Shear-stress controlled dynamics of nematic complex fluids

Based on a mesoscopic theory we investigate the non-equilibrium dynamics of a sheared nematic liquid, with the control parameter being the shear stress $σ_{\mathrm{xy}}$ (rather than the usual shear rate, $\dotγ$). To this end we supplement the equations of motion for the orientational order parameters by an equation for $\dotγ$, 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 $\dotγ$. Pronounced differences when the equilibrium state is nematic. Here, shearing at controlled $\dotγ$ 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 $σ_{\mathrm{xy}}$-$\dotγ$ plane turns out to be tunable by the delay time entering our control scheme for $σ_{\mathrm{xy}}$. Moreover, a sudden change of the control method can {\it stabilize} the chaotic states appearing at fixed $\dotγ$.

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