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.

Keywords

• reaction fronts
• convection
• diffusive instabilities