Singular Damped Twist Waves in Chromonic Liquid Crystals

TL;DR

This paper investigates the formation of singularities in the relaxation dynamics of twist director profiles in chromonic liquid crystals, accounting for dissipation, and provides criteria and estimates validated by numerical simulations.

Contribution

It introduces a criterion for shock formation in dissipative chromonic liquid crystals and estimates the critical time for singularity development based on initial profiles.

Findings

Dissipation affects shock formation in chromonic liquid crystals.

Theoretical estimates match numerical simulations well.

Initial kink profiles determine shock development timing.

Abstract

Chromonics are special classes of nematic liquid crystals, for which a quartic elastic theory seems to be more appropriate than the classical quadratic Oseen-Frank theory. The relaxation dynamics of twist director profiles are known to develop a shock wave in finite time in the inviscid case, where dissipation is neglected. This paper studies the dissipative case. We give a sufficient criterion for the formation of shocks in the presence of dissipation and we estimate the critical time at which these singularities develop. Both criterion and estimate depend on the initial director profile. We put our theory to the test on a class of initial kink profiles and we show how accurate our estimates are by comparing them to the outcomes of numerical solutions.