A porous media approach based on the volume-averaging theory has been proposed to investigate solute diffusion and ultrafiltration processes associated with hemodialysis using a hollow fiber membrane dialyzer. A general set of macroscopic governing equations has been derived for the three individual phases, namely, the blood phase, the dialysate phase, and the membrane phase. Thus, conservations of mass, momentum, and species are considered for blood compartments, dialysate compartments, and membranes within a dialyzer to establish a three concentration equation model. These macroscopic equations can be simultaneously solved for the various cases of inlet velocities of blood and dialysate. An analytic expression for the solute clearance was obtained for the one-dimensional case, in which important dimensionless parameters controlling the dialyzer system are identified for the first time.

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