3 лаб / Formulas

The local kinetic coefficients of the attachment and of the segregation depend on chemical and physical properties of colloidal system. Of the great importance is the structure of the last term in Eq.(2) (recombination). The number of recombined particles is proportional to the number of aggregated particles in a unit volume, on the other side, the recombination probability should be a decreasing function of the number of interparticle bonds and should be dependent on the presence of the free volume in local vicinity of the aggregated particle. Outside the aggregate volume the distribution of single particles concentration is described by ordinary diffusion equation:

At the aggregate boundary conditions of continuity of chemical potential and balance between diffusion flux of particles should be satisfied. Moreover, boundary motion equation is given, therein it is assumed that the boundary moves due to the particle combination (recombination) by the value approximately equal to the particle radius.

The main physical result is the power dependence of aggregated particle concentration on spatial coordinate

where, is the length dimensional coefficient, which may be considered approximately to be equal to the particle radius.

Подпись к рисунку: Fig.1. Radial dependence of the aggregated particle concentration.