Abstract

In hollow fibres dialyzers blood flows in the fibres channel and plasmafiltrates through their permeable wall to feed the flow of the permeate(dialyzate), which takes place among the fibres in the opposite direction.We investigate this fluid dynamical problem exploiting the existence of twoseparate scales: the one in the fibres direction ($\sim \,20\,cm$), and theone along the fibre radius ($\sim \,0.1\,mm$). We formulate a mathematicalmodel based on a two-scale approach providing a full description of theflows of the blood, of the dialyzate and the of the plasma through themembrane, as well as of the progressive increase of the hematocrit. Theproblem is characterized by various rather unusual features like the slipcondition of blood on the membrane and the feedback loop of boundary datafor the hematocrit. Blood rheology is assumed to be of shear-thinning type,with hematocrit dependent coefficients. Under some simplifications explicitsolutions are found. We show how the necessity of respecting severalconstraints and of reaching some specific targets influences the selectionof the geometrical and physical parameters of the system. Once the fluiddynamical problem has been solved, the removal from blood of chemicals likeurea, etc. has been studied.

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