Effect of Dispersion on Solutal Convection 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. Plain Language Summary Pattern formation in simple physical systems is intriguing, and convection in porous media is an example that was thought to be well understood. Convection is controlled by the balance between buoyant driving forces and dissipative mechanisms such as diffusion that smear out the concentration and hence density differences. Here we use simple laboratory experiments to show that the convective pattern is controlled by a different process than previously thought. A Rayleigh number based on mechanical dispersion, which is independent of fluid properties, predicts the flow pattern of solutal convection in bead packs.