Eur. Phys. J. Plus (2017) 132: 469
https://doi.org/10.1140/epjp/i2017-11744-9

Regular Article

Axisymmetric Stokes flow past a composite spheroidal shell of immiscible fluids

Department of Mathematics, National Institute of Technology, Raipur-492010, Chhattisgarh, India

^* e-mail: madaspra.maths@nitrr.ac.in

Received: 15 December 2016
Accepted: 6 October 2017
Published online: 9 November 2017

Abstract

We study the flow of an incompressible Newtonian fluid past a composite spheroidal shell whose shape deviates slightly from that of a sphere. A composite particle referred to in this paper is a spheroidal liquid core covered with a porous layer. The Brinkman equation is used for the flow inside the porous medium and the Stokes equation is used for the flow in the fluid region. We assume that the external and internal viscous fluids are immiscible and the viscosity of the porous medium is different than the viscosity of pure liquid. The Ochoa-Tapia and Whitaker’s stress jump boundary condition for tangential stress is applied on the porous-fluid interface. Velocity and pressure distributions are found and the drag force acting on the spheroidal shell is evaluated. The analytical solution is obtained by dividing the flow into three regions. Both type of spheroids, oblate and prolate are considered. Numerical results of the normalized hydrodynamic drag force acting on the spheroidal shell are tabulated and represented graphically for different values of the parameters characterizing the stress jump coefficient, separation parameter, permeability, deformation parameter, and viscosity ratios. The analysis of the flow pattern is done by plotting streamlines and several renowned cases are deduced.