Concentration-based velocity reconstruction in convective Hele–Shaw flows

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