Analytical and numerical results in the kinetics of particle coagulation and fragmentation processes

General relations in the kinetics of particle coagulation and fragmentation in dispersed systems are presented, a development of the corresponding models is proposed and new analytical and numerical results for the kinetics of these processes are obtained. Versions of the kinetic equation for multiple and pair fragmentation are formulated that enable analytical solutions to be obtained in the case of simplified relations for the rates of these processes. New solutions of the stationary kinetic equation are obtained in a study of stationary conditions and a method is proposed that enables the spectra to be found numerically over a very wide range of particle sizes: when the lower and upper boundaries of the spectrum differ by 11–14 orders of magnitude. The possible types of self-similar conditions are analysed and the conditions necessary for their existence are formulated. It is shown that coagulation with pair fragmentation is a diversified and non-trivial field of study. A set of processes is obtained: a steady-state process, the predominance of coagulation, critical phenomena, a collapsing self-similarity (accumulating particles in the initial size range) and singularity of the particle spectra. The listed diversity of the processes is demonstrated for model coagulation and rates of fragmentation kernels. Both analytical methods and numerical calculations are used in the analysis.