Biomedical Engineering Reference
In-Depth Information
¬
¬
s
F
s
T
-
-
F
=
T
,
T
=
T
-
-
.
[14]
-
-
-
-
®
s
T
®
s
T
The first term on the right-hand side of Eq. [13] is the Coulombic force, and is
dominant at low frequencies. The second term is the dielectric force, and is
dominant at high frequencies. The crossover frequency scales inversely with the
charge relaxation time of the fluid, and typically occurs at around several MHz.
The electrothermal force shown in Eq. [13] is a body force on the fluid. The
motion of the fluid can be determined by solving the Stokes equation for zero
Reynolds number fluid flow, such that
G
G
0
=
P
+
N
2
u
+
F
,
[15]
ET
where
u
G
is the fluid velocity,
P
is the pressure in the fluid, and N is the dynamic
viscosity of the fluid.
3.3. AC Electroosmosis
AC electroosmosis arises when the tangential component of the electric
field interacts with a double layer along a surface. It becomes less important
with increasing electric field frequency. For example, in an aqueous saline solu-
tion with an electrical conductivity of T = 2 + 10
-3
S/m, it is predicted that AC
electroosmosis will not be important above 100 kHz (16).
3.4. Numerical Simulations of Electrothermal Flow
AC electrokinetics can be used to manipulate fluid motion and to enhance
the sensitivity of certain biosensors (20). The finite-element package CFD-ACE
+
(CFD Research, Huntsville, AL) was used to simulate electrothermally induced
flow and subsequent enhanced binding in the cavity. First, the quasistatic poten-
tial field for two long electrodes along the cavity wall is calculated (Figure 7a).
The Joule heating of the fluid from this electric field produces local changes in
temperature. Figure 7b shows the temperature field resulting from Joule heating.
From this temperature field, the electrothermal force,
F
G
, can be estimated
from Eqs. [13] and [14]. The fluid motion can be calculated using the Stokes
equation, Eq. [15]. Figure 7c shows the resulting velocity field. The velocity of
the ETF is on the order of 500
m/s and characterized by a pair of counter-
rotating vortices. This fluid motion will effectively stir the analyte, moving it
toward the immobilized antibodies.
ET
