Biomedical Engineering Reference
In-Depth Information
17.2.2 Key Factors in DeP
17.2.2.1 Clausius-Mossotti Factor
When. the. conductive. losses. (due. to. the. mobile. ions. associated. with. the. particles. them-
selves.and/or.the.liquid.medium).are.considered.in.an.AC-based.DEP,.the.complex.permit-
tivity.of.the.particle.and.the.medium.is.used.instead..It.is.given.by
σ
ω
σ
ω
∗
=
p
∗
=
m
ε
ε
−
j
,
ε
ε
−
j
.
(17.6)
p
p
m
m
.
where
ɛ
p
.is.the.permittivity.of.the.spherical.particle
σ
p
.and.σ
m
.are.the.conductivity.of.the.particle.and.the.medium,.respectively
ω.is.the.angular.frequency.of.the.applied.electric.signal
Correspondingly,.the.complex.Clausius-Mossotti.factor.(
K
*).is.deined.as
*
*
ε
−
+
ε
p
m
*
K
=
.
(17.7)
*
*
ε
2
p
m
.
The.real.part.of.the.complex.Clausius-Mossotti.factor.(Re[
K
*]).can.then.be.written.as
ε
−
+
ε
3
(
ε σ
−
ε σ
)
∗
=
p
m
m p
p m
Re[
K
]
+
.
(17.8)
2
2 2
ε
2
ε
τ
(
σ
+
2
σ
) (
1
+
ω τ
)
.
p
m
MW p
m
MW
where.τ
MW
.is.the.Maxwell-Wagner.charge.relaxation.time.and.is.given.by
ε
+
+ 2
ε
p
m
τ
=
.
(17.9)
MW
σ
σ
.
p
m
The.dielectric.constants.of.common.particles.used.in.DEP.are.provided.in.Table.17.1..As.the.
complex.permittivity.is.dependent.on.the.angular.frequency.(ω).of.the.applied.electric.sig-
nal,.the.sign.and.magnitude.of.Re[
K
*].vary.in.the.frequency.spectrum..At.low.frequency,.the.
TABLe 17.1
Relative.Dielectric.Constant.of.Common.Materials.or.
Medium
Dielectric
Constant (ɛ
r
)
Dielectric
Constant (ɛ
r
)
Materials
Materials
Vacuum
1
Polystyrene
2.4-2.7
Air
1.00054
Silicon
11.68
Water.at.0°C
88
Silica
2.5-3.8
Water.at.20°C
80.1
Glass.bead
3.1
Methanol
32.7
Pyrex
4.7
Ethanol
24.5
Mica
5.4
Isopropanol
17.9
Titanium.oxide
100
Acetone
20.7
Al.powder
1.6-1.8
Toluene
2.38
Silicon.oil
2.2-2.9
