Particle separation distance

Application of Smoluchowski s equations typically results in an overestimation of the growth rate of aggregates due to the assumption that all collisions result in permanent attachment. Recognition of the importance of surface properties in the aggregation of small particles prompted Fuchs [6] to develop expressions to modify Smoluchowski s equations. Fuchs described the effect of the repulsive electrostatic interaction between two particles, which is a function of the particle separation distance, as a reduction in particle coagulation rate, Wy, termed the stability ratio. 

For sterically stabilised dispersions, the resulting energy-distance curve often shows a shallow minimum at particle-particle separation distance h comparable to twice the adsorbed layer thickness 5. For a given material, the depth of this minimum depends upon the particle size R, and adsorbed layer thickness S consequently, decreases with increase in S/R, as illustrated in Figure 11.4. 

Thus, it is seen that both duN/9r and d /dvk functionally represent the sum of all gradients in the functions un and 0, respectively, in terms of the pair-particle separation distances from a given locator molecule at. Because there are no spatial variations in any thermodynamic property for a system at equilibrium, these terms must be independent of the choice of the locator molecule vector with momentum p,. Thus, each term of the sum in Eq. (4.3) must be identical, and since the sum of the terms is zero, each term must be identically zero. For any th... 

There are three main types of particle interaction (Lyklema, 1985) Van der Waals attraction (mainly London forces), electrostatic forces and steric effects. These interactions depend on the shape and size of the particle, surface charge, solution composition (pH, ionic strength etc.) and temperature, and - most importantly, the particle separation distance, h. 

Figure 12.9 shows the overlap of adsorbed layers of uniform concentrations for several geometries for layers that have a thickness of 5 and a particle-to-particle separation distance of H. 

Table 5.7 Polarisation phase obtained using an initial particle separation distance ro = 6.0 A...

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