mg/fi. PSL .557 27 yg/J, PEIM G = 47 sec" 1 , pH r(0) = 0.278 \i S S3 < < 100 200 300 REACTION TIME (min) 400 FIGURE 11. SUPERNATANT TURBIDITY VERSUS THE FOR AGGREGATING PSL .557 100 67 M Q H § < 00 100 mg/£ MIN-U-SIL-5 15 yg/£ PEIM G = 47 sec' " r(0) = 0.55 40 60 REACTION TIME (min) 100 FIGURE 12. SUPERNATANT TURBIDITY VERSUS TIME FOR AGGREGATING MIN-U-SIL 68 polystyrene latex are not included here (see Figure 19) because turbidity values for the comparable settling time (30 minutes) were off-scale for the turbidimeter, i e 09 greater than 100 c The increased settling time (2 5 hours) would tend to mask any small change for short periods of aggregation,, Dilution of the aggregated samples into the range of the instrument was deemed impractical because of aggregate breakup during mixing of the dilution water In conclusion, it should be noted that for the initially mono- dispersed suspensions studied, the particle sizes which developed during aggregation are undoubtedly not uniform Thus these results are not totally analogous to the qualitative predictions of the theory, which is for monodispersed suspensions However, the results serve to illus- trate two essential features for these types of rapidly aggregating systems? (1) the initial turbidity, T(0), is ambiguous and should be avoided in the analysis, and (2) for the exception of very short times of aggregation, turbidity values decrease with increasing time of aggre- gation for reactions of the rates indicated and for initially monodis- persed suspensions with particle radii down to o 012 y 4 2 Comparison of Aggregation Rates Depicted by Turbidity and Numbers of Particles Particle number concentration data were not determined in this study,, However, a qualitative comparison of the rate of decrease as depicted by particle number concentration and by turbidity is available „ The data of Birkner and Morgan (In Press) for 1„3 y diameter polystyrene latex spheres, showing total particle concentration and data collected by the author for 0„796 y diameter polystyrene latex spheres showing 69 supernatant turbidity are shown in Figure 13 „ Both systems were desta- bilized by PEIM at their optimum doses and are identical in all respects except for particle diameter and mass concentration „ The only differ- ence in the aggregation of these two suspensions should be the rate Obviously j no quantitative comparison is possible because of the difference in initial particle radii and the concomitant influence on aggregation rate,, However r turbidity of an aggregating suspension is seen to depict a change in a system property which is qualitatively similar to the change depicted by particle number concentration „ No judgment upon the similarity or dissimilarity of the kinetics depicted by the two types of data is possible This fact has little merit in an argument against the use of turbidity to estimate kinetics because theoretical developments have not advanced to the point that the kinetics are known for the particle number data shown in Figure 13 c It should be noted that the number data for only the first 10 minutes (of the 400 minutes shown) could be fitted to a theoretically derived equation (see Figure 2) and even this limited range of data can be fitted to a form that contradicts the theoretical equation. Thus, at present , particle number concentration data are not of significantly greater value than turbidity data 8 because both must be treated empirically 4 3 Generality of the Assumed Kinetics In order for an empirical equation of aggregation to have general utility in estimating aggregation kinetics it must apply to aggregation induced by all of the known mechanisms of destabilization 8 as described in Section 2 o 3 If the equation is to be useful in reactor design it must apply to aggregation induced by alum or ferric chloride 70 Polystyrene Latex Number Data Turbidity D = 1,3 |i N(0) = 2.1xl0 8 420 ug/£ PEIM 264 mg/£ PSL 1.2xl0" 3 M NaCl D = 0.796 u N(0) = 2.1xl0 8 ca 55 vg/l PEIM 76 mg/2, PSL -3 1.2x10 M NaCl Number Data after Birkner and Morgan, 300 200 H 100 h H Q M m D E-i < W 50 CO 20 100 200 300 REACTION TIME (min) 400 COMPARISON OF AGGREGATION RATE DEPICTED BY TURBIDITY AND NUMBERS OF PARTICLES --'.. . 70 300 — 200 s H 100 H CQ D M 50 fe DO 20 200 300 REACTION TIME (min) FIGURE 13. COMPARISON OF AGGREGATION RATE DEPICTED BY TURBIDITY AND NUMBERS OF PARTICLES 71 To indicate this, results for silica are presented in Figure 14 where the only variable is the type of destabilant, The destabilants are (1) alum g (2) 1M NaCl 8 and (3) polyethyleneimine, a cat ionic polyelec- trolyte, (The lines in Figure 14 are fitted by the method of "least squares ," as are all of the lines in the following figures,,) All three are materials which accomplish destabilization by significantly differ- ent mechanisms o The alum and PEIM doses were at their respective optima for this system,, The results in Figure 14 suggest that second-order kinetics in turbidity is an equally adequate representation of aggregation kinetics regardless of the type of destabilization mechanism,, These results serve as support of the proposal (see Section 2„1 and Figure 1) that destabilization can be viewed as a variable which manifests itself as an effect upon the rate of aggregation,, The noticeably faster rate shown for alum can be rationalized when it is realized the aluminum-hydroxy insoluble material which forms at this alum concentration and pH, actually represent additional par- ticles and thus increase the collision rates Since it is impossible to separate this effect from double layer repression or bridging, it seems pragmatic to view the overall effect of alum upon the rate of aggregation as destabilization Additional data for a number of polymers and a number of types of colloids are presented in the following sections which serve as fur- ther evidence of the generality of the assumed kinetics „ Also additional data are presented below for polymer systems which serve as a more ex- tensive test of the proposed destabilization-aggregation rate relation- ship,, 72 7 20 mg/£ 1 Alum D 15 wg/i PEIM A 1 M NaCl IOC mg/fc MIN-U-SIL G = 47 sec" "I, pH 7 40 60 REACTION TIME (min) 80 100 FIGURE 14. AGGREGATION KINETICS FOR- POLYELECTROLYTE , ALUM AND NaCl DESTABILIZATION 73 4„4 K Dependence on Mixing Intensity app Rationally one would expect that the collision rate of par- ticles and likewise the aggregation rate should increase with an increase in the intensity of mixingc Smoluchowski's equation for laminar flow- induced aggregation predicts a direct proportionality between aggrega- tion rate and intensity of mixing. As pointed out earlier 8 Birkner and Morgan (In Press) found , for the range of intensities they studied , that this was qualitatively true but that the increase in rate was not com- mensurate with the increase predicted by theory For the systems on which mixing intensity effect was studied , a slightly different relationship has been observedc This is shown in Figures 15 and 16 and Tables 6 and 7, where it can be seen that K app increases exponentially with increasing mixing intensity , for the range studied,. The explanation of these observations will be reserved for Section 4„8 which deals with the effects of rapid or flash mixingo Additional background material is required and is more conveniently presented there It was suggested quite some time ago by Camp and Stein (1943) that at a sufficiently high intensity of mixing, decreased efficiencies of plant operation occur,, This is the type of relationship shown in Figure 3 9 after Hudson (1965) This presumably results from the fact that the high shear rates either prevent the formation of aggregates which are large enough to settle, or it results from the breakup of particles which have formed Unfortunately, for the apparatus used, sufficiently high enough intensities of controlled mixing could not be achieved to observe this effect,, However, apparent breakup has been observed for some 74 10 +-> •H C >-, •H -a ■H l£ E-" O 1-1 H < < o w w s o w Q 4 - 2 - 1 100 mg/£ Ludox-TM i I 3.2 mg/£ PEIM - pH 7 /▼ - / .6 _, • G (sec" 1 ) -, / & a rt ^ rt d ^ ▼ (£9) (47) 50 100 G (sec -1 ) — / L / r a — / L s 1^ X^l / y / ^^^^ --(s) — 1 1 10 20 REACTION TIME (min) 30 FIGURE 15, K DEPENDENCE ON MIXING INTENSITY FOR LUD0X app ! I 1 1 1 o o i t ■ 1 □ - O CO O ^ 1 O 0) ro O w o CM — 1 1 O • o o CM H o ( T- nx ddp UTUi) y 100 mg/£ Montmorillonite 20 mg/£ Purifloc C-31 _ pH 8.2 • ^ H 1 O CD V) - — ' 1 o \ 1 (5) ' 1 \ < ■ v i< 75 w H o M =r ^r ^H O i—i o S3 O O 53 CM H O E-i 1— 1 CO ^— > >-T d w O •H E-i O e S3 H ^^ M CJ S3 M M H X M S3 s O M S3 O H o CO c; < w 8 CJ w Q W w o CD a. a. o oo ( T _ni) (*)f o 3- o CM ^ CD M ' noiivohhoov jo 33Hoaa 76 Table 6 K DEPENDENCE ON MIXING INTENSITY FOR LUDOX app Ludox Concentration = 100 rng/H Polymer: 3.2 mg/2. PEIM, P pH 7 ° K app 1 Mixing Intens: •ty T(0) (sec ) (min" 1 TU" 1 ) (TU _1 ) 10 0.063 .021 18 0.093 .11 18 0.082 .15 18 0.080 .17 47 0.22 -.046 80 0.44 -.18 Table 7 K DEPENDENCE ON MIXING INTENSITY apP FOR MONTMORILLONITE Montmorillonite Concentration: 100 mg/2, Polymer: 20 mg/J, Purifloc C-31, P pH 8.2 ° K 1 Mixing Intensity app T( ) (sec" 1 ) (min" 1 TU" 1 ) (TlT 1 ) 18 0.46 -0.47 47 0.95 -1.2 80 2.70 -6.4 77 systems under extended periods of mixing at a constant intensity of mixing j e g , see Figure 18,. This suggests that eventually aggregates may breakup, i e , become smaller , at the same Intensity of shear at which they were formedc This effect has not been previously reported in the literature on aggregation kinetics „ This also will be discussed in Section 4 8 4„5 K Dependence on Colloid Concentration Rationally it should be expected that aggregation rate should increase with an increase in particle concentration for a given particle radius, or with an increase in particle radius for a given particle concentration However, the effect of these two variables on aggrega- tion rate is probably not as straightforward as a number of complicating factors might be anticipated,, Two systems were studied which may illus- trate that this may be the case Results are shown in Figure 17 for MIN-U-SIL and in Figure 18 for Ludox and are given in Tables 8 and 9„ Both of these systems have similar mass concentrations , i e , around 100 mg/£ The 30 to 600 fold difference in reaction rates is in part explained by the vast difference in particle concentration for the two systems, ioe , the number concentrations were calculated to be 3(10) 7 /ml for the MIN-U=SIL and 3(10) 13 /ml for the Ludox, see Table 2„ The MIN-U-SIL system exhibits the expected type of response wherein the rate increases with an increase In particle - or mass - concentration o However, the Ludox system shows just the opposite effect Explanation of these observations is complicated by the fact that tur- bidity is being used to estimate aggregation rate and the initial par- ticle size for one of the suspensions, Ludox, is smaller than the 78 CO ■p •rH C ID >> •H -O ■H & H .£ H O M < < o w w cs w Q o M LD CO 1 D I M Pi O P-i o o M II- < H 53 >-"^ W C CJ •H j3 b o Nw^ CJ |j Q M M o o H J CO J ^ o O o M H ►g U o < H H s CJ M Q w o PL) CN Q a, m « H o 3 H tM ( T _ni) -^-p^ 'N0I1VD3HDDV JO 33HD3Q 79 H I CO +-> •H C D >•> ■P •H •H 3 E- P 2 O H E- < C Pi U u < o w w Pi u w Q o Q c^ o Pm o M < Pi W o o o M O o o o w o w Q w w Q M PL, ( T _ni) i 'NOIlVDSaODV JO 33HD3CI 80 app Table 8 DEPENDENCE ON COLLOID CONCENTRATION FOR MIN-U-SIL G = 47 sec" 1 pH 7 Colloid Cone. (mgA) PEIM Cone. 0ng/£). (min -1 app o TU _1 )xl0 3 (TU _1 )xl0 3 .722 26.4 1.37 4.98 1.24 7.26 1.90 -0.35 50 100 100 200 7.5 15 15 25 app Table 9 DEPENDENCE ON COLLOID CONCENTRATION FOR LUDOX G = 47 sec" 1 pH 7 Colloid Cone. (mg/&) PEIM Cone. (mg/JQ app (min" 1 TU" 1 ) 1 0\ (TU" 1 ) 50 1.5 100 3.2 100 3.2 100 3.2 200 7.6 0.166 0.093 0.082 0.090 0.064 -0.47 0.11 0.15 0.17 0.078 81 wavelength of light, i e , 023 n diameter particles This may indi- cate a limitation of turbidity as a measure of aggregation rate or it may be a reflection of the complicating factors mentioned above „ For example, breakup may be a consideration^ That is, at sufficiently high aggregate volume fractions , a further increase in the initial particle concentration may lead to an apparent decrease in the aggregation rate because fewer particle collisions are lasting due to shear disruption This might be called a crowding effect whereby the allowed aggregate volume fraction is limited by shear intensity c Since polymers occupy space in an aggregate, the aggregate volume fraction increases with increasing degree of aggregation Thus when the initial particle volume fraction is high, shear may limit aggregation „ Such a crowding effect might be reached in a number of waysg (1) by simply increasing the mass concentration 9 (2) by holding constant the number concentration while increasing the radius of the initial particles or, (3) by holding con- stant the mass concentration while decreasing the radius of the initial particles o This latter effect may arise because as the particle radius becomes smaller the aggregate volume fraction becomes larger since more and more interparticle space is occupied by the bridging polymers Another consideration is that the rate dependence on concen= tration may differ for various types of destabilants „ For a simple electrolyte destabilant, particle packing is quite efficient, ioe , essentially no interparticle space is occupied by destabilant molecules, and aggregation would appear to be a direct function of collision prob- ability o However, for polymer destabilants, particle packing is less efficient and aggregation probability may be less than the collision probability This latter fact may be true because in order for a 82 collision to be fruitful, i eu, a bridge to be formed, a colloid having extended polymer segments must encounter the appropriate face of another colloid having open adsorption sites „ Furthermore, a sufficiently- strong bond must be formed before the aggregate becomes exposed to more intense local shear In conclusion, rate dependence on concentration is probably not universal and must be established for a particular case of interest 4 6 K Dependence on Settling Time app ^ All of the values of K employed for separating out the influence of the nine variables (see Figure 1) are reported for a stand- ard settling time* 30 minutes The fact that K values are calculated & 9 app from supernatant turbidity means that the apparent rate of aggregation is dependent upon time of settling,, Note that the rate of aggregation is not dependent upon settling time but that the apparent rate is This poses no problem but in fact can be employed in practical applications since knowledge of the settling properties of the aggregate are essen= tial for settling tank design One approach would be to design an aggregator, ioe , "flocculation" chamber 9 for fixed settling conditions An alternative approach would be to optimize design of both the aggre- gator and settling tank and thus consider settling as a variable The theory for the sedimentation of discrete particles shows that the density and size of the aggregate particles are the properties of interest o Average aggregate size is a function of K and reaction 6 ss s app time, but mainly D, G, and t Aggregate density for a given system is mainly a function of t and G but may also vary with the type of destabi= lant 8 i e 5, particle packing^ and the density of the constituent parti- cles „ 83 Since the primary objective of this work was to establish an aggregation equation B settling time was considered to be a side issue However „ one of the colloids worked with produced aggregates which settled at a noticeably slower rate compared to the other colloids used, i e , they appeared to be virtually non-settleable in the standard 30 minutes time It was decided to take advantage of this measurable settling rate to investigate K as a function of settling time app Results are shown in Figures 19 through 21 for three sizes of polystyrene latex K as a function of settling time is shown in the inserts for these figures The data for the inserts were calculated by the method of "least squares" from turbidity=reaction=time data for the individual settling times shown The data were collected by allowing the series of beakers , for an individual kinetic run, to remain in place, quiescent, and then taking the series of samples (for the six reaction times indicated) for turbidity measurements at the settling times indi- cated in the inserts „ The two sets of data for Figure 21 are for a repeat run For the three sizes of polystyrene latex considerable varia- bility can be seen The extremely slow settling rate for this material is due to the low density of the constituent particles, i e , l o 05 gm/ 3 cm „ The higher settling rate for the o 088 \i diameter PSL can be attributed to the fact that considerably more of the higher density polymer is incorporated into the settling particles, ioe , the optimum dose is 18 mg/£ vs o 055 and 027 mg/£ for the other two PSL systems These results indicate that K , as a function of settling app* time, approaches a steady state value The time for reaching the steady state value appears to be inversely related to K 84 .06 .05 — CO •M •H c ID >■, 4-> •H X) ■H u O l— l H < O < o w w p< o Q .04 .03 T 76.5 mg/l PSL 0.796 y Diameter 55 yg/H PEIM, P 1.2 (10) M NaHCO N(0) = 2.1(10) 8 /ml G = 47 sec™ 1 2.5 hr Settling x 20 40 Settling Time (hr) o 1 - 100 200 300 REACTION THE (min) 400 FIGURE 19. K AS A FUNCTION OF SETTLING TIME FOR PSL .796 app 85 CO ■p •H C ID >^ 4-> •H -d •H H 5 2 O H H < < PL, o w w w Q 20 mg/S, D SL 0.557 y Diameter 27 U g/{L PEIM, P 1.2 (10)" 3 II Ma HCO N(0) = 2.1(10) 8 /ml G = 47 sec -1 30 min Settling 20 Settling Time (hr) 40 100 200 REACTION TIME (min) 300 400 FIGURE 20. K AS A FUNCTION OF SETTLING TIME FOR PSL .557 app 86 15 to +-> •H c 4-J •H •H ■P E- .10 o M H < < o w w o w Q 21 mg/£ PSL 0.088 vi Diameter 0.18 mg/2, PEIM, P 1.2 x 10" 3 M NaHCO = 1.5 x 10 10 /m G = 47 sec 30 min settling a, 4 1 2 4 6! Settling Time (hr) 10 10 20 REACTION TIME (min) 30 EIGURE 21. K AS A FUNCTION OF SETTLING TIME FOR PSL .01 app 87 4 C 7 K Dependence on Destabilization In Figure 1 it is indicated that the degree of destabilization is a variable affecting aggregation rate t The degree of destabilization is determined by the physical and chemical Interactions among the de- stabilant, colloid surface and milieu By appropriate control of vari- ables some of these interactions can be examined by comparisons of K app The variables selected for study are destabilant concentration and pH, i„e t , variables 9 and 5 in Figure l c Destabilant physical and chemical properties (variable 8) is in itself a problem of near encyclopedic proportions and cannot be treated here Rather only the "type" of destabilant polymer is considered here in Section <4 C 7 3 C The relation- ship between destabilant concentration and colloid surface concentration (variables 9 and 7) is treated in Section 4 9 c The physical and chem= ical properties of the colloid surface (variable 7) could not be inves- tigated because it was impossible to obtain different types of colloidal materials with the same particle radii, ioe OS) variables 1 and 2 could not be controlledo This aspect is discussed in Section 4 9„ 4 7ol K Dependence on Destabilant Concentration app Results are shown in Figures 22 through 25 and in Table 10 for montmorillonite and Purifloc C-31 at various polymer concentrations (at pH 8 2, 7 8 6) Figure 22 is a summary of the results from Figures 23 through 25 It can be seen that K is quite variable with polymer dose, at a given pH 9 and goes through an optimum at some particular dose (It also can be seen that at the optimum dose K increases with v app decreasing pH ) The polymer concentration dependence of K is readily understandable when viewed in terms of the polymer-bridging models 88 .4 — pH 8.2 1.2 I I .4 ^ P4 1.6 1.2 — .4 pH 7 DH 6 10 20 30 PURIFLOC C-31 DOSE (mg/£) 40 100 mg/Jl Montmorillonite, G = 47 sec -1 To FIGURE 22. K AS A FUNCTION OF DESTABILANT CONCENTRATION app 89 15 w ■p •H c :z> >1 +J •H T) •H 43 H LO o M H < o u < o w w oi u u Q 1 1 100 mg/£ Montmorillonite i / Purifloc C-31 G = 47 sec -1 pH 8.2 v© a Polymer Dose (mg/£) -^ k/ <> / / ^S^ - wJ^r t""""~ t— -@>— — 1 ■*' 10 15 20 REACTION TIME (min) FIGURE 23. AGGREGATION OF MONTMORILLONITE WITH PURIFLOC C-31 pH 8.2 90 100 w ■H C D >> •H X) •rH X) Pi E- l£ 2 O M H < < o w w s o w Q 80 60 40 20 100 mg/H Montmorillonite Purifloc C-31 G = 47 sec" 1 pH 7 Polymer Dose (mg/£) 40 60 REACTION TIME (min) 100 FIGURE 24. AGGREGATION OF MONTMORILLONITE WITH PURIFLOC C-31 pH 7 91 30 25 H I W ■H ■H C D >, ■P •H X) ■H ,q 20 w 15 Z O M < O CD CD < CM o w w Pi CD W Q L0 100 mg/£ Montmorillonite Purifloc C-31 G = 47 sec -1 pH 6 ■B 20 REACTION TIME (min) FIGURE 25. AGGREGATION OF MONTMORILLONITE WITH PURIFLOC C-31 pH 6 92 section 2.3.1. This model also rationalizes quite nicely the shape of a typical degree of aggregation-polymer dose curve, see Figure 4. Such a curve is conceivably a cross-section out of a three-dimensional surface Table 10 K DEPENDENCE ON DESTABILANT CONCENTRATION app 100 mg/Jl montmorillonite Purifloc C-31 G = 47 sec" pH Polymer Cone. (mg/Ji) K app (min -1 TU -1 ) 1 tToT (TU _1 ) 8.2 20 0.9"S - .47 8.2 18 0.63 - .60 8.2 22 .26 -0.24 8.2 25 .15 0.004 8.2 30 .058 0.118 8.2 50 .0094 0.093 7 18 1.272 -2.36 7 20 0.838 -0.866 7 15 0.456 + 5.04 7 10 0.096 0.49 6 10 1.63 -2.7 6 12 0.758 -0.28 6 5 0.097 .07 6 20 0.033 .04 which incorporates dose, reaction time and degree of aggregation, such as shown schematically in Figure 26. Thus the variable, polymer dose, is related to aggregation rate - the slope of a degree-of-aggregation- vs. -reaction-time curve - as is shown in Figure 26, and the composite of these is compatible with the polymer-bridging model. 4.7.2 K Dependence on pH app * ■ * Since pH is a variable in natural waters and since hydrogen 93 FIGURE 26. 3-D SCHEMATIC DIAGRAM OF DEGPEE-OF-AGGREGATION , REACTION TIME AND DESTABILANT CONCENTRATION 94 ion concentration, in some cases , significantly affects K 8 this app variable is being discussed separately here c Also, through pH effects it is possible to illustrate the role of physical and chemical proper- ties of the polymer Results showing pH effects on K are included for montmoril- y app lonite and four cationic polyelectrolytes as well as montmorillonite and three anionic polyelectrolytes The results for Purifloc C=31, a cationic polyelectrolyte 8 are shown in Figures 22 and 27 (condensed from Figures 23 through 25 and Table 10) „ Figure 22 indicates that the optimum dose 9 P s decreases with decreasing pH and at P , K increases K " o' to r o* app with a decrease in pH Figure 27 indicates that at 20 rng/Jl Purifloc C=31 (P at pH 8) K decreases with decreasing pH. ioe 05) for pH < 8, o app * * over dosing is indicated? The results for three other cationic polymers show a notice- ably different response to pH changes For Primafloc C=7 (Figure 28, Table 11), polyethyleneimine (Figure 29, Table 12) and poly lysine (Figure 30 B Table 13) it is indicated that neither P nor K at P & i o app o are affected by the change of pH from 8 to 5 C These two different trends can be qualitatively explained by reference to titration curves of the polymers and application of the general knowledge of polymer shape and degree of ionization as a func- tion of pH First of all it is assumed that the electrophoretic mobility and the associated surface charge of the montmorillonite does not vary significantly over this pH range „ The results of Black and Hannah (1961) indicate that this is so c Secondly it is generally known that the shape of polyelectrolyte molecules and the charge or degree of 95 1.0 0.8 ' 3 °' 6 % 0.4 0.2 1 1 ' T 100 mg/£ Montmorillonite ^^f^ i 20 rag/ A Purifloc C-31 z "^ G = 47 sec -1 / / / / / / / / / / / / / / i pH FIGURE 27. K DEPENDENCE ON pH FOR M0NTM0RILL.0NITE-PURIFLQC app * C-31 96 100 T T CO ■p •H c •H id •H H IS 80 60 H O M < O < o w w u w o 40 100 mg/i Montmorillonite 4.5 mg/£ Primafloc C-7, P G = 47 sec" 1 20 — pH 8 pH 6 A D pH 5 "a o REACTION TIME (min) 30 40 FIGURE 28. AGGREGATION OF MONTMORILLONITE-PRIMAFLOC C-7 97 60 en 4-> •H C •H T) •H ,Q l£ o M < u < o w w O W Q 50 40 30 20 10 j 100 mg/£ Montmorillonite 3 mg/£ PEIM G = 47 sec" 1 A pH 8 PH 7 • pH 7 D pH 10 20 REACTION TIME (min) FIGURE 29. AGGREGATION OF MONTMORILLONITE-POLYETHYLENEIMINE 98 H I CO ■p •H G D ■P ■H •H & 4-J o M < g u o < O w w Pi u w Q pH 8 D PH 6 A pH 5 A pH 5 100 mg/£ Montmorillonite 15 mg/& Poly lysine G = 18 sec -1 10 15 REACTION TIME (min) 20 FIGURE 30. AGGREGATION OF M0NTMORILL0NITE-P0LYLYSINE 99 Table 11 K DEPENDENCE ON pH, MONTMORILLONITE-C7 app Colloid: 100 mg/& Montmorillonite Polymer: 4.5 mg/A Primafloc C-7, P Mixing Intensity: G = 47 sec-1 K app 1 T(0) PH (min"" L TU" 1 ) (TU" 1 ) 5 4.02 -3.7 6 3.96 -2.4 8 3.64 -1.6 Table 12 K DEPENDENCE ON pH, MONTMORILLONITE-PEIM app H • Colloid: 100 mg/£ Montmorillonite Polymer: 3 mg/& Polyethyleneimine, P Mixing Intensity: G = 47 sec -1 app T(0) pH (min" 1 TU" 1 ) (TU -1 ) 5 3.07 -4.11 7 2.54 +2.1 7 2.75 5.86 8 3.55 -6.32 Table 13 K DEPENDENCE ON pH, M0NTM0RILL0NITE-PL app v » Colloid: 100 mg/£ Montmorillonite Polymer: 15 mg/Jl Poly lysine Mixing Intensity: 18 sec~l - , _ app tToT £H (min" 1 TU -1 ) (TU -1 ) 8 .35 -0.64 6 .32 -0.61 5 .39 -1.07 5 .38 -0.98 100 ionization are directly related to the polymer v s titration curve, i e , pH u As most polyelectrolytes become more and more ionized the shape changes from a spherical random coil to an elongated^ slightly coiled, rod- like shape due to increased intramolecular repulsion by the ionized side chains o Thus, the degree of ionization and the degree of elonga- tion of a cationic polymer increase with decreasing pH„ The precise pH dependence of both of these are related to the titration curve for the particular polymer Thus, a polymer which acts as a weak base and has what is equivalent to a pK of, say, 10 5 will exhibit essentially no increase in ionization or elongation below pH 8, Rationally it might be expected that K for such a polymer would likewise not change below pH 8„ For poly lysine this is exactly what appears to happen, as its pK is approximately 10 5 (Katchalsky et al<, t 1957) „ CL On the other hand polymers with a pK of 7 would exhibit a. changes in degree of ionization and elongation over the pH range 8 to 6, and concomitant K dependence over this pH range In Figure 31 a titration curve for Purifloc C-31 is shown t Though the apparent buffer- ing capacity is not strong, the curve indicates that the inflection point, i e , pK g is in the region of 6o5 This indicates the reason CL for the P and K (at P ) dependence on pH In the case of polyethyleneimine the result is similar to that of poly lysine but the reason for this is slightly different, PEIM is an unusual polymer that exhibits what is called "nearest neighbor effect" (Katchalsky et al a% 1957) It results in the polymer's having no narrow range of pH over which ionization and elongation change dra- matically „ However B for this polymer the change in ionization and elon- gation over the pH range 8 to 5 is approximately 20% of the total 101 CO CO 1 o a ro o o >-l H X Pi D o T3 Ph ID •iH O u, < o 4h s o H 0) H o c 2 0) H o H M J- (0 > E-< d • C7* H w ro D O o M CM Uh 102 change (Shepard and Kitchener 8 1956).., The fact that there is no apparent change in P or K at the same polymer concentration (3 rr ° o app mg/Jt) between pH 8 and 5 may be due to the following : the relatively small change in polymer shape and ionization, and the possibility that this change is small compared with the range of polymer concentration over which P exists „ o A titration curve for Primafloc C-7 is shown in Figure 32 For this polymer the inflection point appears to be about pH 9, though the apparent buffering capacity is not strong c The inference is that essentially no change in the polymer's shape and charge occurs between pH 5 and 7, and possibly to pH 8 C This result tends to substantiate the non-dependence of K and P upon pH (8-5) found for Primafloc C-7 (Figure 28, Table 11) „ Results are included in Figure 40 and Tables 15 through 17 for montmorillonite and three different anionic polymers Results for these systems are only qualitative since they were not found to be reproducible „ as will be discussed in Section HolO, However f a brief discussion seems in order The general trend for the anionic polymers seems to be that K increases with decreasing pH The reasons for app this may be more complicated than in the case of the cationic polymers, This is because the anionic polymers t in certain cases at least t are thought to adsorb to clay primarily at the edges rather than the plate- let faces because of the respective cationic and anionic nature of these surfaces c Clay materials are plate-like structures having two o quite large dimensions g ^=1 y, and a small third dimension, MO A or OoOOl y The two surfaces described by the larger dimensions are re- ferred to as the faces t and at near neutral pH are negatively charged 103 o J- t^ 1 CJ V o o ro ro ►J c lu H < X M P^ TJ PLl •H O p-i < c O M-i ^ CM O o H CD H O < C Pi 0) Eh <-* M nj H > •H P • o o< CM ■H W co s :d u u. Hd 104 The surface parallel to the smaller dimension, the edge g comprises only a small fraction of the total surface area Depending upon the milieu and the history of the clay, it can either be positively or negatively charged but generally it has a net positive charge With decreasing pH the positive charge generally increases (van Olphen, 1963) Though the gross charge or electrophoretic mobility of the clay may not vary sig- nificantly with pH over the range of 8 to 5, the absolute number of positively charged sites on the clay edges increases with decreasing pH Thus the number of adsorption sites for the anionic groups of a polymer may increase with decreasing pH However 9 the degree of ionization and elongation of the polymer increases with increasing pH The pK for cl carboxylic polymers - which is what many of the anionic polymers are - is in the neighborhood of 5 Thus with decreasing pH the anionic poly- mer adsorption due to net decrease in coulombic repulsion more than offsets thiso This leads to a net increase in the destabilization ability In addition it is felt by some that at lower pH values or in the presence of relatively high concentrations of divalent cations, that increased adsorption to the platelet faces takes place in spite of the similar charge on the face and polymer 4o7 3 K Dependence on Type of Destabilant at P The physical=chemical properties of polymers constitute a variable affecting aggregation rate, see Figure 1 Because of the unavailability of polymers with well characterized physical-chemical properties" this variable could not be adequately investigated without "Complete characterization of the physical and chemical properties of a polymer preparation costs about $200,000 - F c R Eirich, personal communication,, 105 considerable diversion from the main topic, aggregation kinetics „ It was not the purpose here to investigate this variable alone „ However, in order to place it in context along with the other eight variables, four different polymers, with presumably different physical-chemical properties, were used which allowed generalizations to be made regard- ing the role of this variable „ For 100 mg/Jl montmorillonite (pH 8 and G = 47 sec ) and four different types of polymeric destabilants the following results were obtained? (1) K = 0„95 (min' 1 TU" 1 ) for Purifloc C-31 9 P = 20 mg/Jl, app o ■ (2) K = 3 64 (min" 1 TU" 1 ) for Primafloc C-7, P = 4 r 5 rng/A , (3) K app * o " app 3 55 (min~ TU ) for polyethyleneimine, P = 3 mg/Jl, and (4) K - OoOl (min TU ) for anionic polyelectrolytes, P - o l mg/Jl (these results are shown in Figures 23, 27, 28 and 40 respectively „ The general trend that can be seen from these results is that for montmorillonite the cationic polymers appear to affect a noticeably higher rate of aggregation than the anionic polymers and that the pre- cise rate varies with the particular polymer „ The higher K values for cationic polyelectrolytes compared to the anionic polyelectrolytes can be rationalized when the optimum dose figures are compared, i e , 3=20 mg/Jl for the cationic polymers and c 01-=0 o 06 mg/Jl for the anionic polymers o (The more appropriate comparison would be moles of adsorbed polymer per unit surface area of colloid but this information is not available o) Since the anionic polymer density at the colloid surface can be reasoned to be comparatively low, and the anionic polymer resides mainly on the platelet edges, it is understandable that the frequency of fruitful collisions, i e , aggregation, is also comparatively low„ 106 The differences In K for the cationic polymers, Primafloc app r J ' C-7 and polyethyleneimine are too small to be explained in the absence of detailed information on properties of the polymer and the details of the adsorbed state of the polymer However, one trend can be recognized for the cationic polymers in general by considering the degree of ioni- zation and the associated charge and polymer elongation c Figures 22 and 27 indicate that the optimum dose decreases and K (at P ) in- app o creases with increasing degree of ionization of polycations The fact that Primafloc C-7 and polyethyleneimine appear to be completely ionized at pH 8 may account for their higher K and lower P compared to Purifloc C-31 This means, at least for the polycations studied, that with increasing ionization the polymer affects a higher rate of aggre- gation at a lower applied concentration 4 8 Rapid Mixing A study of the effect of rapid or flash mixing on the rate of aggregation during the subsequent slow mixing phase was undertaken,, The only variable studied was the time of rapid mixing, i e o , not the intensity of rapid mixing,, It appears that this may be a quite signi- ficant variable o If the results for polymers are indicative of what happens in the case of Al(III) and Fe(lll) destabilants it is possible that this particular variable may hold considerable promise for improving water-treatment plant operation Two colloid-destabilant systems were studiedj Ludox-PEIM and MIN-U-SIL-Alunio Figures 33 and 34 show the results for the Ludox systenu For Figure 33 the slow mix intensity was 47 sec and for Figure 34 it was 18 sec , For these two figures the variable was time of rapid 107 i r apid O 1 ' T 1 T T ! I of R sec) 1 o — > ■rH T-t \ / o ■ 1 \ \ \ \ \ \ / H / ° / o ■ / • / / \ o kp / o -■ o \o / — to c \ \ o V s > Q V \ ■ / — 0) \ / H U \ 1 u^ \ J 1 Q) Uh \ s' r-- o to »h 0) Q ^ i K W O x ^ "~ a. (no r- H +j - ^ v\ D ° X • J- *L o sn ii t3 ^W 3 X) M 1 . N^*"*^ <-. O J fo O ^o * X X O X V) \ \ -H S CT M bOS H v^r ^S. « ?s° e e -o o ^S^/Siro ^V 5 «rH ,Q on o at O -H fl > H CO W (i! W (0 tf3s^v_K 1 1 1 1 1 1 I 1 1 1 1 1 *|^ o 1 00 o (D to C~- J" II o f- u w H S o o CD H E-< < CJ £ •rf fj B C9 O w < in § o h-f H M «^ 2 1— i O E-> O M J" E-i X CJ H < s a 3 o co p-l o H O W tM [i-l o H CM . CO co S o O p-1 U Uh 00 ID It CM O CO ID jj- CM CN CN CM CM CM H ■-) ( T _ru) -^ 'm 3HD 108 i o W CO u C l— I < < o X a M o H o Cm w 3- en o M o co ( T _ni) o o ' *N0I1V33H3DV JO JJJOJQ 109 mixing 0, 10 8 and 60 seconds The symbols for the experimental points are keyed to different runs The subscript numbers indicate the time of rapid mix in seconds For the MIN-U-SIL-Alum system, Figure 35, only and 60 sec of rapid mixing were provided „ The slow mix intensity in this case was 4 7 sec The noticeable trend shown by all three of these figures is that the initial rate of aggregation is increased by rapid mixingo An increase in the length of time of rapid mixing gives rise to a slight increase in the initial rate of aggregation „ However, during extended periods of slow mixing 9 dramatic changes in the clarity develop for samples rapid mixed for different periods of time It is thought that the reasons for the different initial rates of aggregation and the shifts in the apparent breakup may be quite revealing as to the funda- mental nature of the aggregation process As background material for the ensuing discussion two trends noted by visual observation will be mentioned. The trends that were visually observed, though most qualitative, were rather striking and consistent o They became apparent only in conducting kinetic studies of aggregation o For reactions with a rate constant of the order of magni- = 1 = 1 tude K 0„01 (min " TU ), large millimeter size aggregates were seen to develop rather dramatically within a short period of time * This generally happened within one to five minutes after the addition of the destabilant These were large, irregularly shaped, poorly packed aggregates that developed in a field of haze or small particles This "This was "noted" in "sucfi" systems as montmorillonite and cationic polymers, Ludox and PEIM, and MIN-U=SIL and Alum This was not observed in such systems as polystyrene latex and polymer or MIN-U-SIL and polymer 110 10 20 REACTION TIME (min) FIGURE 35. EFFECT OF RAPID MIX ON .AGGREGATION RATE FOR ALUM Ill gave the impression that the particle size distribution was bimodal With an increase in the intensity of mixing these large particles became smaller in size and greater in number , and the time interval before their appearance became smaller This rapid-mix- intensity-aggregate- size relationship was dramatically emphasized when adjacent beakers were rapidly mixed for different lengths of time and then slowly mixed for an extended period „* The difference in the size and number of the larger aggregates was quite apparent „ A second trend for these larger aggregates was observed visually o As the time of slow mixing was extended the large aggregates became smaller , greater in number, more spherical and presumably denser 9 i e , breakup occurred This observation is supported by the experi- mental results of Fair and Gemmell (1964) They determined photograph- ically the mean area per aggregate particle for three different G values as a function of mixing time,, Their results show that the aggregates formed from Fe(III) grew in size up to some point and then began de- creasing in size, i e , breakup was indicated These visual observations combined with the results indicated by Figure 33 are the basis for the ensuing discussion c The singularly critical feature of the process is felt to be the intensity of mixing before and during the period when the large millimeter size aggregates develop c It is critical because the intensity of mixing determines the size and number of the larger aggregates It is primarily these large aggregates formed in the initial stages of aggregation that are "In an effort to be certain of the apparent breakup, e o g , for 60 sec= onds rapid mixing , in Figure 33 , experimental points were obtained for a number of different runs Since rapid mix time could be selected an individual beaker, points for different rapid mix times were in- cluded in the same run, hence the possibility of visual comparison for adjacent beakers with different rapid mixing time 112 responsible for particle removal during the settling stage The most direct route for a small, primary particle to be removed in the sedimen- tation phase is to involve itself in a collision with one of these large settleable particles „ Thus the number and size of these larger par- ticles is quite critical in determining the apparent aggregation rate of settleable particles Of course, filtration tends to obscure these effects but decreased loading of filters increases their efficiency of operation, i e„, length of filter runs„ The above explains the fact that rapid mixing increases the apparent rate of aggregation s Also it suggests why theK dependence app on mixing intensity was exponential rather than linear, Section M-o4 Q That is„ in addition to the mixing effect increasing K , the smaller- ? & & app" size=large=aggregate effect comes into play, i e , not only are more collisions occurring due to the higher mixing intensity, but also due to higher number concentration of "settleable size" aggregates „ The question that must be answered now is why does the break- up begin sooner for the more extended period of rapid mixing, Figure 33 „ For this answer let us return to the observation that large aggregates are constantly reduced in size during the extension of the slow mixing period, ic,e , broken up Combine this with the observation that the initial size of the larger aggregates is reduced with extension of the rapid mix time The indicated result is that the large aggregates are broken down to a non- settleable size sooner, the smaller their initial size,, An additional question is why do aggregates formed in a field of high shear breakup in a field of lower shear? A possible explanation involves consideration of the time of exposure That is, the aggregates 113 are not exposed to the high intensity of shear long enough to reflect the density and degree of organization expected of an aggregate at equilibrium with this environment Traditionally, it has been reasoned that rapid mixing merely served the function of rapidly dispersing the destabilant to a uniform concentration j and thereby allowing the reactions, for the equilibrium concentrations, to get underway sooner This would mean that rapid mixing should eliminate any lag in commencement of a reaction at its "normal" rate However , rapid mixing should not affect the aggregation rate, per se The results in Figures 33 through 35 indicate that this is not the case 4 9 Optimum Dose and the Colloid Surface It is indicated in Figure 1 that the physical and chemical properties of the colloid surface are a variable of destabilization - and in turn K Theoretically it is possible to evaluate the signifi- cance of this variable by using different types of colloids with the same radii Unfortunately such colloidal materials could not be ob- tainedo There is, however, a qualitative comparison which gives insight into the interaction of this variable with the destabilant chemical - however, no judgment on the significance of this variable upon K is app possible o The comparison that is available is to relate the colloid surface concentration of different types of colloids to the optimum dose, P , for a particular polymer for a given milieu In Figure 36 the optimum dose of polyethyleneimine, PEIM, has 2 been plotted as a function of colloid surface concentration, cm l% % for a number of types of colloidal materials „ Table 14 is a tabulation of 114 m bn p •*- T) ti cd 5M 1 3. 3. 3 o o H Q J r- 03 00 -H a H m cn oo 5.; •H rr in C- o H P co 1 m • • I O • 3 1 o o o X o ■M H •^ 1-3 J 1-1 TJ c i-J i—i w CO CO 3 o CO a CM CM CM hJ s: Cm 1 1 - - - • IT) i - - O H \ - - CO ^\ - - H \ - 1 1 1 ^ in i o o • * (Tf/3ui) o in o (TF/Sui) N0IIVHJ.N30N00 HI3J WOWIIdO S3 o w H < Pi E-i C! S3 H M • o o w o < Cm Ctf O O H LO CO o Q ■H M O •— > i-3 o? i-4 O CM O e o CO 03 ^w' o O CO • 22 P4 O M £ H 2 c E-< l-f H w o S to S3 H CD o S3 • o W CJ M S3 CJ O < CJ Cm p£ W o 55 CO M d" Q M o M M * o S3 J W J J o >H o W ►J o CM Cu O ^ , M H Cm O o co CJ 115 H CD H Xi rd E-> O M < Pi S5 W o o a < < w o < Pn- CO l-M o § H O < CO < w CO o Q S M E-| Ph o & to 0) Q) fc /■■■s < CM -H C e lo en C- en in H O Z3 0) a + CM CO CM co CO CO P-, o \ o o o o o o o u rd bO <-i 00 CM H H H ■H ro w a) Mh £ W Ph S-i * — ' (d 3 s CO w P4 4-> CM CN J H CM O CM CM o in cm o o o d- r-i HI J- o m CO H -p c a H H & O e o 3 in i M CO t> ID +- co co m ct> co ii o m o o HD o c o h I I II i g ^ »J J J J H 00 CO CO CO S Ph O, Pl, pL, (fl D, 9 bO u o & q) c m & a) <4h rd -o±£ A | O H o ex w d CO 1 ix^r CO CM H o — (■j/Suj) eso a uinmi P-do A ^s^ D ^-^ n^W-*"*"^ -ds/ X o bO — d> E x ^*7 O i VoOyL o o rHH 1 • o X >i 03 •H d Initiall G = 18 s 6 C E i> in K i 1 Suspensio Age (hr) o CO ( sq.Tun ^TPiq^x) o CM (ST)1 o rH o « w LT> CD < fe O M CO fe; w (X, CO n CO o • X J- o Q :d j PH o ^ 5=5 c^ o ^\ r-f bO H E o O W • g CO W Cm CO o < Q CO W < !zr M w s CO M o u « s w w O J ^2 • >-l M CM X s H H £ W J W O •J P-i >-< X H B j o o CH • rH 2: n> s M H CH O • t- CO o £ D o o M Cm *N0I1VD3HDDV JO 33H33Q 121 amorphous silica and a commensurate decrease in the total surface area = thus a decrease in the polymer demand with age The results in Figure 38 for turbidity- age, indicate that the second alternative is the better one^ That is, the initial turbidity of the 102 mg/£ stock Ludox suspension decreased with suspension age Dissolution of the colloidal particles would decrease the scattering volume of the par- ticles and thus the turbidity since 2r200 hr) was calculated to be 115 mg/Jl as SiO-o This corresponds to 122 0.8 T Initially, 100 mg/£ Ludox TM Reaction @ 1.9 mg/£ PEIM 200 SUSPENSION AGE (hr) 300 .22 .18 — .16 D H ft 12 .08 — .04 400 FIGURE 38. INITIAL SUSPENSION TURBIDITY AND K AS A FUNCTION OF LUDOX SUSPENSION AGE apP 123 H I W ■P •H c D >■, ■P •H -d •H SU iS O M H < g u < o w u 10 20 REACTION TIME (min) FIGUPE 39. AGGREGATION OF LUDOX FOR VARIOUS SUSPENSION AGES 124 the experimentally determined values for the equilibrium concentration of dissolved SiO_ s for amorphous silica at pH 9 and 25°C 8 i e , 100- 150 mg/£ (Stumm s Htiper and Champlin, 1967) This value was calculated from surface area concentrations indicated in Figure 37 s and an initial particle diameter of 023 y, an initial particle specific surface area 6 2 2 of lo 4 x 10 cm /gm, particle density of 1 388 gm/cm , and particle 13 number concentration of 3(10) /ml (Table 4) It was assumed that the particle number concentration was constant and that the dissolved silica came from the decrease in particle diameter from o 023 y down to par- ticle size calculated from the data of Figure 37 „ The latter particle size was calculated by assuming that the decrease in the optimum poly- ethyleneimine dose between 1 and 360 hours represented a decrease in the Ludox surface area concentration and a commensurate decrease in particle diameter, viz , diameter at 360 hours = o 0189 y The aging effect of montmorillonite=anionic polymers was studied less extensively,, The scatter of results which was discovered was quite frustrating since no such effect had been found in the pre- vious studies on montmorillonite-cationic polymers From the results for the first anionic polymer used (Purifloc A-22) it was apparent that aging was occurring,, The results for this anionic polymer are shown in Figure 40 and Table 15 In Figure 40 representative degree-of- aggregation-vso -react longtime data are plotted for suspensions of two ageso The upper inserts show K versus suspension age and the lower insert shows the data for determination of optimum polymer dose at pH 7 and 240 hours of age An attempt was then made to confirm this apparent aging by using other anionic polymers „ Results for two other similar anionic 125 CO +J •H c D >-, ■P •H •H ,Q 5h fc 1.5 o H < CD u CD < o w y CD W Q ^ 0.6 mg/Ji A-22 pH 7 100 200 Suspension Age (hr) ^ pH 7 240 hr 0.5 1.0 A-22 Concentration (mg/£) 100 mg/i, Montmorillonite 0.6 mg/£ Purifloc A-22 G = 47 sec" pH 7 Suspension 20>— Age (hr) FIGURE 40, K app REACTION TIME (min) AS A FUNCTION OF MONTMORILLONITE SUSPENSION AGE FOR AGGREGATION WITH ANIONIC POLYMER 126 polymers, sodium polyacrylate and polyacrylic acid, are given in Tables 16 and 17. The results are not extensive enough to establish the aging trend precisely. However, it definitely is indicated that some change of the clay is occurring which gives rise to a change in K at a given dose of anionic polymer. Since the desired aim of using the clay Table 15 K AS A FUNCTION OF SUSPENSION AGE, M0NTM0RILL0NITE-A22 app Colloid: 100 mg/& Montmorillonite Polymer: 0.6 mgA Purifloc A-22 Mixing Intensity: G = 47 sec"- 1 - Suspension Age (hr) pH K app (min -1 TU -1 ) 1 tTo7 (TU" 1 ) 6 7 .0985 .38 16 7 .0656 .48 20 7 .0475 .24 48 7 .0385 .20 64 7 .0158 .061 140 7 .0226 .048 155 7 .0148 .07 165 7 .0134 .068 190 7 .0253 .02 240 7 .029 .023 21 5 .109 .50 40 8 .0052 .068 system was to approximate nature, i.e., the clay at equilibrium with the environment, it appeared that this system or idea was unsatisfactory. The scatter of results led to a decision to abandon this system in favor of colloids of known size which would allow for investigation of the other major variable, particle collision opportunity. Time did not permit a return to this aging problem. A change in the nature of the clay edges is suspected for 127 Table 16 K AS A FUNCTION OF SUSPENSION AGE, MONTMORILLONITE-PAA app • Colloid: 100 mg/£ Montmorillonite Polymer: 0.1 mg/£ Polyacrylic Acid Mixing Intensity: G = 47 sec -1 Suspension Age (hr) pH K app (min" 1 TU _1 ) 1 tToT (TU" 1 ) 24 8.4 .017 .053 26 7 .034 .017 51 6 .073 -.11 66 6 .054 .054 47 5 .36 .0075 Table 17 K AS A FUNCTION OF SUSPENSION AGE, M0NTM0RILL0NITE-PAC app Colloid: 100 mg/Ji Montmorillonite Polymer: 0.2 mg/fl, Na Polyacrylate Mixing Intensity: G = 47 sec" 1 Suspension K _wv a u a PP T(0) Age pH ii i (hr) (min TU -1 ) (TU -X ) 40 7.6 .117 .133 48 7 .0198 .052 110 7 .0287 .061 115 7 .0382. .0312 117 7 .0377 .0250 46 6 .0496 .0665 44 5 ,0797 .0738 128 three reasons: (1) the suggestion by authors (Ruehrwein and Ward, 1952) that anionic polymers adsorb predominantly at the positively charged edges of the platelets 8 (2) the fact that no apparent aging occurred when cationic polymers were used - which would tend to adsorb on the platelet faces 9 and (3) the extremely low solubility of the clay The change at platelet edges might be a chemical reaction and/or edge to face association of the platelet surfaces (van 01phen 9 1963) The latter is thought to occur because of the opposite charge of the two surfaces Since only a small fraction of the total surface area is edge surface, edge to face association could substantially reduce anionic polymer ad- sorption sites on the edges without significantly affecting the cationic polymer adsorption sites on the faces If edge to face association occurred it was of a limited extent since no effect upon aggregation rate for montmorillonite-cationic polymers was apparent 4 oil Qualitative Description of Aggregation by Polyelectrolytes For purposes of attaining a better understanding of aggrega= tion of dilute colloidal suspensions by polyelectrolytes 9 it seems appropriate to present a qualitative description of the process from the time of addition of the polymer to measurement of supernatant tur- bidity o As the destabilant chemical or polymer is added e diffusion- controlled adsorption occurs (La Mer and Healy, 1963a) The intensity of mixing during the addition determines the speed at which the desta- bilant reaches a uniform concentration Adsorption is accompanied or closely followed by perikinetic aggregation For a reasonably rapid reaction 9 adsorption and perikinetic aggregation are essentially 129 complete in a very short time, e o g , <1 min Due to reactant and/or shear non-homogeneities a few large aggregates grow to millimeter or even centimeter size in a matter of one to two minutes Shortly before the large aggregates appear 8 simultaneous aggregation and breakup begin to occur „ The relative rates of aggregation and breakup depend upon the degree of destabilization f the particle number concentration , par- ticle radius 8 the unique resistance of the aggregates to shear, and the uniformity and intensity of shear The intensity of shear during the formation of the larger aggregates is critical in that it determines the size and number con- centration of the larger aggregates This is critical because the apparent rate of aggregation e as reflected by settleable particles , is noticeably affected by the number concentration and size of these larger particles o With increasing time, the larger particles become smaller , more spherical, denser and greater in number Simultaneously, the smaller particles or microflocs form aggregates amongst themselves, but their prime means for removal in the subsequent settling phase is to be incorporated into the larger aggregates The reasons that superna- tant turbidity decreases throughout this time are that (1) the average particle radius is decreasing (T a l/r) 9 and (2) more and more particles achieve a settleable size and are thus removed from the lights scattering volume of liquid For some systems the reaction may be extended to a point at which the apparent degree of aggregation, tztttv ma Y decrease with time, Tit. ioe , breakup becomes apparent This is due to the fact that a portion of the larger particles have been broken down to an unsettleable size,. 130 During the course of the reaction the particle size distribution may possibly proceed as is shown schematically in Figure 41 In this figure the differential size distribution is shown before and at three times during the course of aggregation for a case where apparent breakup has begun to appear at the longest time Note that the left hand scale is many times larger than the right hand scale This is necessary to depict what is happening to the number and size of the larger aggregates, The ordinate represents the number concentration of particles for a size increment j divided by the average particle size of that increment The figure is intended to show that the large size aggregates are growing in number but decreasing in their maximum size c At the same time the smaller particles 9 which represent the bulk of the number of particles , are decreasing in average radius and number 4 12 Engineering Application The most significant result of this work is that an empirical equation for the rate of aggregation of dilute colloidal suspension has been offered,, It is significant because a method for obtaining rate data for reactor design is possible „ Numerous problems relating to scale-up remain to be solved but the underlying methodology has been developed,, The empirical second-order rate equation in supernatant turbidity can be written for a batch reaction as TTtT = tToT + K app t For relatively fast reactions the intercept 9 ^sT^rrs ^ s essentially zero 131 a) H O > X! C Part II o The Shape of the Adsorbed Molecule j The Adsorption Iso- therm Surface Tension and Pressure Jo Phys Chem 66sl884 Simha, R , Frischj, H L , and Eirich, F R 1953 c The Adsorption of Flexible Macromolecules Jo Phys Chem 57s584 von Smoluchowskig, M 1916 Drei VortrSge liber Diffusion, Brownsche Molekular bewegung und Koagulation von Kolloidterlchen Physik o £0 17s557 von Smoluchowski, M 1917 Versuch uner mathematischen Theorie der Koagulationskinetik kolloider Losungen 155, Z Physiko Chem 92sl29 Standard Methods for the Examination of Water and Waste Water „ 1965 APHA, AWWA, and WPCF, New York, N Y 12th ed Sterbacek, Z , and Tausk, P 1965c Mixing _ in _the_ Chemical Indus try u Pergamon Press, Inc, , New York, N Y Stoeber, W 1967 Formation of Silicic Acid in Aqueous Suspensions of Different Silica Modifications 161-182 Ins Equilibrium Concepts in Natural Water Systems, Adv in Chem 67 ACS Stumm, W 1966 Discussion (see Hudson, 1966) „ J New England Water Works AssoCo ' 80s246 o Stumm, Wo, Hiiper, H , and Champlin, R L 1967 Formation of Polysili- cates as Determined by Coagulation Effects „ Environmental Sci and Techo ls221 Swift, Do L , and Friedlander, S K 1964 The Coagulation of Hydro- sols by Brownian Motion and Laminar Shear Flos Jo Colloid Sci 19s621 Tanford, C 1963 Physical Chemistry of Macromo leculeso John Wiley and Sons, Inc , New York, N Y 145 Thome 8 R S, W„ 1961„ Application of Formazin Standards to Nephelo- metric Estimation of Beer Turbidity J Insto of Brewing,, 67j191 Timasheff, So E 1966 Turbidity as Criterion of Coagulation „ Jo Colloid and Interface Sci 21 5 489 Turkovichj, J„ 1959 The World of Fine Particles „ Am Scientist 47s97„ 146 VITA Roger Miles Jorden was born November 15, 1935, at Carthage, Missouri o He attended William B, Travis High School at Austin, Texas „ He obtained a Bachelor's degree in Geology in 1959 from the University of Texas, Austin, Texas and a Master's degree in Hydrology in 1962 from the University of Arizona, Tucson, Arizona He is a member of the American Water Works Association, Clay Mineral Society, and the Central States Water Pollution Control Association Prior to beginning his appointment as a Research Associate at the University of Illinois in 1964, he was a Research Associate in the Hydrology Division of the Travelers Research Center 8 Inc c , Hartford, Connecticut, from 1962 to 1964 He was a U S c Department of Interior Research Fellow in Civil Engineering, University of Illinois, from September 1967 through January 1968 He was the author of a paper entitled "Electrophoretic Studies of Filtration," Journal of the American Water Works Association, 55 s 771, 1963