Abstract
A method of computing general Stokes flows in the presence of rigid boundaries of arbitrary shape is proposed. The solution satisfies the governing field equations exactly and the boundary conditions approximately. The method has been illustrated with three examples. The advantage of the method lies in the ease of implementation for rigid bodies of arbitrary shape, providing an approximate but analytical solution throughout the domain.
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References
Lighthill S.J.: Mathematical Biofluiddynamics. Society for Industrial and Applied Mathematics, Philadelphia (1975)
Blake J.R., Liron N., Aldis G.K.: Flow patterns around ciliated microorganisms and in ciliated ducts. J. Theor. Biol 98(1), 127–141 (1982)
Chwang A.T., Yao-Tsu Wu T.: Hydromechanics of low Reynolds number flow. Part 1: Rotation of axisymmetric prolate bodies. J. Fluid Mech. 63(3), 607–622 (1974)
Chwang A.T., Yao-Tsu Wu T.: Hydromechanics of low-Reynolds-number flow. Part 2: Singularity method for Stokes flow. J. Fluid Mech. 67(4), 787–815 (1975)
Stokes G.G.: On the theories of internal friction of fluids in motion. Trans. Camb. Phil. Soc 8, 287–305 (1845)
Lamb, H.: Hydrodynamics, 6th edn. Cambridge University Press, Cambridge (1932); New York, Dover (1945)
Palaniappan D., Nigam S.D., Amaranath T., Usha R.: Lamb’s solution of Stokes equations, a sphere theorem. Quart. J. Mech. Appl. Math. 45(1), 47–56 (1992)
Hasimoto H.: Derivation of a sphere theorem for the Stokes flow following Imai’s procedure. Fluid Dyn. Res. 39, 521–525 (2007)
Acrivos A., Taylor T.D.: The Stokes flow past an arbitrary particle—the slightly deformed sphere. Chem. Eng. Sci. 19, 445–451 (1964)
Payne L.E., Pell W.H.: The Stokes flow problem for a class of axially symmetric bodies. J. Fluid Mech. 7, 529–549 (1960)
Oberbeck A.: Ueber stationäre Flüssigkeitsbewegungen mit Berücksichtigung der inneren Reibung. J. Reine. Angew. Math. 81, 62–80 (1876)
Jeffery G.B.: The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–179 (1922)
Kim S., Arunachalam P.V.: The general solution for an ellipsoid in low-Reynolds-number flow. J. Fluid Mech. 178, 535–547 (1987)
Kim S., Karrila S.J.: Microhydrodynamics: Principles and Selected Applications. Butterworth Heinemann Series in Chemical Engineering, London (1991)
Bourot J.M.: Sur l’application d’une méthode de moindres carrés à la résolution approchée du probléme aux limites, pour certaines catégories d’écoulements. J. Méc. Théor. Appl. (France) 8(2), 301–322 (1969)
Bourot J.M.: On the numerical computation of the optimum profile in Stokes flow. J. Fluid Mech. 65, 513–515 (1974)
Hellou M., Coutanceau M.: Cellular Stokes flow induced by rotation of a cylinder in a closed channel. J. Fluid Mech. 236, 557–577 (1992)
Lecoq N., Masmoudi K., Anthore R., Feuillebois F.: Creeping motion of a sphere along the axis of a closed axisymmetric container. J. Fluid Mech. 585, 127–152 (2007)
Radha R., Sri Padmavati B., Amaranath T.: New approximate analytical solutions for creeping flow past axisymmetric rigid bodies. Mech. Res. Commun. 37, 256–260 (2010)
Padmavathi B.S., Rajasekhar G.P., Amaranath T.: A note on complete general solution of Stokes equations. Quart. J. Mech. Appl. Math. 50(3), 383–388 (1998)
Oseen C.W.: Hydrodynamik. Akademische Verlag, Leipzig (1927)
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Radha, R., Sri Padmavati, B. & Amaranath, T. A new approximate analytical solution for arbitrary Stokes flow past rigid bodies. Z. Angew. Math. Phys. 63, 1103–1117 (2012). https://doi.org/10.1007/s00033-012-0218-8
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DOI: https://doi.org/10.1007/s00033-012-0218-8