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How non-Darcy effects influence scaling laws in Hele-Shaw convection experiments

  • Marco De Paoli (a1), Mobin Alipour (a1) (a2) and Alfredo Soldati (a1) (a2)


We examine experimentally the influence of non-Darcy effects on convective dissolution in Hele-Shaw cells. We focus 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 a recent theoretical work (Letelier et al., J. Fluid Mech., vol. 864, 2019, pp. 746–767) demonstrated that a precise limit exists for the parameter $\unicode[STIX]{x1D716}^{2}Ra$ $\unicode[STIX]{x1D716}\sim$ thickness-to-height ratio – beyond which the flow exhibits non-Darcy effects. In this work, we run experiments for solute convection in Rayleigh–Bénard-like configuration. We examine a wide range of the parameters space $(Ra,\unicode[STIX]{x1D716})$ 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 set-ups. 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 attribute an important role to the parameter $\unicode[STIX]{x1D716}^{2}Ra$ , which clearly establishes thresholds beyond which Hele-Shaw experiment results are influenced by three-dimensional effects.


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How non-Darcy effects influence scaling laws in Hele-Shaw convection experiments

  • Marco De Paoli (a1), Mobin Alipour (a1) (a2) and Alfredo Soldati (a1) (a2)


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