Shear-stress controlled dynamics of nematic complex fluids

TL;DR

This paper explores the non-equilibrium dynamics of sheared nematic fluids under stress control, revealing that stress control simplifies the transition landscape and can stabilize chaotic states compared to shear rate control.

Contribution

It introduces a novel stress-controlled modeling approach for nematic fluids, showing how it alters dynamic transitions and stability compared to traditional shear rate control.

Findings

Stress control yields fewer dynamic transitions than shear rate control.

A tunable transition point depends on the delay time in the control scheme.

Stress control can stabilize chaotic states at fixed shear rate.

Abstract

Based on a mesoscopic theory we investigate the non-equilibrium dynamics of a sheared nematic liquid, with the control parameter being the shear stress $\sigma_{\mathrm{xy}}$ (rather than the usual shear rate, $\dot\gamma$). To this end we supplement the equations of motion for the orientational order parameters by an equation for $\dot\gamma$, which then becomes time-dependent. Shearing the system from an isotropic state, the stress- controlled flow properties turn out to be essentially identical to those at fixed $\dot\gamma$. Pronounced differences when the equilibrium state is nematic. Here, shearing at controlled $\dot\gamma$ yields several non-equilibrium transitions between different dynamic states, including chaotic regimes. The corresponding stress-controlled system has only one transition from a regular periodic into a stationary (shear-aligned) state. The position of this transition in the $\sigma_{\mathrm{xy}}$-$\dot\gamma$ plane turns out to be tunable by the delay time entering our control scheme for $\sigma_{\mathrm{xy}}$. Moreover, a sudden change of the control method can {\it stabilize} the chaotic states appearing at fixed $\dot\gamma$.