Double layer model, coagulation

Because the double layer force vanishes in the absence of surface charges, one expects the attractive van der Waals force to cause the coagulation of all neutral (or even weekly charged) colloids. The absence of such a behavior has been explained by the existence of an additional (non-DLVO) force, the hydration interaction, which is due to the structuring of water in the vicinity of hydrophilic surfaces. This chapter is devoted to the identification of the microscopic origin of the hydration force, and to the presentation of a unified treatment of the double layer and hydration forces, the Polarization Model. 

This method of formulation by von Smoluchowski and Fuchs is limited to small concentrations of particles. Then the fixed particle can at most feel the presence of one other particle, and (p is equal to the sum of the van der Waals attraction and the electrical double-layer repulsion poteitial, or, as discussed in previous sections. In this limit it is also legitimate to model the reaction as a second-order reaction (i.e., only two-particle collisions can occur and the higher body collisions are virtually nonexistent). In aerosols, which arc colloidal dispersions in air, there is no significant electrical repulsion betwerai particles. Hence the effect of interparticle forces on the initial coagulation rate is negligible, and we find... 

The Derjaguin and Landau and Verwey and Overbeek, DLVO, theory, the most widely accepted for colloidal stability (13,14), is based on a model in which the rate of coagulation is determined by the diffusion of particles toward each other in the presence of a potential field. This field is the result of molecular attractive forces of the Van der Waals type and repulsive forces due to the interaction of the electric double layer around the particles. The attraction between particles immersed in a fluid is considered in this theory to result from London dispersion forces. Hamaker (15) has shown that the magnitude of the potential due to these forces increases rapidly as the particles are brought closer together. 

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