Structured flows regulate droplet dynamics in phase-separating fluids

Abstract

Liquid-liquid phase separation is a fundamental route by which homogeneous fluids self-organize into mesoscale droplets and domains. In passive mixtures, the fate of these structures is largely dictated by curvature-dependent chemical potentials, which drive interfacial relaxation and Ostwald ripening toward progressively coarser morphologies. Here we show that structured flows can drive phase-separating fluids into flow-selected nonequilibrium states, thereby qualitatively rewriting the droplet dynamics. Using an advective Cahn-Hilliard model, we demonstrate that patterned velocity fields deform droplet interfaces along the streamlines of the imposed flow. The resulting curvature variations reshape the chemical-potential landscape that steers diffusive material transport. The resulting fluxes allow structured vortices to capture droplets, select stable droplet sizes, and invert the conventional ripening hierarchy by rendering larger droplets effectively less stable than smaller ones. In many-droplet systems, periodic and disordered vortex fields arrest coarsening and select steady morphologies whose length scales and symmetries are set by the underlying flow structure. Together, these results establish structured flow as a nonequilibrium route for controlling the thermodynamic driving forces that govern phase-separating fluids.

8 pages and 3 figures