Direct comparison of density-driven convective mixing in a three-dimensional porous medium using experiments and simulation

We perform a direct comparison between experiment and simulation of density-driven convective mixing in three-dimensional (3D) porous media. We find excellent agreement between the experiment and the model in terms of both the convection fingering pattern and the average rate of fluid mixing. In particular, the experiment exhibits dynamic self-organization of columnar plumes into a reticular pattern, which, until now, had only been observed in 3D simulations. We also report good quantitative agreement between the experiment and simulation in the evolution of the state of mixing by comparing, over time, (i) the average concentration at depth, (ii) the variance of the concentration field, (iii) the scalar dissipation rate, and (iv) the dissolution flux. We derive a relation between the scalar dissipation rate and the dissolution flux in a closed system, and we show that the flux in a 3D system is approximately $\sim 30\%$ higher than in a 2D system, confirming previous numerical estimates.