Prior thermocapillary migration experiments revealed that the rate of migration of a partially miscible drop, slowly moving within a vertical temperature gradient, obeyed in a quasi-static sense a theoretical prediction for an immiscible drop. The hydrodynamic theory for a partially miscible drop is developed here for circumstances where the thermal effects of mass transfer are negligible. Analysis shows that rates of growth or shrinkage in these experiments were too small to affect the flow. Nevertheless, for finite growth of shrinkage rates the migration velocity is given by a quasi-static interpretation of the immiscible theory. Moreover, similar results are found for a partially miscible gas bubble moving under conditions of finite Reynolds and small Marangoni numbers in a zero-gravity environment.
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