Axisymmetrical Flow of a Nematic Liquid Crystal around a Sphere

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Abstract
The axisymmetrical steady flow of an incompressible nematic liquid crystal around a sphere is studied on the basis of the Leslie-Ericksen equations. We assume low Reynolds numbers and a fixed director orientation parallel to the moving sphere (or the moving liquid crystal at infinite distance). The influence of the Leslie coefficient a, is neglected. We find a series representation for the streamfunction and the pressure. The force on the sphere, which only depends on the viscosity coefficients η1, and η2 but not on η3, can be represented by a simple formula. Stream line patterns and the pressure distribution on the sphere are presented for several viscosity coefficient ratios. The determination of viscosity coefficients on the basis of the measurement of the force on the sphere is discussed.

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