Biomedical Engineering Reference
In-Depth Information
σ
p
< σ
m
and ε
p
> ε
m
ε
p
> ε
m
ε
p
> ε
m
Re(
k
)
pDEP
+
+
-
-
+
+
-
-
ε
p
ε
p
+
V
-
V
+
V
-
V
+
0
nDEP
ε
m
ε
m
Crossover
frequency
Negative dielectrophoresis
Positive dielectrophoresis
Frequency
(b)
1
σ
p
< σ
m
and ε
p
> ε
m
Re(
k
)
0.5
II
p-DEP
0
0
n-DEP
III
I
-0.5
Crossover
frequency
10
3
10
4
10
5
10
6
10
7
10
8
(a)
Frequency
(c)
Frequency (Hz)
Figure 17.2
(See companion CD for color igure.)
.The.dependence.of.Clausius-Mossotti.(Re[K*]).factor.to.the.frequency.of.
an.electric.signal.and.the.corresponding.particle.motions..The.schematic.of.frequency.spectrum.of.Re[K*].factor.
(a).and.the.corresponding.particle.motions.in.p-DEP.and.n-DEP.(b)..(c).The.simulation.prediction.of.Re[
K
*].under.
an.AC.signal.of.a.broad.frequency.range.for.(i).a.nonconducting.particle.in.water.(ɛ
p
.=.2.4,.ɛ
m
.=.80,.Re[K*]∼−0.5),.
(ii).a.conductive.particle.in.water.(ɛ
p
.=.2.4,.σ
p
.=.0.01),.(iii).a.spherical.dual-shell.particle.(mimicking.a.mammalian.
cell,.with.ɛ
cyto
.=.75,.σ
cyto
.=.0.5.S/m).in.a.0.1.S/m.salt.solution..In.(ii),.the.particle.is.more.conductive.than.water.and.
shows.p-DEP.behaviors.at.low.frequencies,.while.behaviors.similar.to.the.particle.in.(i).at.high.frequencies..In.
(iii),.with.the.increasing.of.the.frequency,.the.multishell.sphere.exhibits.a.transition.from.n-DEP.to.p-DEP.and.
then.back.to.n-DEP.when.the.signal.frequency.reaches.very.high..(c):.Reproduced.with.kind.permission.from.
Springer.Science+Business.Media:.
BioMEMS Biomed. Nanotechnol
.,.Dielectrophoretic.traps.for.cell.manipulation,.
4,.2007,.159-186,.Voldman,.J.,.Springer,.E.D.,.Ferrari,.M.S.,.Bashir,.R.,.and.Wereley,.S.,.Copyright.2007.)
conductivity.dominates.the.magnitude.of.the.DEP.force,.while.the.permittivity.becomes.
the.predominant.factor.at.high.frequency..For.two.ultimate.cases,.
K
0
.(when.ω.=.0).and.
K
∞
.
(when. ω.=.∞),. Re[
K
*]. reduces. to.
Re
∗
∗
σ σ σ σ
,.
respectively..The.sign.of.Re[
K
*].clearly.indicates.two.different.DEP.motions:.negative.DEP.
(n-DEP). and. positive. DEP. (p-DEP),. as. shown. in. Figure. 17.2a.. In. n-DEP,. particles. move.
toward.the.ield.minima.while.in.p-DEP,.particles.move.toward.the.ield.maxima.(Figure.
17.2b).. The. frequency. spectrum. of. Re[
K
*]. is. provided. in. Figure. 17.2c. for. three. different.
cases:.(1).nonconductive.particles.in.an.insulator.liquid,.(2).conductive.particle.in.an.insu-
lator.liquid,.and.(3).conductive.particles.in.a.conductive.liquid..The.crossover.frequency.
(ω
c
).is.given.by
ε
. and.
Re
[
K
]
2
[
K
]
=
ε
−
ε
ε
+
2
=
−
+
0
p
m
p
m
∞
p
m
p
m
(
σ
−
σ σ
)(
+
2
2
σ
)
m
p
p
m
ω
=
.
(17.10)
c
(
ε
−
ε
)(
ε
+
ε
)
m
p
p
m
.
