SUMMARYIn 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 di erentially heated end walls, is studied. The main goal of the analysis is to clarify if and how the drop migration is a ected by the dissolution process. The numerical code is based on a ÿnite volume formulation. A level-set technique is used for describing the dynamics of the interface separating the di erent phases. A thermodynamic constraint ÿxes the concentration jump between the interface sides. This jump, together with that of the concentration normal derivatives, in turn deÿnes the entity of the dissolution cross-ow through the interface and the interface velocity relative to the uid. Since the jump singularity of normal derivatives cannot be easily molliÿed, 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 di erent radii and temperature di erences. The results will be used for the preparation of a sounding rocket space experiment.

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SUMMARYIn the present paper the dissolution of a binary liquid drop having a miscibility gap and migrating due to thermo-solutal capillary convection in a cylindrical cavity is studied numerically. The interest in studying this problem is twofold. From a side, in the absence of gravity, capillary migration is one of the main physical mechanisms to set into motion dispersed liquid phases and from the other side, phase equilibria of multi-component liquid systems, ubiquitous in applications, often exhibit a miscibility gap. The drop capillary migration is due to an imposed temperature gradient between the cavity top and bottom walls. The drop dissolution is due to the fact that initial composition and volume values, and thermal boundary conditions are only compatible with a ÿnal single phase equilibrium state. In order to study the drop migration along the cavity and the coupling with dissolution, a previously developed planar two-dimensional code is extended to treat axis-symmetric geometries. The code is based on a ÿnite volume formulation. A level-set technique is used for describing the dynamics of the interface separating the di erent phases and for mollifying the interface discontinuities between them. The level-set related tools of redistancing and o -interface extension are used to enhance code resolution in the critical interface region. Migration speeds and volume variations are determined for di erent drop radii.

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