Equivalent theories of liquid crystal dynamics

TL;DR

This paper demonstrates the equivalence of two major theories of nematic liquid crystal dynamics using symmetry reduction, unifying the Ericksen-Leslie and Eringen micropolar approaches and including defect dynamics.

Contribution

It introduces a new system that proves the equivalence of the director and micropolar theories, also accounting for disclination defects and extending to complex fluid flows.

Findings

The Ericksen-Leslie and Eringen micropolar theories are mathematically equivalent.

A new system includes disclination dynamics within the equivalent framework.

The approach extends to flowing complex fluids like nematic liquid crystals.

Abstract

There are two competing descriptions of nematic liquid crystal dynamics: the Ericksen-Leslie director theory and the Eringen micropolar approach. Up to this day, these two descriptions have remained distinct in spite of several attempts to show that the micropolar theory comprises the director theory. In this paper we show that this is the case by using symmetry reduction techniques and introducing a new system that is equivalent to the Ericksen-Leslie equations and includes disclination dynamics. The resulting equations of motion are verified to be completely equivalent, although one of the two different reductions offers the possibility of accounting for orientational defects. After applying these two approaches to the ordered micropolar theory of Lhuiller and Rey, all the results are eventually extended to flowing complex fluids, such as nematic liquid crystals.