Biomedical Engineering Reference
In-Depth Information
accumulate.at.the.interface.of.the.particle.and.the.luid..If.in.a.uniform.electric.ield,.the.
attraction. forces. exerted. on. the. particle. from. all. directions. are. equal. in. magnitude. and.
cancel. each. other. so. that. the. particle. remains. stationary. (Figure. 17.1a).. However,. if. the.
electric.ield.is.nonuniform,.the.ield.gradient.induces.a.dipole.moment.on.the.particle.and.
drives.the.polarized.particle.to.move.either.toward.or.against.the.ield.maxima,.depending.
on.the.dielectric.property.of.the.particle.and.its.surrounding.medium.(Figure.17.1b)..The.
nonuniform.electric.ield.can.be.generated.by.either.an.AC.or.a.direct.current.(DC).signal..
Correspondingly,.we.name.them.AC-based.DEP.and.DC-based.DEP.
17.2.1 Derivation of DeP Force
In.a.nonuniform.electric.ield,.the.induced.dipole.can.be.simpliied.as.two.equal.but.oppo-
site.point.changes.with.a.charge.density.of.
q
,.as.shown.in.Figure.17.1c..The.net.force.on.the.
dipole.can.then.be.written.as
Dipole
=
2
F
q
E r d
(
+
)
−
q
E r
( )
=
q
d
⋅∇ +
E
O
(
d
)
.
(17.1)
.
where
r
.refers.to.the.vector.spatial.coordinate
d
.is.the.dipole.length
E
.is.the.applied.electric.ield
When.expanded.with.Taylor.series,.and.when.we.neglect.all.high.order.terms.(which.are.
associated.with.the.quadrupole,.octopole,.and.so.on),.the.resultant.force.is.simpliied.as
F
=
q
d
⋅∇
E
.
(17.2)
.
where.
q
d
.is.the.dipole.moment.of.the.particle.induced.by.the.nonuniform.electric.ield.and.
is.given.by
π ε
q
d
=
(
4
a
K
)
E
.
(17.3)
.
m
where
a
.is.the.radius.of.the.spherical.particle
ɛ
m
.is.the.permittivity.of.the.luid.medium
K
.is.known.as.the.Clausius-Mossotti.factor
Thus,.the.DEP.force.in.Equation.17.2.can.be.written.as
π ε
3
F
=
(
4
a
K
)
E
⋅∇ =
E
(
2
π ε
a
K
)
∇ ⋅
(
E E
)
.
(17.4)
.
m
m
If.the.applied.electric.ield.signal.is.frequency-dependent.(i.e.,.AC-based.DEP),.the.Clausius-
Mossotti.factor.is.a.complex.number.(
K
*)..When.its.real.part.is.substituted.in.Equation.17.4,.
the.time-average.DEP.force.is.reduced.to
∗
∇
3
2
F
=
2
π ε
a
Re[
K
]
E
.
(17.5)
.
DEP
m
rms
