Hydrodynamic permeability of membranes built up by spherical particles covered by porous shells: effect of stress jump condition.

This paper concerns the flow of an incompressible, viscous fluid past a porous spherical particle enclosing a solid core, using particle-in-cell method. The Brinkman's equation in the porous region and the Stokes equation for clear fluid are used. At the fluid-porous interface, the stress jump boundary condition for the tangential stresses along with continuity of normal stress and velocity components are employed. No-slip and impenetrability boundary conditions on the solid spherical core have been used. The hydrodynamic drag force experienced by a porous spherical particle enclosing a solid core and permeability of membrane built up by solid particles with a porous shell are evaluated. It is found that the hydrodynamic drag force and dimensionless hydrodynamic permeability depends not only on the porous shell thickness, particle volume fraction γ and viscosities of porous and fluid medium, but also on the stress jump coefficient. Four known boundary conditions on the hypothetical surface are considered and compared: Happel's, Kuwabara's, Kvashnin's and Cunningham's (Mehta-Morse's condition). Some previous results for the hydrodynamic drag force and dimensionless hydrodynamic permeability have been verified. [ABSTRACT FROM AUTHOR]