Influence of quasi-periodic gravitational modulation on convective instability of reaction fronts in porous media

摘要

The influence of a time-dependent gravity on the convective instability of reaction fronts in porous media is investigated in this paper. It is assumed that the time-dependent modulation is quasi-periodic with two frequencies σ_1, and σ_2 that are incommensurate with each other. The model consists of the heat equation, the equation for the depth of conversion and the equations of motion under the Darcy law. The convective threshold is approximated performing a linear stability analysis on a reduced singular perturbation problem using the matched asymptotic expansion method. The reduced interface problem is solved using numerical simulations. It is shown that if the reacting fluid is heated from below, a stabilizing effect of a reaction fronts in a porous medium can be gained for appropriate values of amplitudes and frequencies ratio σ = σ_2/σ_1 of the quasi-periodic vibration.