Shear-stress controlled dynamics of nematic complex fluids

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 $\dot{\gamma }$.

10 pages, 11 figures

References in corpus (12)

• Control of unstable steady states by time-delayed feedback methods
• Spatio-temporal oscillations and rheochaos in a simple model of shear banding
• Dynamics of delay-coupled excitable neural systems
• Rheological Chaos in a Scalar Shear-Thickening Model
• Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke
• Effect of time delay on feedback control of a flashing ratchet
• Instability and spatiotemporal rheochaos in a shear-thickening fluid model
• Stabilizing continuous-wave output in semiconductor lasers by time-delayed feedback
• Routes to spatiotemporal chaos in the rheology of nematogenic fluids
• A minimal model for chaotic shear banding in shear-thickening fluids
• Delayed feedback induced directed inertia particle transport in a washboard potential
• Nematic-Isotropic Interfaces Under Shear: A Molecular Dynamics Simulation

Cited by in corpus (5)

• Amplitude-phase coupling drives chimera states in globally coupled laser networks
• The connection between shear thinning and biaxial orientation for quasi-ideal rods
• Non-linear rheology of active particle suspensions: Insights from an analytical approach
• Feedback control of flow alignment in sheared liquid crystals
• Binary mixtures of rod-like colloids under shear: microscopically-based equilibrium theory and order--parameter dynamics