Biomedical Engineering Reference
In-Depth Information
10.2.4.4 The Crossover Frequency
From (10.23) and as it is illustrated on Figure 10.12, the behavior of the particles
switches from positive to negative DEP when the frequency of the applied field var-
ies. This frequency is called the crossover frequency and is a particularly convenient
(although far from complete) way to characterize particles. For instance a crossover
frequency spectrum for different conditions such as variable solvent conductivities
characterizes the dielectric constant and conductivity of the considered particle or
complex bioparticles [35].
This frequency is easily calculated by solving the equation Re(
f
CM
) = 0 and its
solution is then given by:
σ σ σ σ
π ε ε ε ε
(
¢
+
2 )(
¢
-
)
1
2
p
l
p
l
f
=
(10.28)
0
(
+
2 )(
-
)
p
l
p
l
where
s
p
¢ is given by (10.25).
A fit of such spectra as a function of the conductivity gives an accurate descrip-
tion of some characteristics of the particle (Figure 10.15).
s
p
¢ is also a function of the particle's radius. Equation (10.28) has been tested
for identical particles of various radii. The excellent agreement between theory and
experiments is a good way to determine the surface conductivity of these particles
(Figure 10.16).
10.2.5 Electrorotation and Traveling Wave
We have seen how DEP could be used to apply a force on polarizable particles in a
solvent in order to trap them. A similar physical principle can be used to set them in
rotation. Consider a polarizable particle in a rotating electric field such as the one
Figure 10.15
Fit of (10.27) (line) over experimental crossover frequencies measured at different
medium conductivities (squares). Particles are 216 nm polystyrene latex beads. (from [50]).
