Environmental Engineering Reference
In-Depth Information
based.on.the.particle.size.
This.results.from.the.vector.settling.force.(
F
↓
),.which.is.a.
function.of.buoyancy.and.gravity.(
g
).
F
=
ρ
V g
Gravity
↓
x
x
F
= −
(
ρ
V g
)
Buoyancy
.
.
(6.1)
↓
f
x
(
)
∴
F
=
V g
ρ
−
ρ
f
Settling Force
↓
x
x
When.expressed.as.force.vectors,.it.becomes.clear.that.the.smaller.the.nanoparticle's.
volume.(
V
x
),.the.lower.the.force.vector,.regardless.of.the.difference.in.either.particu-
late. (ρ
x
). or. luid. (ρ
f
). densities.
The. extremely. small. particle. size. of. nanomaterials.
results.in.a.very.low.settling.force.due.to.the.small.magnitude.of.
V
x
.
In.short,.over.
time,. the. concentration. of. suspended. nanoparticles. will. decline. as. the. larger. par-
ticles.settle.out.of.suspension.while.the.smaller.particles.remain.in.suspension.
The. rate. at. which. particles. settle. out. of. suspension. determines. the. potential. for.
transport.through.the.environment.and.the.ease.of.removal.through.air.or.water.treat-
ment.processes.
The.settling.or.terminal.velocity.(
v
x
).is.a.function.of.the.settling.force.
and.the.luid's.resistance.to.passage.or.viscosity.(η).as.follows:
2
2
9
r g
(
)
.
v
=
⋅
⋅
ρ
−
ρ
.
(6.2)
x
x
f
η
where.
r
. is. the. effective. particle. radius.
Table.6.1. provides. examples. of. the. effect.
of. particle. radius. on. the. settling. rate. of. titanium. dioxide. in. air. and. water.
These.
examples.show.that.as.the.particle.size.decreases,.the.rate.of.settling.decreases.sub-
stantially.and.thus.the.particles.can.stay.in.suspension.more.readily.
At. particle. sizes. below. 100. nm,. the. settling. velocity. has. a. magnitude. akin. to.
rates. of. Brownian. motion,. which. is. the. random. movement. of. small. particles. sus-
pended.in.a.luid.resulting.from.the.thermal.velocity.of.the.particles.in.the.suspend-
ing.medium..As.a.result,.the.particles.can.form.a.stable.suspension..Such.systems,.
referred. to. as. sols,. can. occur. in. luids. such. as. water. (hydrosol). or. gases. such. as.
atmospheric.air.(aerosol).
Suspensions.of.nanoparticles.may.not.be.true.solutions..This.is.because.the.sus-
pension. is. not. the. result. of. an. equilibrium. condition,. but. rather. the. result. of. very.
table .
sedimentation Rate for tio
spheres of Varying size in water and air
(cm/hr)
Particle diameter
settling Rate in water (
v
x
)
settling Rate in air (
v
x
)
1.mm
7.×.10
2
3.×.10
4
1.µm
7.×.10
−4
3.×.10
−2
100.nm
7.×.10
−6
3.×.10
−4
10.nm
7.×.10
−8
3.×.10
−6
Note:
. Pressure.=.1.atm;.Temperature.=.25°C.
