Abstract
We examine the process of convective dissolution in a Hele–Shaw cell. We consider a one-sided configuration and we propose a newly developed method to reconstruct the velocity field from concentration measurements. The great advantage of this Concentration-based Velocity Reconstruction (CVR) method consists of providing both concentration and velocity fields with a single snapshot of the experiment recorded in high resolution. We benchmark our method vis–à–vis against numerical simulations in the instance of Darcy flows, and we also include dispersive effects to the reconstruction process of non-Darcy flows. The absence of laser sources and the presence of one low-speed camera make this method a safe, accurate, and cost-effective alternative to classical PIV/PTV velocimetry processes. Finally, as an example of possible application, we employ the CVR method to analyse the tip splitting phenomena.Graphic abstract
Highlights
The Hele–Shaw cell consists of two paralleled and transparent plates located within a uniform gap
We developed a Concentration-based Velocity Reconstruction (CVR) method to accurately estimate the Eulerian velocity field in Hele-Shaw flows
We show that the CVR algorithm can be adapted to non-Darcy flows and we employ this method to analyse the tip splitting phenomenon
Summary
The Hele–Shaw cell consists of two paralleled and transparent plates located within a uniform gap. Experiments in Fluids (2020) 61:195 force of the flow consists of density differences induced by the presence of a solute and, more precisely, by the solute concentration gradients existing in the domain. In these conditions, under certain assumptions, the Hele–Shaw apparatus may accurately mimic a Darcy flow in a porous medium.
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