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Stokes drag on a disk sedimenting edgewise toward a plane wall. (English) Zbl 0772.76016

Summary: For comparison with the results of current experiments, a concise analytical method is developed to describe the non-axisymmetric flow generated by the edgewise sedimentation of a disk toward a plane wall. Since all Fourier modes contribute to the flow, the use of Abel transforms in earlier work [A. M. J. Davis, Phys. Fluids A 2, No. 3, 301-312 (1990; Zbl 0704.76018)] must be suitably extended in order to again obtain integral equations of the second kind. By expanding the wall effects in powers of \(D^{-1}\), where \(D\) is the distance from the disk axis to the wall, the dimensionless drag coefficient is found to order \(D^{-5}\) without having to solve the flow problem beyond the second Fourier mode.

MSC:

76D07 Stokes and related (Oseen, etc.) flows

Citations:

Zbl 0704.76018
Full Text: DOI

References:

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