Probability Cellular Automaton-Aided Modeling of the Stirring Effect in the Autocatalytic Step of the Belousov−Zhabotinsky Reaction

Abstract

A probability cellular automaton (PCA) is suggested. With its aid, the molecular diffusion, Belousov−Zhabotinsky (BZ) chemical reaction, and turbulent stirring are simulated by the Monte Carlo method. The Oregonator model was taken as the simplest model for the BZ reaction. Lattice maps vividly demonstrate the emergence of nuclei (microheterogeneities) at the autocatalytic step of the BZ reaction. The dependence of the nucleus size on stirring rate and on the molecular diffusion coefficient D0 are shown. S-wise dependencies of the induction period Tind of the autocatalytic step on stirring rate are obtained. The dependencies of the stirring effect magnitude on (1) volume Vm of the PCA elementary cell, (2) coefficient D0, (3) the total number of cells in the PCA lattice, and (4) the rate of the BZ system approach to the critical point are studied. The results of computer simulation are in good agreement with the experimental data.