Onset of double-diffusive convection in a rectangular porous cavity submitted to heat and mass fluxes at the vertical walls.

We studied the onset of double-diffusive convection in a rectangular cell filled with a porous medium saturated with a binary fluid. Uniform heat and mass fluxes are applied to the vertical walls while the horizontal walls are impermeable and adiabatic. When the ratio of resulting solutal to thermal buoyancy forces is equal to -1, we obtain a purely diffusive regime (motionless). We demonstrate that this regime is linearly stable while the thermal Rayleigh number is lower than a critical value, Ra-c, depending of the aspect ratio of the cell, A, and the Lewis number, Le. For a square cavity, we obtained Ra-c\Le-1\ = 209.84 and for an infinite layer, the critical parameters are found to satisfy Ra-c\Le-1\ = 105.33 with a wavenumber k(c) = 2.51. These analytical results are in good agreement with direct numerical simulations. These numerical simulations show that subcritical solutions disappear for a thermal Rayleigh number R-0 < Ra-c, which depends on the aspect ratio of the cell and the Lewis number. For thermal Rayleigh numbers lower than R-0, only the purely diffusive solution is stable. (C) Elsevier, Paris.