Abstract
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, , 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 – thickness-to-height ratio – beyond which the flow exhibits non-Darcy effects. In this work, we run experiments for solute convection in Rayleigh–Benard-like configuration. We examine a wide range of the parameters space 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–Benard-like experiments and simulations in similar contexts. Specifically, we attribute an important role to the parameter , which clearly establishes thresholds beyond which Hele-Shaw experiment results are influenced by three-dimensional effects.
Highlights
Hele-Shaw cells are made by two parallel, transparent plates, which are separated by a gap that – ideally – is infinitesimal
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 flow is controlled by two dimensionless parameters: the Rayleigh–Darcy number, Ra, which measures the relative importance of convection and diffusion, and the anisotropy ratio, proportional to the cell thickness-to-height ratio
Summary
Hele-Shaw cells are made by two parallel, transparent plates, which are separated by a gap that – ideally – is infinitesimal Under this condition, any flow established inside the gap can reproduce a Stokes flow. We focus here on the use of Hele-Shaw cells to investigate flows driven by the differential gravity force acting on fluids of different density, which are initially set in an unstable configuration. This type of experiment is important for a number of applications, since it is simple and can, under certain assumptions, reproduce important features of Darcy flows in porous media.
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