Kinetics of flocculation

Equation (2.33) tends to overestimate the particle flocculation rate for the electrostatically or sterically stabilized colloidal dispersions due to the potential energy barrier established between the approaching particles against particle flocculation. Fuchs [45] was the first to introduce the stability ratio (W) to take into account the fact that not aU the collision events lead to successful coagulation of colloidal particles. 

The reciprocal of the stabihty ratio (1/W) simply represents the fraction of collisions that effectively results in the formation of doublets. The larger the Gibbs free energy of interactions (AG), the larger the stability ratio (W). As a result, a more stable colloidal system is achieved. Under these circumstances, the particle flocculation rate can be written as 

Reerink and Overbeek [46] showed that the maximum Gibbs free energy of interactions between an isolated pair of particles (AG ax) predominates in the slow particle flocculation process and the stability ratio (W) can be estimated by the following equation  

Equation (2.37) predicts that increasing k (or concentration of counterion) results in a significant reduction in both the preexponential term (l/(2Ka)) and AGmax It was also proposed that the influence of the electrolyte concentration (C) on the stability ratio can be described by the following equation  

For those who are interested in the details of the particle flocculation kinetics, refer to references 2, 18, 19, and 39. 

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Overbeek J Th G 1952 Kinetics of flocculation Colloid Science vol I, ed H R Kruyt (Amsterdam Elsevier) pp 278-301... 

As with experimental work on polymer adsorption, experiments in the area of dispersion stability in the presence of polymers require detailed characterisation of the systems under study and the various controlling parameters (discussed above) to be varied in a systematic way. One should seek the answer to several questions. Is the system (thermodynamically) stable If not, what is the nature of the equilibrium state and what are the kinetics of flocculation If it is stable, under what critical conditions ( s, T, x> p etc.) can flocculation be induced ... 

The von Smoluchowski scheme based on Equations 5.326 and 5.327 has found numerous applications. An example for biochemical application is the study of the kinetics of flocculation of latex particles caused by human gamma globulin in the presence of specific key-lock interactions. The infinite set of von Smoluchowski equations (Equation 5.319) was solved by Bak and Heilmann in the particular case when the aggregates cannot grow larger than a given size an explicit analytical solution was obtained by these authors. 

The dependence of the optical density (A) of PSL on the concentration of various types of polyampholytes is presented in Fig. 26. The flocculating effectiveness of polyampholytes is arranged as follows PMAA-fo-PlM4VPCl >AA-VI >MAA-TMVEP >AA-DMVEP and is in good agreement with the sequence of their electrokinetic potential (Fig. 27). The kinetics of flocculation of PSL allow the evaluation of the magnitude of the retardation factor W which characterizes... 

The theoretical description of the mutual approach and coalescence of two emulsion drops is the subject of Sec. IV the Bancroft rule on emulsification is interpreted and generalized in Sec. V and the kinetics of flocculation is considered in Sec. Vt, where the size of the aggregates needed for the creaming to start is estimated. 

Part I deals with the single double layer. Part II with the interaction of two flat plates, and here most of the fundamental results of the theory already come to the fore. Part III gives a treatment of the, interaction of spherical particles, which serves to clarify various details, especially the influence of particle dimensions and of the kinetics of flocculation. 

One can use these principles to study the kinetics of flocculation. Assume that the rate of flocculation in a dilute sample is very small, such that over the... 

Barany S, Meszaros R et al (2011) Effect of polyelectrolyte mixtures on the electrokinetic potential and kinetics of flocculation of clay mineral particles. Colloids Surf A 383 48... 

In studying flocculation in such fixed beds (and also for fluidized beds) it is difficult to follow the kinetics of flocculation, or even to study the reduction... 

The kinetics of flocculation in a fluidized bed are described by the equations in section 4.8. The simplified Smoluchowski equation 4.42 can be modified by the special bimodal distribution of the fluidized bed (floe blanket) particles ... 

The kinetics of flocculation are discussed in chapter VII Chapter VIII gives the synthesis of these two fields resulting in a theory of the stability of colloids This theory is compared with experiments Moreover, as far as experimental data on stability exist which are not yet related to the thepry, they will also be treated in chapter VIII ... 

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