Friction Drag on a Sphere Moving in a Nematic Liquid Crystal

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Abstract
The apparent viscosity ηFB of a nematic liquid crystal measured in a falling ball experiment is computed, assuming that the velocity distribution around the sphere is the same as in isotropic liquids for conditions of creeping flow. It is derived a general expression giving ηFB as a function of the director distribution which allows an easy computation of ηFB when an external field is present. For the case where there is no external field present, the apparent viscosity is also computed, and the result is (to a good approximation) This expression is valid when the hydrodynamic torque is zero and it is rather independent (less than 1%) of the particular distribution of the director provided that the hydrodynamic torque is zero. It is also shown that, for this last situation, director tumbling is expected to occur even when − γ1/γ2 < 1, and that although ηFB is numerically close to the Miesowicz viscosity ηb the nematic director should not be necessarily oriented along the flow direction. These results are compared to the experimental data about MBBA and the agreement found is good.

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