(2bz) Out-of-Equilibrium Generic Framework Predicts Concentration-Dependent Liquid Crystals

My research interests lie in the mathematical understanding of biological systems and their applications to improve human health. This includes, but is not limited to, modeling the growth of organs and understanding complex signaling processes involved in gene regulation circuits. Currently, I work in the theoretical and computational study of multi-component liquid crystals. Liquid Crystals are a state of matter, in between a solid and a liquid state, highly present in biology. Abundant examples are the cell cytoskeleton, the collective motion of animals and the liver. In addition to this, I have a growing interest in the intersection of natural sciences and humanities and social sciences which has led to undertake diverse scientific projects.

Abstract

Experimental data found in active lyotropic Liquid Crystals (LCs), typically a nematic phase coexisting with an isotropic fluid and molecular motors, have displayed complex patterns that remain unexplained. These studies raise questions about the effective parameters transforming such chaotic dynamics into a coherent motion. However, the relationships between their components’ concentration are highly complicated and continue to be unclear. To tackle this challenging problem, we use the GENERIC framework 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. With this, we systematically formulate a set of equations, describing the behavior of multicomponent (lyotropic) LCs with diffuse interfaces, by methodically adding physical mechanisms without the loss of generality and over-specification of our model. By solving our equations using an in-house hybrid lattice Boltzmann code, we show that, in 2D, two passive isotropic droplets within a nematic environment can form stable defect cores with topological charges of +1/2 and -1/2, as observed in chromonic LC data. In 3D, the simulations predict the evolution of an axial droplet configuration, as seen in experiments with surfactants. Additionally, we numerically study the effect of our solutions under different type of flows (passive or active). Our findings demonstrate that experimental results can be quantitatively predicted by the proposed GENERIC set of equations.