Shear induced instabilities in layered liquids

TL;DR

This paper extends smectic A hydrodynamics to include both layering and nematic order, revealing how shear-induced effects can cause layer undulations and instabilities, aligning well with recent experiments and simulations.

Contribution

It introduces a comprehensive hydrodynamic model incorporating layer displacement, director orientation, and their couplings, to explain shear-induced layer instabilities in smectic A systems.

Findings

Layer undulation instability occurs above a certain shear threshold.

The nematic director's coupling to shear influences layer stability.

Material parameters significantly affect the instability behavior.

Abstract

Motivated by the experimentally observed shear-induced destabilization and reorientation of smectic A like systems, we consider an extended formulation of smectic A hydrodynamics. We include both, the smectic layering (via the layer displacement u and the layer normal p) and the director n of the underlying nematic order in our macroscopic hydrodynamic description and allow both directions to differ in non equilibrium situations. In an homeotropically aligned sample the nematic director does couple to an applied simple shear, whereas the smectic layering stays unchanged. This difference leads to a finite (but usually small) angle between n and p, which we find to be equivalent to an effective dilatation of the layers. This effective dilatation leads, above a certain threshold, to an undulation instability of the layers. We generalize our earlier approach [Rheol. Acta, vol.39(3), 15] and include the cross couplings with the velocity field and the order parameters for orientational and positional order and show how the order parameters interact with the undulation instability. We explore the influence of various material parameters on the instability. Comparing our results to recent experiments and molecular dynamic simulations, we find a good qualitative agreement.