MICROPOLAR FLUID FLOWS RELATIVE TO A SWARM OF SPHERICAL POROUS SHELLS

This article investigates the creeping axisymmetric flow of an incompressible micropolar fluid past a swarm of porous shells. Employing the Darcy and a transition Brinkman porous layer, the study presents an analytical model that captures the flow behavior by integrating continuity conditions for velocity, normal and tangential stresses, and microrotations at fluid-porous interface regions. Distinct unit cell techniques, including those proposed by Happel, Kuwabara, Kvashnin, and Mehta and Morse, are analyzed to observe the effects of hydraulic resistivity, porous layer thickness, and porosity on the dimensionless drag for a bounded micropolar fluid system. The results, graphically represented in a series of plots, reveal a complex interplay between these parameters, significantly impacting drag forces and providing insight into the hydrodynamics of a swarm of porous particles, akin to that encountered in oral drug delivery systems. The study identifies a general inverse relationship between hydraulic resistivity and drag and highlights the nuanced effects of porous layer thickness and porosity on fluid resistance, with stark contrasts observed among different unit cell models. These findings underscore the importance of the chosen unit cell technique in predicting and optimizing the flow behavior in micropolar fluid systems.