Numerical simulation of thermo-solutal-capillary migration of a dissolving drop in a cavity

In the present paper the thermo-solutal-capillary migration of a dissolving liquid drop, composed by a binary mixture having a miscibility gap, injected in a closed cavity with differentially heated end walls, is studied. The main goal of the analysis is to clarify if and how the drop migration is affected by the dissolution process. The numerical code is based on a finite volume formulation. A level-set technique is used for describing the dynamics of the interface separating the different phases. A thermodynamic constraint fixes the concentration jump between the interface sides. This jump, together with that of the concentration normal derivatives, in turn defines the entity of the dissolution cross-flow through the interface and the interface velocity relative to the fluid. Since the jump singularity of normal derivatives cannot be easily mollified, while retaining the necessary accuracy, a scheme for the species equation is elaborated that allows sharp jumps and has subcell resolution. Steady migration speeds are determined after the start-up phase for different radii and temperature differences. The results will be used for the preparation of a sounding rocket space experiment.