Biomedical Engineering Reference
In-Depth Information
of pressure-driven flow, different-sized particles can be separated based on the
balance of DEP force and fluid drag force from an electrothermally generated
flow. Figure 5 depicts how particles can be separated by varying sizes under the
influence of DEP and electrothermal flow. By varying the frequency (up to 500
kHz) and the voltage (up to 10 V peak-to-peak), the stable position of the larger
beads can be moved from the electrode edges to position A, or to position B.
DEP has also been demonstrated by Huang (9), (Nanogen Inc., San Diego)
to concentrate a dilute sample of E. coli cells by 20-fold and to separate E. coli
cells from B. globigii cells. A picture of the microfabricated electrode structure
and captured bacteria is shown in Figure 6.
3.2. Electrothermally Driven Flow
Electrothermal body forces are created by nonuniform Joule heating of the
medium. The Joule heating is a source term in the temperature equation, and
creates spatial variations in conductivity and permittivity, which in turn create
Coulomb and dielectric body forces in the presence of an externally applied
electric field. The resulting fluid motion can be determined by solving the Na-
vier-Stokes equation with the electrothermal body force. Electrothermally driven
flow can be simulated by solving for the quasistatic electric field in a specific
geometry. The nonuniform electric field gives rise to nonuniform temperature
fields through Joule heating. Ignoring unsteady effects and convection, and bal-
ancing thermal diffusion with Joule heating yields
k / 2 T + T E 2 = 0,
[12]
where T is temperature and E 2 is the magnitude squared of the electric field,
given by E
G
, where k and T are the thermal and electrical conductivity.
Gradients in temperature produce gradients in permittivity and conductivity
in the fluid. For water (1/T)(0T/0 T ) = +2% and (1/F)(0F/0 T ) = -0.4% per degree
Kelvin. These variations in electric properties produce gradients in charge den-
sity and perturb the electric field. Assuming the perturbed electric field is much
smaller than the applied electric field, and that advection of electric charge is
small compared to conduction, the time-averaged electrothermal force per unit
volume for a non-dispersive fluid can be written as (17)
=
V
G
G
 
G
G
¯
¬
-
TF
F
E
2
¡
°
F
=
0.5
E
rms
+
0.5
E
F
,
[13]
-
--
¡
°
rms
2
rms
TF
®
1( )
+
U
¢
±
where U = F/T is the charge relaxation time of the fluid medium and the incre-
mental temperature-dependent changes are
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