Out-of-Equilibrium GENERIC Modeling Predicts Lyotropic Liquid Crystal Emulsions with Diffuse Interfaces

Recent active Liquid Crystals (LCs) experiments, typically consisting of a nematic phase dispersed in an isotropic fluid, have displayed complex patterns that remain unexplained. These lyotropic LCs studies raise questions about the effective parameters that can transform their chaotic dynamics into a coherent motion. To tackle this challenging problem, we use the GENERIC formalism to construct a thermodynamically consistent model. In this framework, the time-evolution equations of out-of-equilibrium systems are naturally described by the sum of energy and entropy contributions. Hence, we systematically formulate a set of equations, aiming to describe the behavior of multiphasic LCs, by methodically adding physical mechanisms without the loss of generality and over-specification of our model. The numerical 2D solutions of our equations show that two isotropic droplets immersed in a nematic environment can form defect cores with topological charges of +1/2 and -1/2, as observed in chromonic LC experimental data, by simultaneously imposing planar anchoring at the interface. In 3D, the simulations predicted the evolution of an axial droplet configuration. Our findings demonstrate that experimental results can be quantitatively predicted by the proposed GENERIC set of equations.