The helicity and vorticity of liquid crystal flows

TL;DR

This paper derives explicit expressions for helicity conservation in nematic liquid crystal flows, revealing Euler-like equations for modified vorticity that resemble ideal fluid dynamics and extend to particles of arbitrary shape.

Contribution

It introduces a minimal coupling approach to obtain Euler-like equations for modified vorticity in liquid crystal flows, applicable to complex particle shapes and broken rotational symmetry.

Findings

Helicity conservation expressions for nematic liquid crystals.

Euler-like equations for modified vorticity involving velocity and structure fields.

Extension of results to particles with arbitrary shapes.

Abstract

We present explicit expressions of the helicity conservation in nematic liquid crystal flows, for both the Ericksen-Leslie and Landau-de Gennes theories. This is done by using a minimal coupling argument that leads to an Euler-like equation for a modified vorticity involving both velocity and structure fields (e.g. director and alignment tensor). This equation for the modified vorticity shares many relevant properties with ideal fluid dynamics and it allows for vortex filament configurations as well as point vortices in 2D. We extend all these results to particles of arbitrary shape by considering systems with fully broken rotational symmetry.