M. Krishna Prasad

Creeping flow past a porous approximately spherical shell: stress jump boundary condition

The creeping flow of an incompressible viscous liquid past a porous approximately spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier–Stokes equations. The flow within the porous annular region of the shell is governed by Brinkman’s model. The boundary conditions used at the interface are continuity of the velocity, continuity of the pressure and Ochoa-Tapia and Whitaker’s stress jump condition. An exact solution for the problem and an expression for the drag on the porous approximately spherical shell are obtained. The drag is evaluated numerically for several values of the parameters governing the flow. doi:10.1017/S144618111100071X

Axisymmetric Stokes flow past a composite spheroidal shell of immiscible fluids

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.