Domain growth in cholesteric blue phases: Hybrid lattice Boltzmann simulations

Here we review a hybrid lattice Boltzmann algorithm to solve the equations of motion of cholesteric liquid crystals. The method consists in coupling a lattice Boltzmann solver for the Navier-Stokes equation to a finite difference method to solve the dynamical equations governing the evolution of the liquid crystalline order parameter. We apply this method to study the growth of cholesteric blue phase domains, within a cholesteric phase. We focus on the growth of blue phase II and on a thin slab geometry in which the domain wall is flat. Our results show that, depending on the chirality, the growing blue phase is either BPII with no or few defects, or another structure with hexagonal ordering. We hope that our simulations will spur further experimental investigations on quenches in micron-size blue phase samples. The computational size that our hybrid lattice Boltzmann scheme can handle suggest that large scale simulations of new generation of blue phase liquid crystal device are within reach.