Analytical Study of Creeping Flow through Porous Media Using Stress-Jump Condition

Abstract

This work investigates the creeping flow problem via a swarm of porous circular cylindrical particles using the cell model technique. Brinkman equation inside the porous cylindrical region is used, and Stokes equation for the clear fluid would be satisfied. The stress-jump condition, together with the continuity of the velocity components and the continuity of normal stress, are employed at the porous-liquid interfaces. In contrast, no-couple stress condition and no-spin condition are used on the outer boundary of the cell. In addition, we are applying no-slip boundary conditions on the surface of the solid core. Our problem is solved analytically, and stream function expressions are derived for the inside and outside flow fields. The influence of the drag force on each porous cylindrical particle in the cell is calculated. The graph depicts the variation of hydrodynamic permeability with various parameters and especially the impact of the jump coefficient. The results of this model may be used to examine the membrane filtration process.