Influence of non-Darcy effects on scaling laws of convection in Hele-Shaw flows

In this work, we examined the influence of non-Darcy terms on convective dissolution in confined porous media. We performed experiments in Hele-Shaw configuration and we focused on buoyancy-driven convection, where the flow is controlled by the Rayleigh-Darcy number, Ra, which measures the strength of convection compared to diffusion. The Hele-Shaw cell is suitable to mimic Darcy flows only under certain geometrical constraints, and precise limits exist for Ra and cell geometry beyond which the flow exhibits non-Darcy effects. We performed experiments in Rayleigh-Bénard-like configuration and we clearly identify the application limits of Darcy flow assumptions. Besides confirming previous theoretical predictions, current results are of relevance in the context of porous media flows - which are often studied experimentally with Hele-Shaw setups. Using our original datasets, we have been able to explain and reconcile the discrepancies observed between scaling laws previously proposed for Rayleigh-Bénard-like experiments and simulations in similar contexts. Specifically, we discuss the conditions beyond which Hele-Shaw experiment results are influenced by three-dimensional effects.