Da. Vasquez et C. Lengacher, LINEAR-STABILITY ANALYSIS OF CONVECTIVE CHEMICAL FRONTS IN A VERTICALSLAB, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(5), 1998, pp. 6865-6868
A chemical reaction front propagating in a viscous fluid separates two
liquids of different densities leading to convection. Convection enha
nces the speed and changes the curvature of the front. We analyze the
effects of convection as the front propagates in a two-dimensional ver
tical 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 de
pending on the slab width and gap thickness. The steady state solution
s 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 w
idth is increased. [S1063-651X(98)09711-6].