Biomedical Engineering Reference
In-Depth Information
biotechnology community mainly because of its potential when coupled to
microstructures.
By definition, DEP is the motion induced by
nonuniform
electric fields and is
due to a contrast of polarizabilities between the particle and its solvent. For the
interested reader, there are some good textbooks that provide a far more detailed
description than the present short chapter [33-35].
Let us consider a particle in a solvent in the presence of an electric field. Because
of this field, charges accumulate nonuniformly at the interface with the surround-
ing medium. This charge distribution creates a dipole that itself interacts with the
electric field. If the field is not homogeneous and thus different on both sides of the
particle, a net force acts upon it that drives it toward the high electric field areas if
its polarizability is higher than that of the medium, and in the other direction if it
is smaller.
More quantitatively, the basic Maxwell equations tell us that a particle of po-
larizability
a
and of radius
a
experiences a force F in the presence of an external
electric field E given by:
2
3
2
3
F
=
π α
Ñ
E
(10.19)
The particles we are interested in are “lossy dielectrics.” This means that, on top of
the intrinsic permitivity of the particles, one has also to consider their conductivity
and the energy dissipated via this ionic conduction. In this framework, expressing
the polarizability in (10.19) leads to:
3
2
F
=
2
π ε ε
a
Re(
f
)
Ñ
E
(10.20)
0
r l
,
CM
where
e
0
is the vacuum permitivity,
e
r
,l
is the relative permitivity of the solvent,
f
CM
is the Clausius-Mossoti factor, and Re(f
CM
) is its real part:
*
*
ε ε
ε ε
-
p
l
f
=
(10.21)
CM
*
*
+
p
l
where
e
p
*
and
e
l
*
are respectively the complex permitivities of the particle and the
solvent:
j
σ
*
ε ε ε
=
-
(10.22)
0
r
ω
where
e
r
is the relative permitivity,
s
the conductivity and
w
the frequency of the
electric field.
We also note
e
l
=
e
0
·
e
r
,
l
and
e
p
=
e
0
·
e
r
,
p
Several consequences can be immediately derived from this expression:
·
The direction of the force exerted on the particle depends on the sign of the
real part of the Clausius Mosssoti factor: if Re(f
CM
) > 0, the particle is at-
tracted to the regions where the field is maximum (as illustrated on Figure
10.11): this is what is usually called positive dielectrophoresis. In the other
case, it is repelled from these areas (actually, it is the solvent that is attracted
