Minimal model for transient swimming in a liquid crystal

TL;DR

This paper investigates how the startup time of swimming in a liquid crystal depends on anchoring strength, Ericksen number, and viscosity ratios, revealing the dynamics of transient swimming in complex fluids.

Contribution

It introduces a minimal two-dimensional model to analyze transient swimming in liquid crystals, highlighting the effects of anchoring and Ericksen number on startup time.

Findings

Startup time increases with the ratio of rotational to shear viscosity.

Flow starts immediately under strong anchoring, but velocity reaches steady state after a relaxation time.

High Ericksen number results in behavior similar to strong anchoring conditions.

Abstract

When a microorganism begins swimming from rest in a Newtonian fluid such as water, it rapidly attains its steady-state swimming speed since changes in the velocity field spread quickly when the Reynolds number is small. However, swimming microorganisms are commonly found or studied in complex fluids. Because these fluids have long relaxation times, the time to attain the steady- state swimming speed can also be long. In this article we study the swimming startup problem in the simplest liquid crystalline fluid: a two-dimensional hexatic liquid crystal film. We study the dependence of startup time on anchoring strength and Ericksen number, which is the ratio of viscous to elastic stresses. For strong anchoring, the fluid flow starts up immediately but the liquid crystal field and swimming velocity attain their sinusoidal steady-state values after a time proportional to the relaxation time of the liquid crystal. When the Ericksen number is high, the behavior is the same as in the strong anchoring case for any anchoring strength. We also find that the startup time increases with the ratio of the rotational viscosity to the shear viscosity, and then ultimately saturates once the rotational viscosity is much greater than the shear viscosity.