Steady Oseen’s flow past a deformed sphere: an analytical approach

• Autorzy: Srivastava D. K. , Yadav R. R. , Yadav S.
• Języki publikacji: EN

Abstrakty

EN

In a recent authors’ paper, the general expression of Stokes drag experienced by a deformed sphere in both longitudinal and transverse flow situations was calculated in terms of the deformation parameter up to the second order. In this paper, Oseen’s correction to the axial Stokes drag on the deformed sphere is presented by using Brenner’s formula in general, first and then applied to prolate and oblate the deformed spheroid up to the second order of the deformation parameter. Numerical values of Oseen’s correction is obtained with respect to the deformation parameter and Reynolds number. The corresponding variations are depicted in figures. Some particular cases of a needle shaped body and flat circular disk are considered and found to be in good agreement with those existing in the literature. The import ant applications are also highlighted.

Słowa kluczowe

EN

Stokes drag; Oseen’s drag; axially symmetric arbitrary body; axial flow

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2013
• Tom: Vol. 51 nr 3
• Strony: 661--673
• Opis fizyczny: Bibliogr. 21 poz., rys., tab.

Twórcy

autor

Srivastava D. K.

• University of Lucknow, Department of Mathematics, Lucknow, India

autor

Yadav R. R.

• University of Lucknow, Department of Mathematics, Lucknow, India

autor

Yadav S.

• University of Lucknow, Department of Mathematics, Lucknow, India

Bibliografia

• 1. Brenner H., 1961, The Oseen resistance of a particle of arbitrary shape, Journal of Fluid Mechanics , 11, 604-610
• 2. Chang I.D., 1960, Stokes flow of a conducting fluid past an axially symmetric body in the presence of a uniform magnetic field, Journal of Fluid Mechanics, 9, 3, 473-477
• 3. Chang I.D., 1961, On the wall effect correction of the Stokes drag formula for axially symmetric bodies moving inside a cylindrical tube, Zeitschrift f¨ur angewandte Mathematik und Physik, 12, 1, 6-14
• 4. Chang Y.C., Keh H.J., 2009, Translation and rotation of slightly deformed colloidal spheres experiencing slip, Journal of Colloid and Interface Science, 330, 201-210
• 5. Chester, W., 1962, On Oseen’s approximation, Journal of Fluid Mechanics, 13, 557-569
• 6. Chwang A.T.,Wu T.Y., 1976, Hydromechanics of low Reynolds number flow. Part 4: Translation of spheroids, Journal of Fluid Mechanics, 75, 677-689
• 7. Datta S., Srivastava D.K., 1999, Stokes drag on axially symmetric bodies: a new approach, Proceedings of the Indian Academy of Sciences, Mathematical Sciences, 109, 4, 441-452
• 8. Dyer T.W., Ohkawa T., 1992, Acoustic levitation by Oseen drag, Journal of the Acoustical Society of America, 92, 4, 2207-2211
• 9. Happel J., Brenner H., 1964, Low Reynolds Number Hydrodynamics, Nijhoff, Dordrecht, The Nederlands
• 10. Kaplun S., 1957, Low Reynolds number flow past a circular cylinder, Journal of Mathematics and Mechanics, 6, 595-603
• 11. Kaplun S., Lagerstrom P.A., 1957, Asymptotic expansions of Navier-Stokes solution for small Reynolds numbers, Journal of Mathematics and Mechanics, 6, 585-593
• 12. Krasovitskaya R.A., Ermolaev M.I., Mukhin A.A., Mil’shenko R.S., 1970, Use of Oseen’s correction in sedimentation analysis of powders, Chemistry and Materials Science (Refractories and Industrial Ceramics), 11, 7/8, 518-520
• 13. Lagerstrom P.A., Cole J.D., 1955, Examples illustrating expansion procedures for the Navier-Stokes equations, Journal of Rational Mechanics and Analysis, 4, 817-882
• 14. Oseen C.W., 1927, Neuere Methoden und Ergebnisse in der Hydrodynamik, Leipzig: Akademische Verlagsgesellschaft
• 15. Proudman I., Pearson J.R.A., 1957, Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder, Journal of Fluid Mechanics, 2, 237-262
• 16. Senchenko S., Keh H.J., 2006, Slipping Stokes flow around a slightly deformed sphere, Physics of Fluids, 18, 088101-04
• 17. Srivastava D.K., 2001, A note on Stokes drag on axi-symmetric bodies: a new approach, The Nepali Mathematical Science Report, 19, 1/2, 29-34
• 18. Srivastava D.K., 2012, Slender body theory for Stokes flow past axisymmetric bodies: a review article, International Journal of Applied Mathematics and Mechanics, 8, 15, 14-39
• 19. Srivastava D.K., Yadav R.R., Yadav S., 2012, Steady Stokes flow around deformed sphere: class of oblate bodies, International Journal of Applied Mathematics and Mechanics, 8, 9, 17-53
• 20. Stokes G.G., 1851, On the effect of the internal friction of fluids on the motion of pendulums, Transactions of the Cambridge Philosophical Society, 9, 182-187
• 21. Whitehead A.N., 1889, Second approximations to viscous fluid motion, Quarterly Journal of Mathematics, 23, 1, 143-152