Far Field Asymptotics of Nematic Flows Around a Small Spherical Particle

TL;DR

This paper analyzes the far field flow behavior of nematic liquid crystals around a small sphere, deriving analytical expressions for flow velocity and comparing them to classical Stokes flow results.

Contribution

It provides the first analytical characterization of nematic flow far from a small particle, simplifying the governing equations to linear PDEs.

Findings

Flow velocity can be explicitly computed analytically.

Flow behavior closely resembles classical Stokes flow at large distances.

Analytical and numerical methods are used to determine flow velocity.

Abstract

Given a small spherical particle, we consider flow of a nematic liquid crystal in the corresponding exterior domain. Our focus is on precise far field asymptotic behavior of the flow in a parameter regime when the governing equations can be reduced to a system of linear partial differential equations. We are able to analytically characterize the velocity of the flow and compare it to the classical expression for the Stokes flow. The expression for velocity away from the particle can be computed either numerically or symbolically.