Summary
A general expression for the force exerted on a sphere excuting longitudinal oscillations, with small amplitude, in an incompressible micropolar fluid is obtained. This is accomplished by using direct integral consequences of the full field and the constitutive equations written in cartesian coordinates. The results which are independent of any boundary conditions are then applied to calculate the hydrodynamic force experienced by a sphere moving with rectilinear oscillating velocityu(t)=(u oeiλt, 0, 0) in an unbounded micropolar fluid. As a special case, a general expression for the drag in a similar viscous flow is also derived.
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References
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Sran, K.S. Longitudinal oscillations of a sphere in a micropolar fluid. Acta Mechanica 85, 71–78 (1990). https://doi.org/10.1007/BF01213543
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DOI: https://doi.org/10.1007/BF01213543