This paper is focused on investigating the boundary effects of the steady translational motion of a semipermeable sphere located at the center of a spherical envelope filled with an incompressible micropolar fluid. Stokes equations of micropolar fluid are employed inside the spherical envelope and Darcy’s law governs in semipermeable region. On the surface of semipermeable sphere, the boundary conditions used are continuity of normal velocity, vanishing of tangential velocity of micropolar fluid, and continuity of pressure. On the surface of the spherical envelope, the Happel’s, Kuwabara’s, Kvashnin’s, and Cunningham’s boundary conditions, are used along with no spin boundary condition. The expression for the hydrodynamic normalized drag force acting on the semipermeable sphere is obtained. The limiting cases of drag expression exerted on the semipermeable sphere and impermeable solid sphere in cell models filled with Newtonian fluid are obtained. Also, in absence of envelope, the drag expression for the micropolar fluid past a semipermeable sphere is obtained.
Cell Models for Non-Newtonian Fluid Past a Semipermeable Sphere
