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A theorem for a fluid Stokes flow

Published online by Cambridge University Press:  17 February 2009

D. Palaniappan ,
S. D. Nigam  and
T. Amaranath
D. Palaniappan
Affiliation:
School of Math. and Comp./Inf. Sc, University of Hyderabad, India.
S. D. Nigam
Affiliation:
School of Math. and Comp./Inf. Sc, University of Hyderabad, India.
T. Amaranath
Affiliation:
School of Math. and Comp./Inf. Sc, University of Hyderabad, India.
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Abstract

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A sphere theorem for non-axisymmetric Stokes flow of a viscous fluid of viscosity μe past a fluid sphere of viscosity μi is stated and proved. The existing sphere theorems in Stokes flow follow as special cases from the present theorem. It is observed that the expression for drag on the fluid sphere is a linear combination of rigid and shear-free drags.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 3 , January 1994 , pp. 335 - 347
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Butler, S. F. J., “A note on Stokes stream function for the motion of a spherical boundary”, Proc. Camb. Phil. Soc. 49 (1953) 168–174.CrossRefGoogle Scholar
[2]Collins, W. D., “Note on a sphere theorem for the axisymmetric Stokes flow of a viscous fluid”, Mathematika 5 (1958) 118–121.CrossRefGoogle Scholar
[3]Fuentes, Y. O., Kim, S. and Jeffrey, D. J., “Mobility functions for two unequal viscous drops in Stokes flow I Axisymmetric motions”, Phy. Fluids 31 (1988) 2445–2455.CrossRefGoogle Scholar
[4]Fuentes, Y. O., Kim, S. and Jeffrey, D. J., “Mobility functions for two unequal viscous drops in Stokes flow II Axisymmetric motions”, Phy. Fluids A 1 (1989) 61–76.CrossRefGoogle Scholar
[5]Hackborn, W., O'Neill, M. E. and Ranger, K. B., “The structure of an asymmetric Stokes flow”, Q. J. Mech. Appl. Math. 39 (1986) 1–14.CrossRefGoogle Scholar
[6]Hadamard, J. S., Compt. Rend. Acad. Sci. (Paris) 152 and 154 (1911 and 1912) 1735 and 109.Google Scholar
[7]Harper, J. F., “Axisymmetric Stokes flow images in spherical free surfaces with applications to rising bubbles”, J. Aust. Math. Soc. Ser. B 25 (1983) 217–231.CrossRefGoogle Scholar
[8]Hetsroni, G. and Haber, S., “The flow in and around a droplet or bubble submerged in an unbound arbitrary velocity field”, Rheol. Acta 9 (1970) 488–496.CrossRefGoogle Scholar
[9]Higdon, J. J. L., “A hydrodynamic analysis of flagellar propulsion”, J. Fluid Mech. 90 (1979) 685–711.CrossRefGoogle Scholar
[10]Lamb, H., Hydrodynamics, (Dover, 1945) 596.Google Scholar
[11]Oseen, C. W., Hydrodynamik (Acad. Verlag, Leipzig, 1927).Google Scholar
[12]Palaniappan, D., Nigam, S. D., Amaranath, T. and Usha, R., “A theorem for a shear-free sphere in Stokes flow”, Mech. Res. Comm. 17 (1990) 429–435.CrossRefGoogle Scholar
[13]Palaniappan, D., Nigam, S. D., Amaranath, T. and Usha, R., “Lamb's solution of the Stokes equations - A sphere theorem”, Q. J. Mech. Appl. Math. 45 (1992) 47–56.CrossRefGoogle Scholar
[14]Rallison, J. M., “Note on Faxen relations for a particle in Stokes flow”, J. Fluid Mech. 88 (1978) 529–533.CrossRefGoogle Scholar
[15]Rybczynski, W., Bull. Acad. Sci. Cracovie Ser. A (1911) 40.Google Scholar
[16]Shail, R., “A note on some asymmetric Stokes flows within a sphere”, Q. J. Mech. Appl. Math. 40 (1987) 223–233.CrossRefGoogle Scholar
[17]Shail, R. and Onslow, S. H., “Some Stokes flows exterior to a spherical boundary”, Mathematika 35 (1988) 233–246.CrossRefGoogle Scholar