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Stationary bifurcations and tricriticality in a creeping nematic polymer flow. (English) Zbl 0812.76010

Numerical solutions to the Leslie-Ericksen equations for the transient and steady shear flows of a model rigid-rod nematic polymer are obtained using Galerkin finite elements, computational bifurcation methods, and gyroscopic torque balances.
Ten types of solutions are found and fully characterized. The stability of these ten types of solutions is established using both computational bifurcation methods and dynamic simulations.
Analogies between phase transitions, instabilities, and bifurcations are implemented. The novel result of coexistence of first- and second-order transitions, known as tricriticality, or equivalently, coexistence of supercritical and subcritical bifurcations, is fully characterized. The mechanism of the orientational transitions is established by computing the Frank elastic energy, the viscous and elastic torques acting on the director, and by a detailed parametric study of the effect of the controlling twist-bend elastic anisotropy.

MSC:

76A15 Liquid crystals
76E99 Hydrodynamic stability
76M10 Finite element methods applied to problems in fluid mechanics
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