Dynamic simulations of shear-flow-induced chirality and twisted-texture transitions of a liquid-crystalline polymer

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Abstract
An alternative computational adaptive method to solve the Leslie-Ericksen equations of nematic hydrodynamics is presented. The method uses adaptive torque balances and is able to accurately compute arbitrary three-dimensional orientation fields. The method is applied, in conjunction with computational bifurcation methods, to solve the governing equations for a model rigid-rod, nonaligning, nematic polymer, in steady and transient rectilinear simple shear flows, using fixed parallel director anchoring. The five-component solution vector consists of the primary and secondary velocity components and the three-dimensional director field n. The parameter space is the line representing the magnitudes of the Ericksen number (scrE). According to the magnitude of scrE, seven types of stable steady-state solutions are found and fully characterized. The seven types of solutions are classified as in-plane solutions if the director remains within the shear plane, defined by the flow direction and the velocity gradient, and as out-of-plane (OP) solutions if the director field is out of the shear plane (three-dimensional orientation). The six OP solutions are three pairs of mirror-image solutions that differ from each other by their rotation number (Λ). Two pairs of out-of-plane solution branches are achiral (Λ=0) and display one-way twisting from the shear plane. One pair of out-of-shear-plane solution branches is chiral (Λ=±1) and displays a full 2π director rotation when going from the bottom plate to the top plate.