Kinetic aggregation models leading to morphological memory of formed structures

Kinetic equations describing the evolution of dispersed particles with different properties (such as the size, velocity, center-of-mass coordinates, etc.) are discussed. The goal is to develop an a priori mathematical model and to determine the coefficients of the resulting equations from experimentally obtained distribution functions. Accordingly, the task is to derive valid (physicochemically justified) aggregation equations. The system of equations describing the evolution of the discrete distribution function of dispersed particles is used to obtain continuum equations of the Fokker–Planck or Einstein–Kolmogorov type or a diffusion approximation to the distribution function of aggregating particles differing in the level of aggregation and in the number of constituent molecules. Distribution functions approximating experimental data are considered, and they are used to determine the coefficients of a Fokker–Planck-type equation.