Biomedical Engineering Reference
In-Depth Information
Figure 7
. Simulation of ETF in a 2000 + 40
m cavity: (
a
) Quasistatic electric potential field,
calculated from two electrodes with potentials of +/- 7 V
rms
(1O-V peak-to-peak). (
b
) Tempera-
ture field resulting from a balance of Joule heating and thermal diffusion. The fluid has an
increase in temperature between the electrodes; electrodes conduct heat to the environment. (
c
)
Velocity vectors from 2D simulation of electrothermally generated fluid motion.
The convective scalar equation can be used to calculate the effect of electro-
thermally induced fluid motion on the analyte concentration in the cavity and the
analyte binding on a cavity wall:
s
C
G
2
+
uCDC
ΒΈ
=
,
[16]
s
t
where
C
is the concentration of antigen in the outer flow,
u
G
is the fluid velocity,
D
is the diffusivity of the antigen, and
t
is the time. Following the model given
by Myszka et al. (14), the rate of association is
k
a
C
(
R
T
-
B
), where
k
a
is the asso-
ciation constant,
C
is the concentration of antigen at the surface, and
R
T
-
B
is
the available antibody concentration. The rate of dissociation is
k
d
B
, where
k
d
is
the dissociation constant and
B
is the concentration of bound antigen. The time
