Biomedical Engineering Reference
In-Depth Information
Figure 6.24
Contour plot of concentration at four different times after injection. The calculation
has been performed in a (
r
,
z
) coordinate system and only half of the channel is represented. The
solid wall is located at the bottom of each picture. The velocity field is given by the Hagen-Poiseuille
solution.
6.2.11 Determination of the Diffusion Coefficient
Measurement of liquid phase diffusion coefficients is based on the observation of
the spreading of the diffusing substance/solute. Diffusion coefficients are very small,
and measurements in macroscopic systems are not reliable because of uncontrolled
fluctuations of velocity. Because they are very laminar, easily controllable, and not
distorted, microflows are well adapted to the measurements of liquid phase diffu-
sion coefficients. The experimental principle is based on the mixing of the buffer
liquid alone and the buffer liquid with a concentration of the targeted substance, as
shown in Figure 6.25.
In the diffusing zone the streamlines are parallel and directed along the
x
-axis;
the substance/solute progressively diffuse in the
y
direction and there is a growing
distance
d
(
x
) of the concentration gradient. It can be shown that the concentration
profile is given by the relation [2, 11, 12].
æ
ö
1
y U
(6.80)
c x y
( , )
c
1
erf
=
-
ç
÷
0
2
4
Dx
è
ø
where
U
is the mean flow velocity. A fit of the relation (6.80) with the experimen-
tal concentration profile produces the value of the diffusion coefficient
D
(Figure
6.26).
