Coagulation hydrodynamic effects

Szpyrkowicz, L. (2005) Hydrodynamic effects on the performance of electro-coagulation/electro-flotation for the removal of dyes from textile wastewater. Ind. Eng. Chem. Res. 44,7844-7853. 

In the absence of better information, it is sometimes assumed that errors from the two assumptions in the Smoluchowski approach compensate for each other. Reductions in collisions resulting from hydrodynamic effects are assumed to be offset by increases in collision rates as aggregate volume increases while coagulation proceeds. The Smoluchowski approach modified to include hydrodynamic interactions is useful at the onset of aggregation processes, when the inclusion of fluid within aggregate pores is small. 

A second factor reducing the rale of collision arises from the fact that, as two particles approach closely, liquid has to flow out from the region between them. Experimental evidence based on measurements of rapid coagulation (which is similarly affected by this hydrodynamic effect) indicates that the collision rate is reduced to about half its expected value. 

As in the case of iron, the hydrodynamic regime of the water basin has a considerable effect on the processes of accumulation of siUca. In the case of simultaneous deposition of silica and iron, the sols of their hydroxides are usually converted to gels having the composition of ferruginous chlorites. In the case of coagulation of silica sol around submarine active springs with constant discharge, only small lenticular intercalations of spilite are formed. 

Hydrodynamic Models. The coagulation kernels are usually calculated for solid spheres with hydrodynamic models of different sophistication. The simplest calculation uses fluid flow in the absence of any effect of either particle on the flow. This flow level is known as rectilinear flow. The next level of sophistication involves calculating the flow around one particle, usually the larger of the two interacting particles. This level of calculation is known as curvilinear flow. Further levels of sophistication can be obtained by considering the particle trajectories as affected by the interacting flow fields of the particles, as well as any attractive or repulsive forces between them. 

Below, in Sections 5.2 and 5.3, we consider effects related to the surface tension of surfactant solution and capillarity. In Section 5.4 we present a review of the surface forces due to intermo-lecular interactions. In Section 5.5 we describe the hydrodynamic interparticle forces originating from the effects of bulk and surface viscosity and related to surfactant diffusion. Section 5.6 is devoted to the kinetics of coagulation in dispersions. Section 5.7 regards foams containing oil drops and solid particulates in relation to the antifoaming mechanisms and the exhaustion of antifoams. Finally, Sections 5.8 and 5.9 address the electrokinetic and optical properties of dispersions. 

The terms oc(i,j)s and A(i,/)s collectively describe a kinetic coefficient for the coagulation or aggregation of suspended particles of sizes i and j. They have analogies with but are not identical to the terms a(p, c) and tj(p, c) used previously in describing the kinetics of particle deposition processes in porous media. Like q p, c), the term l i,j)s incorporates information about various processes of particle transport, although as used here hydrodynamic retardation is not considered. Unlike t/(p, c), X(iJ)s is not a ratio of fluxes. It is a rate coefficient that includes most physical aspects the second-order coagulation reaction. Like a(p, c), the term a(i, j)s incorporates chemical aspects of the interactions between two colliding solids however, as used here, the effects of hydrodynamic retardation are subsumed in ot(iJ)s. The term a(i,j)s is a ratio defined here as follows ... 

Hydrodynamic Forces Fluid mechanical interactions between particles arise because a particle in motion in a fluid induces velocity gradients in the fluid that influence the motion of other particles when they approach its vicinity. Because the fluid resists being squeezed out from between the approaching particles, the effect of so-called viscous forces is to retard the coagulation rate from that in their absence. 

The role of hydrodynamic interaction in Brownian diffusion was discussed in Section 8.2. Consider now its effect on turbulent coagulation. Formally, it can be taken into account in the same manner as in Brownian motion, by introducing a correction multiplier into the factor of turbulent diffusion (10.57). Another, more correct way (see Section 11.3) is to use the Langevin equation that helped us determine the factor of Brownian diffusion in Section 8.2. As was demonstrated in [60], the factor of turbulent diffusion is inversely proportional to the second power of the hydrodynamic resistance factor ... 

Honig E. P., Roebersen G., Wiersema P. H., Effect of hydrodynamic interaction on the coagulation rate of... 

The principal shortcoming of the turbulent coagulation model offered by Levich [19] and rejected by many researchers is that it seriously overestimates the collision frequency of drops. Therefore the shear coagulation model [110] of particle coagulation in a turbulent flow has emerged as by far the most popular one. Since Levidfs model does not take into account the hydrodynamic interaction of particles, let us estimate the effect of this interaction on the collision frequency. 

For Browrtian diffusion of small particles, the influence of hydrodynamic interaction on the collision frequency was studied in works [28, 29], which also mention the decrease in the collision frequency by a factor of 1.5-2. This decrease is not as large as in the case of turbulent coagulation. There are two reasons why the effect of hydrodynamic interaction on the collision frequency of particles differs so substantially in the cases of turbulent flow and Brownian motion. First, the particle size is different in these two cases (the characteristic size of particles participating in Brownian motion is smaller than that of particles in a turbulent emulsion flow). Second, the hydrodynamic force behaves differently (the factor of Browrtian diffusion is inversely proportional to the first power of the hydrodynamic resistance factor h, and the factor of turbulent diffusion - to the second power of h). 

A helpful presentation which illustrates the effect of shear rate on dispersions is to use dimensionless quantities as the axes. In this way the colloidal forces can be represented as the ratio of electrostatic repulsive terms to the attractive term, i.e. ereo i R/A and the hydrodynamic terms as the ratio of the shear term to the attractive term, i.e. (mr)R y/A. Following Zeichner and Schowalter [90] this is illustrated in Figure 3.30. Thus as illustrated by the arrow the impact of a shear gradient can move particles out of the secondary minimum association into a region of stability. However, as the shear rate increases still further primary minimum coagulation can occur until at even higher shear rates the particles are redispersed again. 

Hydrodynamic and solvation factors, emulsion stability, microemulsions, multiple emulsions, coagulation and flocculation theory, foam stability, demulsiflcation and defoaming, the effects of adsorbed polymers on stability and flocculation... 

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