Dynamic Simulation of Mixing-Limited Symmetric and Asymmetric Patterns in Homogeneous Autocatalytic Reactors

Abstract

In this paper, we study the dynamic evolution of mixing-limited patterns in homogeneous autocatalytic reactors. Using a regularized low-dimensional model derived through the spatial averaging of the 3-D convection-diffusion-reaction equation using Liapunov-Schmidt technique of the classical bifurcation theory, we simulate the process of formation of asymmetric patterns that develop from differences in mixing and reaction time scales, and are widely observed in experimental studies. We also perform a detailed parametric analysis in order to quantify the effects of the parameters Pe, p, and Da on the formation, evolution and stability of patterns. Our nonlinear dynamic simulations show that increased transverse mixing limitations in the reactor help excite a broad spectrum of eigen modes that produce patterns of various length scales and axes of symmetry. These patterns coexist and superimpose to generate asymmetric patterns that are more stable than the symmetric ones formed from lower eigen modes.