Cell models for viscous fluid past a micropolar fluid spheroidal droplet

Abstract

The axisymmetric Stokes flow of an incompressible viscous fluid past a micropolar fluid spheroid whose shape deviates slightly from that of a sphere is studied analytically using the cell model technique. The boundary conditions used are the vanishing of the normal velocities, the continuity of the tangential velocities, the continuity of shear stresses and the spin-vorticity relation at the surface of the inner micropolar fluid spheroid. On the outer spheroidal cell containing viscous fluid, four known boundary conditions, namely Happel’s, Kvashnin’s, Kuwabara’s and Cunningham’s (Mehta–Morse) are considered. The wall correction factor exerted on the micropolar fluid spheroid is evaluated for all the four models and its dependence on the spin parameter, viscosity ratio, volume fraction, deformation parameter and micropolarity parameter is studied numerically and its variation is presented graphically. In limiting cases, the drag acting on the fluid spheroid in an unbounded medium is obtained. The drag expression is presented for the case of fluid spheroid when both the fluids are Newtonian.