  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.
