  Demixing of binary liquids is a ubiquitous transition, which is explained
using a well-established thermodynamic formalism that requires equality of
intensive thermodynamics parameters across the phase boundaries. Demixing
transitions also occur when binary fluid mixtures are driven away from
equilibrium, for example, by external shear flow. Predicting demixing
transition under non-equilibrium non-potential conditions remains, however, a
challenge. We drive liquid-liquid phase separation (LLPS) of attractive DNA
nanostar molecules away from equilibrium using an internally driven
microtubule-based active fluid. Activity lowers the critical temperature and
narrows the coexistence concentrations, but only when there are mechanical
bonds between the liquid droplets and the reconfiguring active fluid. Similar
behaviors are observed in numerical simulations, suggesting that activity
suppression of liquid-liquid phase separation is a generic feature of active
LLPS. Our work describes a platform for building soft active materials with
feedback control while also providing insight into cell biology, where phase
separation emerged as a ubiquitous self-organizational principle.
