Abstract
A theoretical investigation of ultrafiltration through hollow fibers used in artificial kidney applications is presented. The mass transfer through the semipermeable membranes is based on Starling’s hypothesis. The rheological problem is treated by regarding the blood as a multiple-structured fluid consisting of a Casson fluid and a surrounding cell-free plasma layer. The present model takes into account the effect of concentration polarization of plasma proteins at the fiber walls. In addition to the implicit character of the viscosity law, a difficulty arises from the fact that the viscosity of the blood plasma, which depends on the local plasma protein concentration, varies along the axis of the fiber and is not known a priori. The numerical solution of the theoretical model yields the total filtration rate as well as local quantities like the transmembrane fluid velocity and the protein concentration as functions of the fiber characteristics and transmembrane pressure drop. A particular application of the present model is the simulation of hemodilution and its effect on the ultrafiltration efficiency of the hollow fibers.
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