Flow in a spherical cavity due to a stokeslet |
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| Affiliation: | 1. Environmental Fluid Mechanics, Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, Stevinweg 1, 2600 GA Delft, The Netherlands;2. Department of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;1. Neuroscience Research Australia and Prince of Wales Clinical School, University of New South Wales, Australia;2. Department of Clinical Medicine, Macquarie University, Australia;3. School of Chemical and Biomolecular Engineering, The University of Sydney, Australia |
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| Abstract: | The earth is considered as a rigid spherical cavity of radius a filled with a highly viscous incompressible fluid of viscosity η. The non-axisymmetric problem of flow due to a stokeslet of strength F/8πη located at (0, 0, c), c < a with its axis along OX, O being the centre of the sphere, is discussed for small Reynolds numbers. The expressions for velocity and pressure are obtained in terms of A(r, θ, φ) and B(r, θ, φ), biharmonic and harmonic functions respectively, using a sphere theorem for non-axisymmetric flow inside a sphere. The drag on the sphere exerted by the fluid is found to be independent of the location of the stokeslet. |
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