Rheology of Lamellar Liquid Crystals in Two and Three Dimensions: A Simulation Study

TL;DR

This study uses large-scale simulations to explore how lamellar liquid crystals respond to shear in two and three dimensions, revealing shear-induced alignment, defect dynamics, and the impact of dimensionality on rheological behavior.

Contribution

It provides new insights into the shear rheology of lamellar phases, including defect proliferation in 2D and shear-induced ordering in 3D, with a scaling analysis of critical shear rates.

Findings

Shear aligns lamellar phases and stabilizes ordered structures in 2D at modest shear rates.

High shear rates in 2D cause defect proliferation and memory effects.

3D simulations show shear-induced ordering persists at high shear rates.

Abstract

We present large scale computer simulations of the nonlinear bulk rheology of lamellar phases (smectic liquid crystals) at moderate to large values of the shear rate (Peclet numbers 10-100), in both two and three dimensions. In two dimensions we find that modest shear rates align the system and stabilise an almost regular lamellar phase, but high shear rates induce the nucleation and proliferation of defects, which in steady state is balanced by the annihilation of defects of opposite sign. The critical shear rate at onset of this second regime is controlled by thermodynamic and kinetic parameters; we offer a scaling analysis that relates the critical shear rate to a critical "capillary number" involving those variables. Within the defect proliferation regime, the defects may be partially annealed by slowly decreasing the applied shear rate; this causes marked memory effects, and history-dependent rheology. Simulations in three dimensions show instead shear-induced ordering even at the highest shear rates studied here. This suggests that the critical shear rate shifts markedly upward on increasing dimensionality. This may in part reflect the reduced constraints on defect motion, allowing them to find and annihilate each other more easily. Residual edge defects in the 3D aligned state mostly point along the flow velocity, an orientation impossible in two dimensions.