Limited flocculation theory

The collision theory [15] and the concept of the limited flocculation process were originally used to calculate the values of Rc and Rf, respectively. Later, the diffusion theory [17,18] was adopted by Fitch to calculate the value of Rc [31]. It was pointed out that the concentration of oligomeric radicals with chain length of j in the continuous aqueous phase, which was required to carry out the calculation, was very difficult to be determined. 

While the model was in general agreement with the limited experimental data published on bulk PVC particle size distribution, there is still no generally applicable theory describing particle growth and flocculation in the presences of mechanical agitation for precipitation polymerizations. 

Studies on orthokinetic flocculation (shear flow dominating over Brownian motion) show a more ambiguous picture. Both rate increases (9,10) and decreases (11,12) compared with orthokinetic coagulation have been observed. Gregory (12) treated polymer adsorption as a collision process and used Smoluchowski theory to predict that the adsorption step may become rate limiting in orthokinetic flocculation. Qualitative evidence to this effect was found for flocculation of polystyrene latex, particle diameter 1.68 pm, in laminar tube flow. Furthermore, pretreatment of half of the latex with polymer resulted in collision efficiencies that were more than twice as high as for coagulation. 

In summary, polymeric flocculants generally increase peri-kinetic flocculation rates compared with perikinetic coagulation rates. This is not necessarily true for orthokinetic flocculation, and experimental results in the literature are seemingly in conflict. Collision rate theory predicts that the polymer adsorption step may become rate limiting in orthokinetic flocculation. The present study was designed to elucidate the relationship between polymer adsorption rates and particle flocculation rates under orthokinetic conditions. 

The potentials (7-1), (7-2), and (7-4a), when combined, form the basis of the celebrated DLVO (Derjaguin and Landau, 1941 Verwey and Overbeek, 1948) theory of colloid stability. This theory is useful in predicting the conditions of surface potential, ionic strength, and so on, under which flocculation will occur. But the theory has important limitations, in part because it only considers van der Waals, electrostatic, and hard-core interactions. 

From the survey of the above literature, it is concluded that only a limited work is done on such type of problems. In the present study, the stability of emulsion has been discussed in the light of Derjaguin, Landau, Vervey and Overbeek theory (8) using Deoxyribonucleic acid and ribonucleic acid as flocculants for the emulsion stabilized by the drug sulphapyridine. 

Abstract A united mathematical model for the rheological and transport properties of saturated clays is proposed. The foundation of the model is the unification of filtration s consolidation theory and the theory of the stability of lyophobic colloids, which is based on the conception of disjoining pressure as a surplus in relation to hydraulic pressure. This pressure is caused by surface capacities and exists in water films between clay particles. In this work it is shown that the problem of the shrinkage of a clay layer can be reduced to the well known problem. We obtained the approximate solution for pressing the water out of a clay layer. The solution that we obtained requires introduction of a concept for the limit shear stress for clays. We investigated the model, and explained some characteristic features of transfer processes in clays (the existence of anomalous high pressures in clays, the flocculation at diffusion in clays, etc.). It is shown that solutions which we received are in harmony with results of experiments. 

Qualitative predictions of the theory Provided that L3 is not excessively small, the interpenetrational domain will determine the flocculation behaviour in heterosterically stabilized systems, just as it does in homosteric stabilization. In the limit of small L3, the interpenetrational-plus-compressional domain may well become important in predicting incipient instability. The elaboration of the general principles that govern heterosteric stabilization is then quite different. 

The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of charged colloids [58] predicts a substantial decrease in stability against flocculation with decreasing particle radius. Most likely the newly formed nuclei are not yet stabilized, and stability sets in only after a certain radius is obtained. After this size is reached, particles grow through monomer addition either reaction- or diffusion-limited, but with an overall rate still depending on the hydrolysis. 

This simplification will be the less detrimental the larger the size of the particles. If we tahe (more or less arbitrarily), as the limit of applicability, that the edge length of the particles (imagined to be cubes) b must be at least 5 X the double layer thickness or the characteristic length 1/k, we find that for 1—1 valent electrolytes the present theory may be roughly applied if the particles are > 5.10 cm, ( flocculating x-value about 10 ). For 2—2 valent electrolytes we find in the same way as a limit b > 2.10 cm, for 3—3 valent electrolytes b > 5.10 cm. 

One of the simplifications used in the theory of colloid stability given above is that we have associate the flocculation limit more or less arbitrarily with a total potential energy curve for which the point V/ -b = 0 coincides with the maximum of the curve. If we now drop this simplification we shall have to consider that the sol particles are able to pass over an energy barrier owing to their thermal motion. 

The intersection points in both sets of curves will now give the ionic concentrations corresponding to the flocculation limit for the three values of the double layer potential giveo above. The difference from the more simple theory is clearly illustrated. The values of the electric potential <1, ) in the different cases are appreciably lower than the double layer potential pQ. In comparison to our simpler theory, working with... 

The emulsification process is so dynamic and complex that an accurate model and theoretical treatment is almost impossible. With certain limitations its is possible to obtain order-of-magnitude estimates of such steps as droplet formation rate and surfactant transport and adsorption rates. However, the work involved is seldom worth the trouble in practice. Flocculation and coagulation rates during preparation are difficult to analyze because of the dynamics of the process and the turbidity of the flow involved. Collision rate theory... 

Flocculation is a kinetic process and the rate at which a colloidal suspension flocculates forms one of its most important characteristics. Smoluchowski (1917) distinguished between rapid flocculation and slow flocculation and developed a theory based on the rate of collision between the particles (2). Rapid flocculation is considered to take place in the absence of a potential barrier and is limited only by the rate of diffusion of the particles towards one another. The flocculation time, defined as the time tia required for the number of particles to be reduced by one-half of the initial value is given by... 

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