The influence of interface curvature on solutal Marangoni convection in the Hele-Shaw cell

We study numerically the impact of interfacial curvature onto the Marangoni convection in a two-layer system of immiscible liquids with mass transfer of an alcohol. Assuming a parabolic velocity profile and constant solute concentration across the gap, the simulations solve Navier-Stokes equations coupled to advection-diffusion equations in both phases. Interfacial curvature imposes concentration gradients along the interface as soon as the mass transfer starts. This leads to an immediate interfacial convection which is superimposed later by the onset of the actual Marangoni roll cells. Prominent impact of interfacial curvature onto the Marangoni cells is the occurrence of a locking effect, i.e., the Marangoni roll cells adapt to the shape of the interface. Whereas mass transfer is enhanced by interfacial curvature compared to the planar interface in the beginning, locking drastically reduces the mass transfer rate. Even for small interface curvature significant differences to the planar case are found, which might explain the accelerated growth of cells in experiments compared to that in numerical simulation recently observed in Koellner et al. [EJP ST 224 (2015), 261-276].