Countercurrent Flow Hemodialyzer
This Demonstration models a countercurrent hemodialyzer. In a typical hemodialyzer, blood flows through a bundle of approximately 10,000 hollow fibers, each with an inner diameter of about 200 micrometers, wall thickness of 20 micrometers and a length of 16 to 25 cm. The walls of the hollow fibers function as the dialysis membrane; dialyzate flows countercurrently in the shell side .[more]
Solutes are removed from the blood at different rates depending on their molecular weight and diffusivity; thus the blood is recirculated until all solutes reach a desirable level in the patient's blood. Use the sliders to vary the solute diffusion coefficient and the average velocities of the blood and dialyzate to observe the effects on the dialyzate concentrations.[less]
Following are the details of the mathematical model.
The system is at steady state.
The physical properties are constant.
There is fully developed laminar flow in the blood side and plug flow in the dialyzate side.
All fibers have the same diameter, fluid flow and mass transfer characteristics.
The equation for continuity of the solute for the blood side is:
subject to the boundary conditions:
The equation for continuity of the solute for the dialyzate side is:
with boundary condition
The average (cup) concentrations of the solute in the blood and the dialyzate are:
and are the average velocities of the blood and the dialyzate, respectively
and are the axial and radial coordinates
and are the inner and outer diameters of the fiber
is the number of fibers
is the length of the fiber
is the diffusivity of the solute in the blood
is a mass transfer coefficient
is the Sherwood number, defined as the ratio of convective mass transfer rate to diffusion rate
 C. Ronco, A. Brendolan, C. Crepaldi, M. Rodighiero and M. Scabardi, "Blood and Dialysate Flow Distributions in Hollow-Fiber Hemodialyzer Analyzed by Computerized Helical Scanning Technique," Journal of the American Society of Nephrology, 13(Suppl 1), 2002 S53–S61. jasn.asnjournals.org/content/13/suppl_1/S53.