Convection and Pattern Formation Induced by Autocatalytic Chemical Reactions

Abstract

A brief overview is given on chemical patterns that form due to the coupling between nonlinear reactions with transport processes. Emphasis lies on experimental reaction-diffusion systems such as the methyleneblue-sulfide-oxygen (MBO)reaction, in which stationary Turing patterns are observed, and the Belousov-Zhabotinsky (BZ) reaction, which is a frequently used example for an excitable medium showing propagating oxidation waves. When traveling in a liquid solution without a gel, such chemical waves are known to induce a convective flow in the reaction medium. We summarize the different types of flow behavior in a thin layer of BZ solution. Large chemical wavelengths lead to individual flow patterns, each associated with a single wave front. Short chemical wavelengths induce a cooperative phenomenon in the form of large global flow waves traveling through the fluid layer. The chemical reaction can induce this convection by producing local density changes as well as by generating gradients of surface tension due to local changes in the chemical composition of the medium. These phenomena are modeled by coupling reaction-diffusion equations to the underlying hydrodynamic equations. Close to the instability onset envelope equations can be derived provided the spatial variations are sufficiently smooth. Using this technique we demonstrate that chemically driven convection can stabilize Turing patterns. By direct numerical simulation of the basic equations we show that a large scale collective hydrodynamic flow can be generated by the concentration dependence of the surface tension. In this case rapid spatial variations of the concentrations preclude a description in terms of envelope equations.