FILTRATIOLV IN FLOCCULATION AND REDISPERSION OF COLLOIDAL SYSTEMS
Nov., 1963
2417
THE ROLE OF FILTRATION IN INVESTIGATING FLOCCULATION AND REDISPERSION OF COLLOIDAL DISPERSIONS BY VICTORK. LA MER AND THOMAS W. HEALY DeparIments of Mineral Engineering and Chemistry, Columbia University, S e w York 97, Xew York Received M a y 25, 1963 The state of flocculation and redispersion of colloidal systems may be followed by measurements of turbidity, rate of subsidence, sediment volume, or rate of filtration. Filtration has proven t o be the most quantitative method and can now be interpreted in terms of basic theory. The adsorption process upon which the theory depends has been examined quantitatively, and its relation to Langmuir’s isotherm is discussed. Evidence is presented that the terms coagulation and flocculation do not represent identical concepts or mechanisms. They should be distinguished; criteria for their distinction are given on the bases of theory and of observation.
Introduction When high molecular weight natural or synthetic polymers are a,dded to colloidal dispersioiis of solids in liquids, they frequently induce, over limited ranges of concentrations, a dramatic flocculation of the dispersion. As the coiicentration of the polymer is increased, the successive changes of state from dispersed to flocculated to redispersed may be followed by measurements of turbidity, rate of subsideiice, or rate of filtration of the flocculated suspensions. La RIer and co-workers, in an extensive study of this subject, have found that measurements of the refiltration rate offeir a means of characterizing quantitatively the state of flocculation. The technique is simple, and the data can be reproduced with surprisingly high precision under controlled conditions. For the flocculated state, the rate of refiltration through a cake approaches a maximum value, whereas for the dispersed state it is a minimum. Filtration rate measurements are of particular value in characterizing the state of flocculated systems, since they take cognizance of the presence of both the large flocs which yield large pores and the incompletely flocculated material called “haze” which obstructs the pores. The theory of Smellie and La Ner2 utilizes a limiting form of the IZozeny--Carman equation for filtration through a porous bed to correlate filtration rate (Le., the measure of extent of flocculation) with the concentration of added polymer. In this form of the equation only the geometry of flocs and pores are involved. The predictions of the filtration theory have been verified for many polymer-solid system^.^-^ Recently, Healy and La Mer3 modified the theory by iiicorporating molecular parameters for the solid surface and the polymer molecule in the original adsorption equations. It wa,s shown that the optimum polymer coiiceiitration p,, i.e., that coiiceiitratioii which produces the maximum filtratioii rate for a giveii system, is given by
P,
=:
(1
+ bk/P)2/b
(1)
Here p is the number of segments of an adsorbed molecule that cover surface sites, and b is the ratio of rate (1) V. IC. La Mer and R. H. Smellie, Jr., J . Coolloid Sei.,11, 704, 710, 720 (1966); 13, 589 (1958); V. K. La Mer, R. H. Smellie, Jr., and P. K. Lee, ibid., 12, 230, 566 (1957). A summary of this work appears a s a chapter in “Clays and Clay ILlinerals,” Vol. 9, Pergamon Press, New York, N. Y., 1961, p. 295. (2) R. H. Smellie, Jr., and V. K. La Mer, J . Colloid Sei.,13, 589 (1968). (3) T. W.Healy aIid V. K. La Mer. J . Phws. Chem., 66, 1835 (1962). (4) J. C. Xane, V. K. La Mer, and H. B. Linford, ibid., 67, 1977 (1963).
coiistaiits for adsorption-desorption of segmeiits a t the surface. IC is given by lc
8x0
= -
N
where s is the number of adsorption sites per unit area, So is the specific surface area, arid N is Avogadro’s number. With the aid of eq. 1 and other equations of the flocculation t h e ~ r y , ~ it -is~now possible to give a more detailed analysis of the reactions occurring between the polymer molecules and the dispersed colloid. For further details the reader is referred to a recent comprehensive review of the literature pertaining to both polymer adsorption and polymer flocc~lation.~ Theory I n their initial preseiitatioa, Smellie and La Xer2 proposed that adsorption of the polymer at the solidliquid interface be described by an adsorption equation of the form of Langmuir’s, vix.
e ~
1-e
=
bP
(3)
where 0 is the fraction of surface covered, P is the residual polymer coiicentration (in moles of polymer/g. of solid), and b is an adsorption constaiit, defined as the ratio of adsorption-desorption rate constants for the reaction of the adsorbing species with the solid surface. We have shown previously (eq. 1,ref. 3) that
P
=
p0 - ke/p
(4)
where Po is the added or initial concentratioii of polymer. Combining eq. 3 and 4 and rearranging
where, as before, k is defined by eq. 2 . Plots of eq. 5 are linear from which values of P / k and b have been obtained for each molecular weight and time of agitation. Substitution of these values in eq. 1 gives values of P, which have been designated as P, (adsorption). The filtration theory of Smellie and La Mer, and the modified theory also, yields as a final equation
where Qo is the measured filtratioii rate of the dispersion in the absence of added polymer, and Q is the filtration ( 5 ) V.
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