Liquid-liquid phase separation is key to understanding aqueous two-phase systems (ATPS) arising throughout cell biology, medical science, and the pharmaceutical industry. Controlling the detailed morphology of phase-separating compound droplets leads to new technologies for efficient single-cell analysis, targeted drug delivery, and effective cell scaffolds for wound healing. We present a computational model of liquid-liquid phase separation relevant to recent laboratory experiments with gelatin-polyethylene glycol mixtures. We include buoyancy and surface-tension-driven finite viscosity fluid dynamics with thermally induced phase separation. We show that the fluid dynamics greatly alters the evolution and equilibria of the phase separation problem. Notably, buoyancy plays a critical role in driving the ATPS to energy-minimizing crescent-shaped morphologies, and shear flows can generate a tenfold speedup in particle formation. Neglecting fluid dynamics produces incorrect minimum-energy droplet shapes. The model allows for optimization of current manufacturing procedures for structured microparticles and improves understanding of ATPS evolution in confined and flowing settings important in biology and biotechnology.
