Stochastic rotation dynamics for nematic liquid crystals

Abstract

We introduce a new mesoscopic model for nematic liquid crystals (LCs). We extend the particle-based stochastic rotation dynamics method, which reproduces the Navier-Stokes equation, to anisotropic fluids by including a simplified Ericksen-Leslie formulation of nematodynamics. We verify the applicability of this hybrid model by studying the equilibrium isotropic-nematic phase transition and nonequilibrium problems, such as the dynamics of topological defects and the rheology of sheared LCs. Our simulation results show that this hybrid model captures many essential aspects of LC physics at the mesoscopic scale, while preserving microscopic thermal fluctuations.

Field-driven pattern formation in nematic liquid crystals: mesoscopic simulations of electroconvection

“…The alignment mechanism of the external eld is introduced in a similar way to the LC particle alignment, so that the electric eld strength is expressed as the rst term on the right-hand side of eqn (3). The model above is a modication of the existing one, 13 and it can be seen that the angular momentum change due to the external electric eld is balanced in the Navier-Stokes equation.…”

“…The validation of a liquid crystal model using SRD was proposed by Lee et al, 13 and, almost simultaneously, an independently developed model was also proposed by Shendruk and Yeomans.…”

“…The numerical procedures, similar to those used by Lee et al, 13 are to use particle-based SRD to replace most parts of the Navier-Stokes equation. The linear momentum is further corrected by the angular momentum from the LC rotations, due to particle alignment and the external electric eld, which are the last two terms in eqn (1).…”

“…Our numerical approach is based on the recently developed LC SRD model by Lee et al, 13 in which they studied the rheology of a nematic LC in Couette ow, and the dynamics of its topological defects. In their work the thermal uctuation determines the nematic-isotropic phase transition in the NLC, and, similarly, the EC generation discussed here is also a phase transition that is controlled by the thermal uctuation.…”

Particle-based modeling of heterogeneous chemical kinetics including mass transfer

“…[8][9][10][11][12][13][14]. SRD has been implemented to study various systems such as polymer flow [15,16], phase separation in binary and tertiary mixtures [17], colloidal suspensions [18], vesicles in shear flow [19], enzyme catalysis [20], and anisotropic interaction in liquid separation [21].…”