Darcy-Brinkman flow of a viscous fluid through a porous duct: Application in blood filtration process

Abstract

This article explores the problem arising in the filtration process of blood through a membrane of hemodialyzer. The blood is assumed to behave like a viscous Newtonian fluid moving through a 2D channel with permeable boundaries containing a Darcian porous medium. The well known Brinkman model is adopted in the balance of momentum transfer during the blood filtration process. Construction of exact solutions is furnished due to the vanishing of Reynolds number in slow flow situation. The distributions of velocities, pressure, flow rate and the leakage flux are derived and analyzed. The applicability of the theoretical results during the filtration process of blood in flat plate dialyzer is also investigated categorically. The computed values of the filtration coefficient and the dialyzer mean pressure drop from the present model are found to be in excellent agreement with the existing experimental values during the filtration process. Therefore, it is hoped that the present model provides promising measurements during blood purification processes in artificial kidneys.