Fuzzy Markov chains modeling of aggregation processes

Abstract

In this paper, the fuzzy Markov chain method is proposed as a new discrete solution of a population balance equation for an aggregation process. In order to validate the proposed method, analytical solution of an aggregation equation is compared with the fuzzy Markov chain method for the constant aggregation kernel. According to the results, if the size range of the system is divided into a sufficient number of states and an appropriate transition time step is chosen, then the fuzzy Markov chain method displays a good approximation for the particle size distribution(PSD) while the main equation is driven by a constant aggregation kernel.