Viscoelastic nematodynamics

TL;DR

This paper introduces a comprehensive viscoelastic model for nematic liquid crystals that captures their complex acoustic and rheological behaviors, including anisotropic sound propagation and frequency-dependent viscosity, across various shear rates.

Contribution

The authors extend previous theories to include compressibility, anisotropic elasticity, and dynamic relaxation, providing a unified model that explains solid-like and fluid-like features of nematics at different frequencies.

Findings

Model agrees with Ericksen-Leslie theory at low frequencies

Captures relaxation mechanisms at intermediate frequencies

Identifies four relaxation times consistent with uniaxial symmetry

Abstract

Nematic liquid crystals exhibit both crystal-like and fluid-like features. In particular, the propagation of an acoustic wave shows an unexpected occurrence of some of the solid-like features at the hydrodynamic level, namely, the frequency-dependent anisotropy of sound velocity and acoustic attenuation. The non-Newtonian behavior of nematics also emerges from the frequency-dependent viscosity coefficients. To account for these phenomena, we put forward a viscoelastic model of nematic liquid crystals, and we extend our previous theory to fully include the combined effects of compressibility, anisotropic elasticity and dynamic relaxation, at any shear rate. The low-frequency limit agrees with the compressible Ericksen-Leslie theory, while at intermediate frequencies the model correctly captures the relaxation mechanisms underlying finite shear and bulk elastic moduli. We show that there are only four relaxation times allowed by the uniaxial symmetry.