Structures and Instabilities in Reaction Fronts Separating Fluids of Different Densities

Abstract

Density gradients across reaction fronts propagating vertically can lead to Rayleigh–Taylor instabilities. Reaction fronts can also become unstable due to diffusive instabilities, regardless the presence of a mass density gradient. In this paper, we study the interaction between density driven convection and fronts with diffusive instabilities. We focus in fluids confined in Hele–Shaw cells or porous media, with the hydrodynamics modeled by Brinkman’s equation. The time evolution of the front is described with a Kuramoto–Sivashinsky (KS) equation coupled to the fluid velocity. A linear stability analysis shows a transition to convection that depends on the density differences between reacted and unreacted fluids. A stabilizing density gradient can surpress the effects of diffusive instabilities. The two-dimensional numerical solutions of the nonlinear equations show an increase of speed due to convection. Brinkman’s equation lead to the same results as Darcy’s laws for narrow gap Hele–Shaw cells. For large gaps, modeling the hydrodynamics using Stokes’ flow lead to the same results.