Biomedical Engineering Reference
In-Depth Information
FIGURE 14.23
Diffusion of wastes, ions, and water in the radial direction across a dialysis capillary tube pore.
section on fluid flow (momentum transport). The dialysate flow rate is typically much
higher than the blood flow rate in order to move the “dirty” dialysate (now having
received the wastes and excess ions from the blood) out of the dialyzer cartridge and bring
in clean dialysate. This keeps the concentration gradient for mass transfer large. A typical
blood flow rate through the cartridge is 200 ml/min, while the dialysate flow rate is
500-800 ml/min.
Blood entering the top of the dialyzer cartridge is cleared of wastes and excess ions by
the time blood leaves through the bottom of the cartridge. However, this blood is then
returned to the bloodstream to be mixed with the remainder of the blood. Therefore, in
order to completely clean the entire blood supply within the body, dialysis requires four
hours to complete.
Fick's Law describes the concentration-driven diffusion between blood and dialysate
across the pores of the capillary tubes. As such, each layer of Figure 14.23 indicates a diffu-
sivity (D), a thickness of the diffusion zone (
X), and a concentration gradient (C
b
-C
b
*),
which are all factors associated with one-dimensional Fick's Law. Each layer has its own
diffusivity, since D is a function of both the substance to be transported along with the
material through which it moves. Each layer has its own diffusion thickness and concentra-
tion gradient. It is true that the mass transfer of a given substance is the same for all three
layers, since there is no accumulation of any substance in an individual layer. Therefore, an
overall mass transfer rate across all three layers can be derived as shown on the bottom of
Figure 14.23 that uses the overall concentration gradient but incorporates the individual dif-
fusivities and individual thicknesses.
Water transport via dialysis cannot be conducted by means of concentration-driven
diffusion, since the water concentration gradient is in the wrong direction (from dialysate
toward blood). Therefore, water transport from blood to dialysate is controlled by means
of a hydrostatic pressure gradient, as shown in Figure 14.24.
The water transport is actually controlled via the dialysate flow rate, per the Bernoulli
effect, similar to the way a vacuum cleaner works. By having a large flow rate near an
r
