Phase separating active fluids form dynamical filamentary networks

Understanding liquid-liquid phase separation is of immense biological importance, with relevance from intracellular biomolecular condensates to multi-cellular aggregates. Inspired by recent in-vitro experiments, we use a continuum theory to model phase separation between an extensile active liquid crystal and a passive isotropic fluid. We find that emergent active anchoring drives self-generated stretching flows within the active domains, leading to the formation of system-spanning filamentary active fluid networks. These dynamically robust networks are present at steady state even at very low volume fractions of the active fluid. The behavior depends strongly on dimensionality: two-dimensional fluids organize into a steady state emulsion where the active fluid forms a system-spanning network, with passive droplets filling the remaining space, while three-dimensional fluids develop a bicontinuous steady state structure. The network topology and geometry are controlled by a balance between active flows and diffusive fluxes governed by the equilibrium surface tension. Our work may provide an initial understanding of biological regulation of phase-separation and serves as a first step towards engineering activity-driven tools to control fluid microstructure.