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Abstrakty
The present paper deals with the problem of an incompressible axisymmetric creeping flow caused by a porous spherical particle in a spherical cavity filled with micropolar fluid. Depending on the kind of cell model, appropriate boundary conditions are used on the surface of sphere and spherical cavity. Drag force on the porous particle in the presence of a cavity is calculated to determine the correction factor to the Stokes law. A general expression for the hydrodynamic force acting on the porous sphere and, hence, for the wall correction factor of the sphere are obtained. The special cases of the porous sphere in viscous fluid, zero permeability solid sphere in micropolar fluid and viscous fluid are obtained in open and closed cavity respectively.
Rocznik
Tom
Strony
41--51
Opis fizyczny
Bibliogr. 25 poz., rys., tab.
Twórcy
autor
- Department of Mathematics, National Institute of Technology, Raipur-492010 Chhatisgarh, India
Bibliografia
- [1] Happel, J., & Brenner, H. (1965). Low Reynolds Number Hydrodynamics. N.J.: Prentice-Hall, Englewood Cliffs.
- [2] Joseph, D.D., & Tao, L.N. (1964). The effect of permeability in the slow motion of a porous sphere in a viscous liquid. Journal of Applied Mathematics and Mechanics, 44, 361-364.
- [3] Beavers, G.S., & Joseph, D.D. (1967). Boundary conditions at a naturally permeable wall. Journal of Fluid Mechanics, 30, 197-207.
- [4] Jones, I.P. (1973). Low Reynolds number flow past a porous spherical shell. Mathematical Proceedings of the Cambridge Philosophical Society, 73, 231-238.
- [5] Davis, R.H., & Stone, A.H. (1993). Flow through beds of porous particles. Chemical Engineering Science, 48(23), 3993-4005.
- [6] Srinivasacharya, D. (2007). Flow past a porous approximate spherical shell. Journal of Applied Mathematics and Physics, 58, 646-658.
- [7] Dassios, G., Hadjinicolaou, M., Coutelieris, F.A., & Payatakes, A.C. (1995). Stokes flow in spheroidal particle-in-cell models with Happel Kuwabara boundary conditions. International Journal of Engineering Science, 33, 1465-1490.
- [8] Faltas, M.S., & Saad, E.I. (2011). Stokes flow past an assemblage of slip eccentric spherical particle-in-cell models. Mathematical Methods in the Applied Sciences, 34, 1594-1605.
- [9] Eringen, A.C. (1966). Theory of micropolar fluids. Journal of Mathematics and Mechanics, 16, 1-18.
- [10] Eringen, A.C. (2001). Microcontinuum Field Theories II. New York: Springer, Fluent media.
- [11] Ariman, T., Turk, M.A., & Sylvester, N.D. (1974). Applications of microcontinuum fluid mechanics. International Journal of Engineering Science, 12, 273-293.
- [12] Lukaszewicz, G. (1999). Micropolar fluids-theory and applications. Basel: Birkhauser.
- [13] Rao, S.K.L., Rao, P.B. (1970). The slow stationary flow of a micropolar liquid past a sphere. Journal of Engineering Mathematics, 4, 209-217.
- [14] Ramkissoon, H., Majumdar, S.R. (1976). Drag on an axially symmetric body in the Stokes flow of micropolar fluid. Physics of Fluids, 19, 16-21.
- [15] Hoffmann, K.H., Marx, D., & Botkin, N.D. (2007). Drag on spheres in micropolar fluids with non-zero boundary conditions for microrotations. Journal of Fluid Mechanics, 590, 319-330.
- [16] Saad, E.I. (2008). Motion of a spheroidal particle in a micropolar fluid contained in a spherical envelope. Canadian Journal of Physics, 86, 1039-1056.
- [17] Sherief, H.H., Faltas, M.S., & Saad, E.I.(2013). Slip at the surface of an oscillating spheroidal particle in a micropolar fluid. ANZIAM Journal, 55, E1-E50.
- [18] Sherief, H.H., Faltas, M.S., Ashmawy, E.A., & Nashwan, M.G. (2015). Stokes flow of a micropolar fluid past an assemblage of spheroidal particle-in-cell models with slip. Physica Scripta, 90(5), 055203.
- [19] Saad, E.I.(2014). Motion of a slip sphere in a nonconcentric fictitious spherical envelope of micropolar fluid. ANZIAM J., 55, 383-401.
- [20] Sherief, H.H., Faltas, M.S., & El-Sapa, S. (2019) Axisymmetric creeping motion caused by a spherical particle in a micropolar fluid within a nonconcentric spherical cavity. European Journal of Mechanics-B Fluids, 77, 211-220.
- [21] Sherief, H.H., Faltas, M.S., & El-Sapa, S. (2019). Interaction between two rigid spheres moving in a micropolar fluid with slip surfaces. Journal of Molecular Liquids, 290, 111165.
- [22] Iyengar, T.K.V., & Radhika, T. (2011). Stokes flow of an incompressible micropolar fluid past a porous spheroidal shell. Bulletin of the Polish Academy of Sciences: Technical Sciences, 59, 63-74.
- [23] Mishra, V., & Gupta, B.R. (2017). Motion of a permeable shell in a spherical container filled with non-Newtonian fluid. Applied Mathematics and Mechanics, 38(12), 1697-1708.
- [24] Happel, J. (1958). Viscous flow in multiparticle systems, Slow motion of fluids relative to beds of spherical particles. AIChE Journal, 4, 197-201.
- [25] Kuwabara, S. (1959). The forces experienced by randomly distributed parallel circular cylinders or spheres in a viscous flow at small Reynolds numbers. Journal of the Physical Society of Japan, 14, 527-532.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9831231e-2534-42f9-80ae-162ccb948735