Local Nonlinear Stability of the Steady State in an Isothermal Catalyst

Abstract

A first-order, irreversible, exothermic reaction in a bounded porous catalyst is considered, with smooth boundary, of one, two, or three dimensions. For small Prater and Nusselt numbers, ,3 and I>, and a large Sherwood number, o, two isothermal models are derived. An analysis of linear stability of the steady states of such models shows that oscillatory instabilities appear for appropriate values of the Damk6hler number if the nondimensional activation energy is larger than 7* and the Lewis number is sufficiently large, where y* = 4 if m = v/,8o-c 1 and y* = (m + 1)2/ m if m > 1. A local Hopf bifurcation analysis is carried out at neutral stability points in order to ascertain whether such bifurcation is subcritical or supercritical.