Non-local mathematical models for aggregation processes in dispersive media

Particles aggregation is widespread in different technological processes and nature, and there are many approaches to modeling this phenomenon. However, the time non-locality effects with witch these processes are often accompanied leave to be none well elaborated at present. This problem is justified especially in reference to nano-technological processes. The paper is devoted to the non-local modification of Smoluchowski equation that is the key point for describing influence of synchrony and asynchrony delays in aggregation processes for clusters of different orders. The main scientific contribution consists in deriving the non-linear wave equation describing the evolution of different orders clusters concentration under aggregation processes in polydispersed systems with following for the mentioned non-locality. The practical significance lies in the fact that the results obtained can serve as the basis for the engineering calculation of the kinetics of aggregation in polydisperse nano-systems. The research methodology is based on mathematical modeling with the help of the relaxation transfer kernels approach. Succeeding analysis of aggregation processes on the base of submitted ideology can be directed to generalizing master equations with allowing for space non-locality too. The submitted approach opens up fresh opportunities for detailed study of influence of relaxation times hierarchy on the intensity of aggregation and gelation processes in non-crystalline media containing dispersed solid phase.