Biomedical Engineering Reference
In-Depth Information
Figure 5.17
Schematic view of the primers concentration and the PCR reaction regions (drawing
not to scale).
In the following we present two approaches to calculate the diffusion inside
the capillary. The first one is an analytical approach, based on the simplification
that the concentration in primers—after a few seconds—is uniform in a cross sec-
tion of the tube. The second approach consists in numerically solving the diffusion
equation after it has been rendered nondimensional. The advantage of this second
solution is that it gives insight on the diffusion barrier.
5.3.8.2 Analytical Model for Diffusion Inside a Tube
First, taking into account that the ratio L/R between the tube length and the tube
radius is large, we show that we can assume the concentration in primers uniform
in any cross section in a very short time after their release from the wall. A charac-
teristic diffusion time for a primer to diffuse on the length
R
is
2
R
D
τ
»
(5.34)
4
Primers have a diffusion coefficient of the order
D
= 10
-10
m
2
/s, and suppose
that the radius of the tube is
R
= 50
m
m. The characteristic time is then
t
= 6 sec-
Figure 5.18
Schematic view of the concentration profile of the different PCR reaction products.
