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.

本文探讨了通过血液透析仪膜过滤血液的过程中出现的问题。假定血液的行为像粘性牛顿流体一样，它流过2D通道，并带有包含Darcian多孔介质的可渗透边界。在血液过滤过程中动量传递的平衡中采用了众所周知的Brinkman模型。由于在慢流量情况下雷诺数的消失，因此提供了精确的解决方案。推导并分析了速度，压力，流量和泄漏通量的分布。还对平板透析器中血液过滤过程中理论结果的适用性进行了分类研究。从本模型计算出的过滤系数和透析器平均压降的计算值与过滤过程中的现有实验值非常吻合。因此，希望本模型在人造肾脏的血液净化过程中提供有希望的测量。