Engineering Transactions, 70, 3, pp. 287–299, 2022

Exact Solution for Non-Newtonian Fluid Flow Beyond a Contaminated Fluid Sphere

Vijaya Lakshmi KUNCHE
VIT-AP University Amaravati

Phani Kumar MEDURI
VIT-AP University Amaravati

Stokes flow of non-Newtonian fluid beyond a partially contaminated non-Newtonian fluid sphere with interfacial slip condition is considered. An analytic solution for the flow fields indicated by the stream function and the drag force over the sphere was obtained. Special well-known cases are reduced. It was observed that with an increase in slip parameter values, there is a rise in drag coefficient values.

Keywords: micropolar fluid; Gegenbauer function; modified Bessel’s function; stagnant cap
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).


Basset A.B., A Treatise on Hydrodynamics, London: Bell and Co., 1888.

Happel J., Brenner H., Low Reynolds Number Hydrodynamics, Martinus Nijoff Publishers, The Hague, 1983.

Feng Z.G., Michaelides E.E.., Mao S., On the drag force of a viscous sphere with interfacial slip at small but finite Reynolds numbers, Fluid Dynamics Research, 44(2): 025502, 2012,

Eringen A.C., Simple microfluids, International Journal of Engineering Science, 2(2): 205–217, 1964,

Eringen A.C., Linear theory of micropolar elasticity, Journal of Mathematics and Mechanics, 15(6): 909–923, 1966,

Łukaszewicz G., Micropolar Fluids: Theory and Applications, Birkhauser, Boston-Basel-Berlin, 1999.

Ramkissoon H., Majumdar S.R., Drag on axially symmetric body in the Stokes’ flow of micropolar fluid, The Physics of Fluids, 19(1): 16–21, 1976,

Jaiswal S., Yadav P.K.., Flow of micropolar-Newtonian fluids through composite porous layered channel with movable interfaces, Arabian Journal of Science and Engineering, 45(2): 921–934, 2020, /10.1007/s13369-019-04157-2.

Dang R.K., Goyal D., Chauhan A., Dhami S.S., Effect of non-Newtonian lubricants on static and dynamic characteristics of journal bearings, Materials Today: Proceedings, 28(Part 3): 1345–1349, 2020,

Alouaoui R., Ferhat S., Bouaziz M.N., MHD and stability for convective flow of micropolar fluid over a moving and vertical permeable plate, Defect and Diffusion Forum, 408: 51–65, 2021,

Rybczyński W., About the progressive movement of a liquid sphere in a viscous medium [in German: Über die fortschreitende Bewegung einer flüssigen Kugel in einem zähen Medium], Bulletin International de L'Académie des Science de Cracovie, 1: 40–46, 1911.

Hadamard J.S., Slow permanent motion of a liquid and viscous sphere in a viscous liquid [in French: Mouvement permanent lent d'une sphère liquide et visqueuse dans un liquide visqueux], Comptes Rendus Hebdomadaires des Seances de l Academie des Sciences, 152: 1735–1738, 1911.

Clift R., Grace J., Weber M.E., Bubble, Drops and Particles, New York: Academic Press, 1978.

Michaelidies E.E., Particles, Bubbles and Drops: Their Motion, Heat and Mass Transfer, Singapore: World Scientific, 2006.

Niefer R., Kaloni P.N., On the motion of a micropolar fluid drop in a viscous fluid, Journal of Engineering Mathematics, 14(2): 107–116, 1980,

Ramkissoon H., Flow of a micropolar fluid past a Newtonian fluid sphere, ZAMM – Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 65(12): 635–637, 1985,

Ramkissoon H., Majumdar S.R, Micropolar flow past a slightly deformed fluid sphere, ZAMM – Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 68(3): 155–160, 1988,

Hoffmann K.H., Marx D., Botkin N.D., Drag on spheres in micropolar fluids with non-zero boundary conditions for microrotations, Journal of Fluid Mechanics, 590: 319–330, 2007,

Deo S., Shukla P., Creeping flow of micropolar fluid past a fluid sphere with a non-zero spin boundary condition, International Journal of Engineering and Technology, 1(2): 67–76, 2012,

Sadhal S.S., Johnson R.E., Stokes flow past bubbles and drops partially coated with thin films. Part 1. Stagnant cap of surfactant film – exact solution, Journal of Fluid Mechanics, 126: 237–250, 1983,

Saboni A., Alexandrova S., Mory M., Flow around a contaminated fluid sphere, International Journal of Multiphase Flow, 36(6): 503–512, 2010,

Ramana Murthy J.V., Phani Kumar M., Drag over contaminated fluid sphere with slip condition, International Journal of Scientific & Engineering Research, 5(5): 719–727, 2014.

Ramana Murthy J.V.R, Phani Kumar M., Exact solution for flow over a contaminated fluid sphere for Stokes flow, Journal of Physics: Conference Series, 662(1): 012016, 2015,

Saboni A., Alexandrova S., Kaarsheva M., Effects of interface contamination on mass transfer into a spherical bubble, Journal of Chemical Technology and Metallurgy, 50(5), 589–596, 2015.

Abramowitz M., Stegun I.A., Handbook of Mathematical Functions, Dover Publications, New York, 1970.

DOI: 10.24423/EngTrans.1417.20220726