(443e) Out-of-Equilibrium Generic Modeling Predicts Isotropic-Nematic Emulsions with Diffuse Interfaces

Recent experimental data found in lyotropic active Liquid Crystals (LCs), typically consisting of an active nematic phase dispersed in an isotropic fluid, have displayed complex patterns that remain unexplained. These studies raise questions about the general conditions that can transform their chaotic dynamics into a coherent motion. Furthermore, the theoretical understanding of the effective parameters and mechanisms triggering the movement of such systems has received little attention. To tackle this challenging problem, we use the GENERIC (general equation for the nonequilibrium reversible-irreversible coupling) formalism to construct a thermodynamically consistent model. In this framework, the time-evolution equations of out-of-equilibrium systems, such as lyotropic LCs, are naturally described by the sum of energy and entropy contributions. By doing that, we also preserve the first and second law of thermodynamics. Therefore, we systematically formulate a set of equations, aiming to describe the behavior of these biphasic LCs, by methodically adding physical mechanisms without the loss of generality and over-specification of our model. For this description, we consider two components, a nematic liquid crystal and an isotropic fluid forming an emulsion with diffuse interfaces. We hypothesize that our theoretical analysis can explain, as a first attempt, the topological defect cores observed in lyotropic chromonic nematics. By solving our equations using an in-house hybrid lattice Boltzmann simulation code, we show that two isotropic droplets immersed in a liquid crystal environment can form stable defect cores with topological charges of +1/2 and -1/2 by simultaneously imposing planar anchoring at the interface and treating the interfacial thickness to be of the order of the spacing size in our computational grid. Our findings demonstrate that experimental data can be quantitatively predicted by the proposed GENERIC set of equations.