Article révisé par les pairs
Résumé : A miscible horizontal interface separating two solutions of different solutes in the gravity field can deform into convective finger structures due to the Rayleigh-Taylor (RT) instability, or the double-diffusive (DD) and diffusive-layer-convection (DLC) instabilities, triggered by differential diffusion of the solutes. We analyse here numerically the nonlinear dynamics of these buoyancy-driven instabilities in porous medium flows by an integration of Darcy's law coupled to advection-diffusion equations for the concentrations of the two solutes. After a diffusive growth, the mixing length, defined as the vertical extent of the mixing zone, starts to grow linearly when convection sets in. We compute the mixing velocity as the slope of this linear growth. In the one-species RT regime, is proportional to, the initial density difference between the two layers. In the two-species problem, differential diffusion effects can induce non-monotonic density profiles characterised by an adverse density difference, defined as the density jump across the spatial domain where the density decreases along the direction of gravity. We find that, in the parameter space spanned by the buoyancy ratio, and the ratio of diffusion coefficients of the two species, the mixing velocity scales linearly with this dynamic density difference. It is computed analytically from the diffusive base-state density profile and can be significantly larger than. Our results evidence the possibility of controlling the mixing of RT, DD and DLC instabilities in two-species stratifications by a careful choice of the nature and thus diffusivity of the species involved.