Effect of dispersion on convective mixing in porous media

Solutal convection in porous media is thought to be controlled by the molecular Rayleigh number, Ra_m, the ratio of the buoyant driving force over diffusive dissipation. The mass flux should increase linearly with $Ra_m$ and the finger spacing should decrease as Ra_m^-1/2. Instead our experiments find that flux levels off at large Ra_m and finger spacing increases with Ra_m. Here we show that the convective pattern is controlled by a dispersive Rayleigh number, Ra_d, balancing buoyancy and dispersion. Increasing the bead size of the porous medium increases Ra_m but decreases Ra_d and hence coarsens the pattern. While the flux is predominantly controlled by Ra_m, the anisotropy of mechanical dispersion leads to an asymmetry in the pattern that limits the flux at large bead sizes.