Linear stability analysis of high- and low-dimensional models for describing mixing-limited pattern formation in homogeneous autocatalytic reactors

Abstract

Abstract In this paper, we perform linear stability analysis of high- and low-dimensional models for describing mixing-limited pattern formation in fast, homogeneous autocatalytic reactions occurring in isothermal tubular reactors. We consider three different models of varying dimensionality—the 3D convection-diffusion-reaction (CDR) model is the high dimensional one, and the Liapunov–Schmidt reduction based spatially averaged two-dimensional CDR model and its regularized form are the two low-dimensional ones. For each of these three models, steady state bifurcation diagrams that show the presence of multiple steady states were obtained and the stability of these multiple steady states to transverse perturbations was analyzed using linear stability analysis. Parametric analysis of the steady state bifurcation diagrams shows that for sufficiently large values of transverse Peclet number p, mixing-limited patterns may emerge from the unstable middle branch that connects the ignition and extinction points of an S-shaped bifurcation curve. Comparison of the bifurcation diagrams and the stability boundaries of the two low-dimensional models with that of the 3D CDR model reveals that the regularized form of the low-dimensional model has higher accuracy and a larger region of validity than the averaged form and is therefore recommended over the latter.