Linear stability analysis of convective chemical fronts in a vertical slab

A chemical reaction front propagating in a viscous fluid separates two liquids of different densities leading to convection. Convection enhances the speed and changes the curvature of the front. We analyze the effects of convection as the front propagates in a two-dimensional vertical slab. In this geometry, the fluid motion can be described using Brinkman’s equations [Appl. Sci. Res., Sect. A 1, 27 (1947)]. This set of equations is coupled to a front evolution equation describing the motion of the convective chemical front. Convection will be present depending on the slab width and gap thickness. The steady state solutions can be axisymmetric or nonaxisymmetric fronts depending on the slab width. A linear stability analysis for the solutions shows a region of bistability for narrow gaps. The bistability disappears as the slab width is increased.