Two-phase flow: Buoyancy driven flow of a partially miscible droplet at low Reynolds number

Mass transfer between droplets and a surrounding fluid is of central importance in many industrial processes such as liquid extraction and the aeration of bioreactors. In the low Reynolds number regime ( Re << 1), the buoyancy-driven motion of a droplet in a partially miscible high viscosity fluid is accompanied by compositional gradients and is found to be qualitatively different from the classical motion of an immiscible droplet as given by the Hadamard-Rybczynski solution. Previous experimental studies have shown that a 'puddle' region develops on the bottom side of the droplet due to convective-diffusive flows. In this work, we examined a single droplet partially miscible with an infinite fluid phase and presented an analysis that took into account the partial miscibility of the droplet with the ambient fluid. We qualitatively compared the predictions of this study with previous experimental results.