(18d) Computational and Mathematical Modeling of Active Lyotropic Liquid Crystals

Active Lyotropic Liquid Crystals (LCs) are partially ordered states of matter whose properties depend on constituent concentrations and continuously convert energy into mechanical work. These materials, found in living systems such as the liver and bacterial suspensions, present significant challenges in controlling their dynamic behavior due to unclear effective parameters governing their composition.

To address this, we employ the GENERIC (General Equation for Non-Equilibrium Reactions) framework to construct a thermodynamically consistent model, describing the time evolution of out-of-equilibrium systems through energy and entropy contributions. We solve the resulting set of equations using LiquidCrystalGLB.jl, an open-source Julia-based solver that combines an upwind finite difference scheme with the Lattice Boltzmann method (LBM), integrated via the Trixi.jl package, a library in Julia. In our solver, 'G' refers to the GENERIC framework, 'LB' to the Lattice Boltzmann method.

Our simulations provide several key insights. In 2D, we model a binary mixture resembling experimental chromonic LC data, capturing topological defects with charges of +1/2 and -1/2. In 3D, we observe phenomena such as the Fréedericksz transition under external electric fields. Additionally, we investigate the behavior of an LC droplet subject to a velocity parabolic profile and explore the effect of biochemical activity, which leads to turbulent flow patterns similar to biological systems like microtubules or actin experiments.

These results demonstrate that our hybrid computational approach, grounded in the GENERIC framework, successfully predicts experimental data and offers valuable insights into the dynamic behavior of active LCs, with implications for both material science and biological systems.