Cell Model of a Fibrous Medium (Membrane). Comparison between Two Different Approaches to Varying Liquid Viscosity

Abstract

The paper concerns numerical study of a Stokes-Brinkman system with varying liquid viscosity that describes the fluid flow along a set of partially porous parallel cylindrical particles, which form a fibrous membrane, using the cell modeling. We have applied two different approaches to varying viscosity inside a porous layer: exponential and power decaying laws and compared the results. We proposed new numerical scheme based on Variation Iteration Method in order to solve the boundary value problems under consideration and compared results for velocity profiles near a porous cylindrical particle with an impermeable core placed into concentric liquid shell. We calculated the hydrodynamic permeability of a membrane, regarded as a swarm of such parallelly packed particles (fibers), being perpendicular to the membrane surface, in case of liquid flow normal to the membrane surface for both cell models mentioned above. The existence and uniqueness of the solutions obtained as well as some uniform estimates are also discussed.