Biomedical Engineering Reference
In-Depth Information
occurs for the particle either more or less polarizable than the suspending medium
as shown in Fig.
11.1a, b
, respectively. On the other hand, consider a particle more
polarizable than the medium in a spatially nonuniform electric field (Fig.
11.1c
).
Because the electric field near the left electrode is higher, the columbic force on the
left side is larger (
F
Q
>
F
q
). As a result, the net force attracts the particle to the high
electric field region. This motion is known as positive DEP (pDEP). In contrast,
when a particle is less polarizable than the suspending medium, the net force repels
the particle to be away from the high electric field region (Fig.
11.1d
). This motion
is known as negative DEP (nDEP).
Under an AC electric field,
E
ac
~
ð
, the DEP force acting on a dielectric particle
can be quantified by using the effective dipole moment method [
25
]. Assuming that
the particle and suspending medium have dielectric permittivities of
e
p
and
e
m
, and
conductivities of
s
p
and
s
m
, respectively, the time-average DEP force acting on the
particle with radius
a
can be expressed as
r
;
t
¼
F
DEP
2
pe
m
a
3
Re K
ðoÞ
E
rms
½
(11.1)
p
denotes the time-average,
E
rms
;
ac
¼ E
ac
where
hi
is the root-mean-square
magnitude of the applied AC electric field and
r
denotes a gradient operator.
Re
K
ðoÞ
K
½
is the real part of the Clausius-Mossotti (CM) factor and
0
:
5
Re
½
1.
K
ðÞ
ðÞ
is a function of electric field frequency and complex permittivities
of the particle and the suspending medium, and it can be expressed as
e
p
e
m
e
p
þ
K
ðÞ¼
(11.2)
2
e
m
where
e
p
¼ e
p
and
e
m
¼ e
m
are the complex permittivities of the
particle and the suspending medium, respectively,
i
is
p
=
is
m
=
p
, and
o ¼
2
pf
is the
radian field frequency. From (
11.1
), under the same applied electric field condition,
the sign and magnitude of the DEP force depends on both
Re K
ðoÞ
¼
½
and particle
size. When
Re K
ðoÞ
0, it is indicated that the particle is more polarizable than the
suspending medium and it experiences a pDEP force (Fig.
11.1c
). On the other
hand,
Re K
ðoÞ
½
>
0 indicates that the particle is less polarizable than the suspending
medium and it experiences an nDEP force (Fig.
11.1d
). Furthermore, as
Re K
ðo½
becomes zero, both particle and the suspending medium are equally polarizable and
the corresponding frequency is known as the cross-over frequency where the DEP
force vanishes. Therefore, cells of the same size possessing distinct polarizabilities
(nDEP and pDEP) can be separated from each other. In some cases where cells have
the same polarizability but are of different size, larger cells experiencing a stronger
nDEP force can be repelled farther away from the high electric field region than the
smaller ones, thus achieving separation. In addition, due to the complex structure of
biological cells such as yeast and bacterial cells, the CM factor can be determined
by modeling the structure of a cell as consisting of three concentric layers. For yeast
cells, the three layers are wall, cytoplasm, and nucleus [
26
]. For bacterial cells, the
½
<
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