The horizontal spreading of thermal and chemical deposits in a porous medium

This is an analytical and numerical study of the buoyancy-driven horizontal spreading of heat and chemical species through a fluid-saturated porous medium. The buoyancy effect is due to both temperature and concentration gradients. It is shown that when the flow is driven primarily by temperature gradients the approach to eventual thermal equilibrium can take place along two distinct routes, one dominated by convection (high Ra) effects, and the other dominated by diffusion. In the convection dominated regime, for example, the porous medium reaches an intermediate state of stable stratification (horizontal layering) before the final state of uniform temperature. It is shown also that the species migration processes that ride on flows driven by temperature gradients can be sorted out similarly, depending on whether mass convection is important. The scaling trends and estimates discovered analytically are confirmed by extensive numerical experiments conducted in the range 10 < Ra < 103, 0.01 < Le < 100 and 1 < L/H < 4. The distinct regimes and respective heat and mass transfer scales of the flows driven primarily by buoyancy due to concentration gradients are also documented. A closed form analytical solution is developed for the limit of infinitely shallow layers, L/H → ∞.