Mixing in confined porous media: effect of dimensionality, fluid properties and boundary interface constraints

We investigate the role of the fluid properties and of the boundary conditions on convective mixing in confined porous media. We consider two miscible fluid layers in which the density of the fluid is controlled by the presence of a solute, quantified by its value of concentration. When these fluids combine, the density of the resulting mixture increases, originating hydrodynamic convective instabilities that further enhance mixing. The relative importance of driving (i.e., convective) and dissipative (i.e., diffusive) mechanisms is quantified by the Rayleigh-Darcy number. We perform numerical simulations to analyse the behaviour of different fluids, in which the density is (non-)monotonic function of the solute concentration, and we focus on high Rayleigh-Darcy numbers. We analyse the impact of the density-concentration law by looking at two effects: (i) the density contrast between the mixture and the starting fluids, and (ii) the position of the concentration value that maximizes the density, relative to the concentration of the starting fluids. We show that in all the cases considered, the mixing process is controlled by the mean scalar dissipation, and we derive simple physical models to explain this behaviour. We also explore the role of different boundary conditions, and analyse the mixing rate to identify optimal conditions for mixing. Finally, we investigate the effects of the dimensionality of the system, and we draw possible implications for geophysical flows.