INFLUENCE OF MAGNETIC FIELD ON THE STOKES FLOW THROUGH POROUS SPHEROID: HYDRODYNAMIC PERMEABILITY OF A MEMBRANE USING CELL MODEL TECHNIQUE

Abstract

The present work concerns an analysis of the creeping flow of steady, axisymmetric Stokes flow of an electrically conducting, viscous, incompressible fluid through a swarm of porous spheroidal particles in the presence of a uniform magnetic field. Cell model technique has been used to model the problem. Four known boundary conditions, Happel's, Kuwabara's, Kvashnin's, and Cunningham's (Mehta-Morse's), are used to find the hydrodynamic permeability of the membrane built up by porous spheroidal particles by using the perturbation method. The stress jump boundary condition for tangential stresses, along with the continuity of normal stress and velocity components, is used at the fluid-porous interface. The variation of the dimensionless hydrodynamic permeability of the membrane with the stress jump coefficient, the Hartmann number, and the dimensionless permeability of the porous region and particle volume fraction are discussed. The presented model can be used for the evaluation of changing hydrodynamic permeability of a membrane under the influence of a uniform magnetic field in pressure-driven processes (nano-, reverse osmosis, and microfiltration).