Minimization principle for shear alignment of liquid crystals

TL;DR

This paper investigates whether liquid crystal director configurations under shear flow tend to minimize an effective potential, deriving equations and using simulations to demonstrate relaxation toward such minima in specific flow scenarios.

Contribution

The authors derive the Leslie-Ericksen equations for dissipative dynamics and show through theory and simulations that certain shear flow configurations relax toward an effective potential minimum.

Findings

Director configurations relax toward an effective potential minimum under shear flow.

Demonstrated relaxation in reverse tilt domains under simple shear.

Shown relaxation in dowser configurations under plane Poiseuille flow.

Abstract

If a static perturbation is applied to a liquid crystal, the director configuration changes to minimize the free energy. If a shear flow is applied to a liquid crystal, one might ask: Does the director configuration change to minimize any effective potential? To address that question, we derive the Leslie-Ericksen equations for dissipative dynamics, and determine whether they can be expressed as relaxation toward a minimum. The answer may be yes or no, depending on the number of degrees of freedom. Using theory and simulations, we consider two specific examples, reverse tilt domains under simple shear flow and dowser configurations under plane Poiseuille flow, and demonstrate that each example shows relaxation toward the minimum of an effective potential.