Biomedical Engineering Reference
In-Depth Information
Figure 10.12
Evolution of the real part of the Clausius-Mossoti factor with the frequency. The point
s
is the crossover frequency (see more details in section 10.2.4.3).
We have plotted on Figure 10.12 the expression of Re(
f
CM
) in this high-
frequency regime. The low-frequency regime down to dc behavior cannot be de-
scribed by this curve. Below typically 1-10 kHz, Re(
f
CM
) decreases and the particles
may even take a negative DEP behavior.
10.2.3 Optimization of the Electric Field
10.2.3.1 Electrode Geometries
The exact three-dimensional landscape of the electric field intensity shapes the force
acting on the particles. Depending whether the final application is to trap them, to
set them into motion or in rotation, or to combine trapping and another force field
(such as a hydrodynamic flow), the constraints on the geometry of the electrodes
are different. For instance, one of the early geometries used “castellated electrodes”
that provided a good array of traps [40]. The exact calculation of the electric field
spatial variations can be performed via a finite elements analysis and the optimiza-
tion of their shapes and disposition in space becomes possible. Planar four elec-
trodes geometry can give precisely located trapping site in negative DEP but, when
possible, three-dimensional arrangements of two sets of four electrodes facing each
other give the best trapping cages (Figure 10.13) [41].
10.2.3.2 Electrodeless DEP
Practically, DEP comes inevitably with electrohydrodynamic flows that we will
detail in Section 10.2.6.2. In microstructures, even for modest applied voltages,
electric field can become extremely high and can easily trigger electrochemical in-
stabilities at the surface of the electrodes. This drawback is even worse when using
2-D electrodes in a channel or chamber having some depth (although there are some
