Creeping flow of Micropolar fluid past a fluid sphere with non-zero spin boundary condition
About this article
Abstract
Abstract: This paper concerns the problem of creeping flow of an incompressible micropolar fluid past a fluid sphere with non-homogeneous boundary condition for micro rotation vector i.e. the micro rotation on the boundary of the fluid sphere is assumed to be proportional to the rotation rate of the velocity field on the boundary. The stream functions are determined by matching the solution of micropolar field equation for flow outside the fluid sphere with that of the Stokes equation for the flow inside the fluid sphere. The drag force experienced by a fluid sphere is evaluated and its variation is studied with respect to the material parameters. Some well-known results are then deduced.
References
[1] Eringen, A.C.: Simple microfluids, Int. J. Engng. Sci., 2, 205-217(1964).
[2] Eringen, A.C.: Linear theory of micropolar elasticity, J. Math. Mech., 15(6), 909-923(1966).
[3] Rao, S.K.L. and Rao, P.B.: Slow stationary micropolar fluid past a sphere, J. Eng. Math., 4, 209-217(1970).
[4] Ramkissoon, H. & Majumdar, S. R.: Drag on axially symmetric body in the Stokes’ flow of micropolar fluid. Phys. Fluids 19(1), 16–21 (1976).
[5] Ramkissoon, H.: Flow of micropolar fluid past a Newtonian fluid sphere. Z. Angew. Math. Mech., 65(12), 635-637(1985).
View more references (4)
[6] Ramkissoon, H.: Micropolar flow past a slightly deformed fluid sphere. Z. Angew. Math. Mech., 68(3), 155-160(2006).
[7] Hoffmann, K.H., Marx, D. Botkin, N.D.: Drag on spheres in micropolar fluids with non-zero boundary conditions for microrotations, J. Fluid Mech., 590, 319-330 (2007).
[8] J. Happel and H. Brenner; Low Reynolds Number Hydrodynamics, Martinus Nijoff Publishers, The Hague, 1983.
[9] M. Abramowitz and I.A. Stegun, I.A. Handbook of Mathematical Functions, Dover Publications, New York, 1970.