Juliacon 2024

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 coherent motion. 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 concentration-dependent (lyotropic) LCs. We solved our equations by using a hybrid lattice Boltzmann code written in Julia that combines 1) finite differences (inspired by DiffEqOperators.jl) and 2) the Lattice Boltzmann method (found in Trixi.jl); the time evolution is integrated using DifferentialEquations.jl. 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 equations and by this numerical approach.