Liquid-Liquid Phase Separation in a Liquid Crystalline Environment

Understanding liquid-liquid phase separation in liquid crystalline environments is essential for uncovering the physical mechanisms that govern the behavior of various soft matter systems. Motivated by recent experiments on phase separation of a fluid of DNA nanostars immersed in an entangled actin gel, we investigate the structural and coarsening properties of Cahn-Hilliard droplets coupled to liquid crystalline degrees of freedom that capture the onset of nematic order in the surrounding gel. We perform linear stability tests for the mixed state to explore the early-time phase separation behavior of the system. We also find numerically that the coupling of the director field to interfacial deformations can generate local nematic order at the droplet interfaces and arrest the coarsening process. These results suggest routes to controlling phase separation in engineered systems or complex environments like living cells.