Rate of flocculation

By combining the Rayleigh theory with the Smoluchowski-Fuchs theory of flocculation kinetics [7, 8], the following expression can be obtained for the variation of turbidity with time. 

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Fig. XIV-9. Effects of electrolyte on the rate of flocculation of Aerosol MA-stabilized emulsions. (From Ref. 35.)...

The natural process of bringing particles and polyelectrolytes together by Brownian motion, ie, perikinetic flocculation, often is assisted by orthokinetic flocculation which increases particle coUisions through the motion of the fluid and velocity gradients in the flow. This is the idea behind the use of in-line mixers or paddle-type flocculators in front of some separation equipment like gravity clarifiers. The rate of flocculation in clarifiers is also increased by recycling the floes to increase the rate of particle—particle coUisions through the increase in soUds concentration. 

It was found that [5-7] the rate of flocculation of particles produced by the bridging action of polymer is the slower process and, consequently, the rate-determining step. The primary adsorption of polymer is fairly rapid, but the slow attainment of the adsorption equilibrium under agitation arises at least in part from the breakdown of floes offering new surfaces for adsorption. Thus, the bridging step is slow because a polymer adsorbed on one particle must find another particle having a free surface available to complete the bridge. 

Polymers are suspended as microparticles in the latex and interactions between these microparticles are prevented by the presence of adsorbed suspending agent and soap molecules. Blending results in a random suspension of dissimilar particles in the mixture of latexes, each unaffected by the other. Rate of flocculation depends entirely on the stabilizer and not on the polymer characteristics as such. Coagulated mass contains an intimate mixture of the polymers. Acrylonitrile butadiene styrene (ABS) polymers [23-25] may be prepared by this method. 

For each type of polymer, the rate of flocculation and settlement tends to improve with increase in MW however, very rapid settling may lead to fines being left in suspension. 

The principle of this method is that the initial slope (time = zero) of the optical density-time curve is proportional to the rate of flocculation. This initial slope increases with increasing electrolyte concentration until it reaches a limiting value. The stability ratio W is defined as reciprocal ratio of the limiting initial slope to the initial slope measured at lower electrolyte concentration. A log W-log electrolyte concentration plot shows a sharp inflection at the critical coagulation concentration (W = 1), which is a measure of the stability to added electrolyte. Reerink and Overbeek (12) have shown that the value of W is determined mainly by the height of the primary repulsion maximum in the potential energy-distance curve. 

Having considered the factors that govern the extent or rate of flocculation in an aerosol, it is also important to consider the effects of flocculation on the properties of an aerosol. Consider a large sphere of diameter Dpl, with its surface covered with small particles of diameter Dpi. If the adhering particles are no more than one layer thick, it can be shown as a good first approximation that... 

Ambipolar charges can give increased deposition but such deposition depends for the most part on image effects. In this sense the rate of deposition will be comparable with the rate of flocculation of ambipolar aerosols. Improved deposition rates by such means are likely to be small. 

The rate of flocculation of selenium sols by solutions of potassium or barium chloride of various concentrations at temperatures between 15° and 20° C. has been determined.8 Results show that a very high concentration of these electrolytes is necessary for rapid flocculation. Smoluchowski s theory holds when the velocity of flocculation is not far removed from that obtaining when the colloidal particles are totally discharged. The results, however, deviate largely from this theory when the concentrations of the electrolytes are lower.3... 

Each particle is considered as a center to which other particles diffuse by Browian motion. Thus the rate of flocculation is proportional to the square of the number of particles. The original treatment assumed that all interparticle collisions were effective in causing flocculation. Later modifications (6) assumed that the potential energy barrier between particles resists flocculation and that only those collisions with sufficient energy to overcome this barrier will cause flocculation. The agitation-induced flocculation has also been analyzed theoretically (7). 

Flocculation processes are complicated phenomena because of the varieties of both particle morphology and chemical reactions they encompass.34 A few concepts of a general nature have emerged, however, and they will be the focus of this chapter. From the perspective of kinetics, perhaps the most important of these broad generalizations is the distinction that can be made between transport-controlled and reaction-controlled flocculation, parallel to the classification of adsorption processes described in Section 4.5. Flocculation kinetics are said to exhibit transport control if the rate-limiting step is the movement of two (or more) particles toward one another prior to their close encounter and subsequent combination into a larger particle. Reaction control occurs if it is particle combination instead of particle movement (toward collision) that limits the rate of flocculation. 

Since z > 0 for an increasing cluster size with time (Eq. 6.44), 6 < 1 in Eq. 6.48. Thus the homogeneity condition satisfied by the second-order rate coefficient determines the rate of floccule growth and the corresponding decline in the number of floccules (Eqs. 6.42 and 6.44). 

Surface electric potential control (or surface charge control) of the rate of flocculation is possible for any adsorptive that forms a surface complex with suspended particles, as discussed in Section 6.1 and in Chapter 4 (cf. Table 4.2). Among these adsorptives for soil colloids are oxyanions, such as phosphate or oxalate, and transition metal cations. An expression analogous to Eq. 6.78 can be developed to define points of zero charge for any such adsorptive, as illustrated in Fig. 6.9.42... 

St. Clair states that the lowest frequency which is found effective for small particles is about 4000 cycles. About 7000 cycles are required for tobacco smoke. With regard to rate of flocculation, St. Clair (1940) found that the rate of flocculation was proportional to the power input and almost proportional to the concentration of suspended material. By rate of flocculation is meant the relation between the final and initial average particle-size determined by optical methods similar to those implied in Eq (9-30). 

The experiments with aqueous dispersions (4) indicated a somewhat different behavior, both with respect to the initial rate of flocculation and the equilibrium state. The initial rate of flocculation increased from zero to a maximum value and decreased to zero as the free polymer concentration was further increased, indicating restabilization at higher concentrations. The amount of floe phase formed has also been observed to go through a maximum with increasing free polymer concentration. The restabilization phenomenon at higher polymer concentrations could not be detected in nonaqueous dispersions (1-3). 

The stability ratio usually is measured by determining the initial rate of flocculation under reaction or transport control, with these two conditions... 

For CFC-based suspension formulations, a surfactant was typically included. A variety of surfactants were used in these systems, e.g., lecithin, oleic acid, sorbitan trioleate. " All these surfactants were freely soluble in the CFC propellants and allowed for a degree of control over the suspension characteristics. Rates of flocculation, sedimentation, and creaming could be controlled and deposition on the internal container components was minimized. The transition to HFA-based MDIs has created significant issues in that none of the surfactants, previously used with the CFC products are soluble in HFA propellants alone. Some formulations have still used these surfactants, but the addition of a cosolvent (ethanol) has been required to solubilize the surfactant. 

The present paper deals with kinetics of coagulation of Phthallylsulfathiazole stabilized xylene in water emulsion in the presence of some cationic detergents. Rate of flocculation, rate of coalescence and rate of creaming have been determined. To estimate the stability of the present systems their zeta potentials have been measured and stability factors calculated. Temperature effect on the system was also studied. 

Rate of flocculation was determined by counting the number of particles haemocytometrically using an improved Neubauer model. 

Figure 3 shows the effect of increasing particle size on the relative rates of creaming and gravity-induced flocculation. As the particle size increases, the rate of flocculation increases faster than the creaming rate of the particles. This is a result which, at first, one wouldn t expect. According to Equations (4), (10), and (11), the total rate of particle loss due to creaming R is... 

Another mechanism of flocculation is that involving the secondary minimum (Gmin) which is few kT units. In this case, the flocculation is weak and reversible and hence both the rate of flocculation (forward rate k ) and deflocculation (backward rate k ) must be considered. In this case, the rate or decrease of particle number with time is given by the expression ... 

Two main procedures can be applied for the characterisation of suspensions and assessment of their stability (such as flocculation). The first method depends on the measurement of particle size distribution and the rate of flocculation and/or Ostwald ripening after dilution of the suspension with the dispersion medium, while the second procedure depends on measurement of the state of suspension without dilution, using rheological techniques. As both methods are described in detail in Chapters 19 and 20, only a summary will be provided here. 

The backward reaction (break-up of weak floes) reduces the overall rate of flocculation. 

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