Study on the Formation of Complex Chemical Waveforms by Different Computational Methods

Jiali Ai,Wei Sun,Chi Zhai

doi:10.3390/pr8040393

Abstract

Chemical wave is a special phenomenon that presents periodic patterns in space-time domain, and the Belousov–Zhabotinsky (B-Z) reaction is the first well-known reaction-diffusion system that exhibits organized patterns out of a homogeneous environment. In this paper, the B-Z reaction kinetics is described by the Oregonator model, and formation and evolution of chemical waves are simulated based on this model. Two different simulation methods, partial differential equations (PDEs) and cellular automata (CA) are implemented to simulate the formation of chemical waveform patterns, i.e., target wave and spiral wave on a two-dimensional plane. For the PDEs method, reaction caused changes of molecules at different location are considered, as well as diffusion driven by local concentration difference. Specifically, a PDE model of the B-Z reaction is first established based on the B-Z reaction kinetics and mass transfer theory, and it is solved by a nine-point finite difference (FD) method to simulate the formation of chemical waves. The CA method is based on system theory, and interaction relations with the cells nearest neighbors are mainly concerned. By comparing these two different simulation strategies, mechanisms that cause the formation of complex chemical waves are explored, which provides a reference for the subsequent research on complex systems.

Highlights

In a reaction-diffusion system, the concentration distribution of its components could exhibit periodic changes in time and space under certain conditions, and this phenomenon is called a chemical wave [1]
There is common understanding regarding the formation of chemical waves [1,6,10–12], i.e., when far away from thermodynamic equilibrium, a system is influenced by the interaction among coupling reactions, and the concentration of each location may fluctuate periodically, and together with the influence of diffusion, the system changes from disorder to order, i.e., chemical wave
The aim of this work is to compare chemical waveform formation processes by the two above-mentioned simulation methods, and by comparing these two different simulation strategies, mechanisms that cause the formation of complex chemical waves are explored, which provides a reference for the subsequent research on complex systems

Summary

Introduction

In a reaction-diffusion system, the concentration distribution of its components could exhibit periodic changes in time and space under certain conditions, and this phenomenon is called a chemical wave [1]. Researchers have observed various chemical waves, such as pulse waves along one dimension [2], target waves and spiral waves on a two-dimensional plane [3,4], scroll waves in a three-dimensional space [5]. It is a macroscopic pattern developing from chemical reaction coupling with diffusion [6] and is a typical self-organizing phenomenon [7–9]. There is common understanding regarding the formation of chemical waves [1,6,10–12], i.e., when far away from thermodynamic equilibrium, a system is influenced by the interaction among coupling reactions, and the concentration of each location may fluctuate periodically, and together with the influence of diffusion, the system changes from disorder to order, i.e., chemical wave. It can be observed that the color of Processes 2020, 8, 393; doi:10.3390/pr8040393 www.mdpi.com/journal/processes

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