A reaction-diffusion model captures the essence of liquid-liquid phase separation

In this work we propose the formulation of a continuum model for liquid-liquid phase separation(LLPS) using reaction diffusion framework. We consider a well mixed liquid consisting of three phases, the dense droplet phase, the dilute phase and the remaining part to be solvent phase. As a key feature, the model includes both the spatial and temporal aspects and a free energy functional between dense and dilute phase that is physically motivated by reference molecular simulation. The exhaustive numerical simulations of model captures the dynamical formation of droplets and existence of LLPS. As the time progresses, simulation reveal that smaller droplets gradually vanish, and a single droplet undergoes continuous growth until it reaches a stable size. The model predicts that that extent of diffusivity of dense and dilute phase as well as their mutual interaction would modulate the kinetics of droplet formation. Finally we show that introduction of fluctuation in the model accelerate the phase separation process.