(232c) Using the Level Set Method to Model Droplet Motion through An Ambient Miscible Fluid

Droplet systems (liquid/liquid, liquid/gas) have widespread applications in the medical, industrial, and research fields, examples of which are aerosolized drugs, spray drying, printing, and liquid-liquid extraction. Most applications use immiscible fluid pairs, which are also the most studied and best understood cases. The classical 1911 Hadamard-Rybczynski solution broke new ground when the two scientists presented the creeping flow solution for the flow around and in an immiscible drop. Miscible pairs have been less tractable for analytical/modeling studies, and comparably little work has been done in this area. Arce and coworkers have presented low Reynolds number results for the buoyancy-driven motion of a droplet in a partially miscible high viscosity fluid which are qualitatively different from the classical motion of an immiscible droplet. Their experimental studies have shown that a puddle region develops on the back side of the drop due to convective-diffusive flows. In this paper, we present our modeling results for a single droplet partially miscible with an infinite fluid phase and compare the predictions of this study with the experimental results of Arce and coworkers.