Numerical simulation of oscillatory zonation patterns in reaction-diffusion systems

The oscillatory zonation patterns in reaction diffusion systems are numerically simulated by lattice Boltzmann method (LBM). The formation of Liesegang patterns in rectangular enclosures is modeled in the perspective of supersaturation mechanism based on Ostwald´s theory. The approach, originated from the microscopic dynamics of cellular automata, includes the essential features of reaction-diffusion systems, and the nucleation and aggregation of reaction products. The oscillatory zonations have been observed from the numerical results of both one dimensional and two dimensional simulations. The local wavelengths of the quasi-periodical precipitation in the Liesegang patterns are characterized by the Jablczynski spacing law and the width law. The interactions between the waves of the precipitation have been identified. The LBM provides a feasible approach to simulate the pattern formation of Liesegang band in reaction-diffusion systems.