Biomedical Engineering Reference
In-Depth Information
the.electrode.pairs.or.on.their.edges..For.ROT.applications,.the.AC.electric.signals.on.the.
four.electrodes.have.a.90°.phase.difference.and.four.difference.phases.(0°,.90°,.180°,.and.
270°).rotated.repeatedly.between.them.with.the.same.order.(0°→90°→180°→270°→0°),.as.
shown.in.Figure.17.5d.through.f..It.results.in.the.rotational.motion.of.particles.that.enter.
the.electrode.area..Both.the.rotational.speed.and.the.direction.are.determined.by.the.elec-
tric. voltage. and. the. angular. frequency. of. the. applied.AC. waveforms.. The. time-average.
torque.(⟨
T
⟩).for.such.ROTs.can.be.expressed.as
3
*
E
2
T
= −
4
πε
a
Im[
K
(
ω
)]
.
(17.12)
m
rms
.
For.a.homogeneous.spherical.particle.in.a.luid.medium,.this.torque.is.given.by
3
2
6
πε
a
E
(1
−
τ
/ )
τ ωτ
m
rms
m
p
MW
T
= −
.
(17.13)
2
(1 2 / )(1
+
ε
ε
+
σ
/2
σ
)[1 (
+
ωτ
) ]
.
m
p
p
m
MW
As.indicated.in.Equation.17.13,.the.magnitude.of.the.DEP.torque.varies.with.the.angular.
frequency.and.it.reaches.the.maximum.when.the.frequency.is.equal.to.τ
MW
..The.rotation.
direction.is.decided.by.the.polarization.difference.between.particles.and.their.surrounding.
luid,.indicated.by.the.sign.of.the.torque:.(+).means.rotating.with.the.electric.ield.and.(−).
means.against.the.electric.ield.
When.used.in.TWD,.the.quadrupole.electrode.usually.has.a.spiral.structure.with.four.
parallel. metallic. electrode. lines. extending. outward. with. a. square. or. circle. concentric.
geometry,. as. shown. in. Figure. 17.5e. and. f.. If. viewing. from. one. side,. it. is. similar. to. the.
parallel.track.design.aforementioned..The.spiral.design.has.several.advantages.over. the.
parallel.track.design,.namely,.its.simple.design.and.easy.fabrication,.in.TWD.applications..
However,. it. also. carries. several. drawbacks,. such. as. the. large. area. occupation. and.
unchangeable. transportation. patterns. of. particles. (always. in. the. radical. direction,. not.
from. one. ixed. position. to. another).. Like. the. polynomial. electrode. in. ROT,. the. phase. of.
waveform.on.the.four.poles.also.differs.by.90°.in.TWD.
To. obtain. the. desired. TWD. effect,. the. electrode. design. should. follow. the. following.
general.rules:.(1).The.gap.between.the.electrodes.is.kept.at.its.minimum;.the.smaller.the.gap,.
the.higher.ield.strength.when.the.amplitude.of.signal.is.the.same;.the.high.ield.strength.
beneits.with.large.DEP.force.and.reduced.thermal.effects;.the.optimal.distance.is.often.
comparable.to.the.size.of.the.target.particles..(2).Thin.electrode.layer;.thick.electrode.layers.
often.affect.the.translational.movements.of.particles.along.the.rails..(3).Good.conductivity;.
the. electrode. material. must. be. highly. conductive. while. chemically. inert.. Gold. is. one. of.
the.popular.materials.used.in.electrodes..Indium.tin.oxide.(ITO).is.another.widely.used.
material,.particularly.for.applications.that.require.clear.viewing.of.DEP.motions.
17.3.3 electrodeless DeP
By.means.of.geometrical.constrictions.on.discrete.structures.made.of.insulator.materials,.
the.nonuniform.electric.ield.needed.in.DEP.can.also.be.generated.locally.in.a.low.channel.
with. electrodes. positioned. in. remote. locations.. The. associated. DEP. motions. agitated. in.
this.way.are.called.electrodeless.DEP.(EDEP)..The.low.permittivity.of.involved.insulator.
patterns. allows. the. electric. ield. lines. to. bend. around. the. geometrical. constrictions. so.
that.the.ield.strength.is.concentrated.there.(Figure.17.6)..The.insulator.constrictions.used.
in. EDEP. are. often. made. of. polymers,. glass,. or. silicon. related. materials. with. geometries.
like. sudden. or. gradual. contractions. of. the. entire. low. channel. (Figure. 17.6a. through. c).
