Environmental Engineering Reference
In-Depth Information
simpliied.by.assuming.the.airway.is.composed.of.a.series.of.relatively.uniform.pas-
sages.(nasal,.pharyngeal,.tracheal,.bronchi,.bronchioles,.and.alveoli)..With.an.intrin-
sically.constant.surface.area.(
A
).and.radius.(
r
a
).within.each.grouping,.lux.dynamics.
(
dn/dt
,.where.
n
.is.the.number.of.particles).can.be.expressed.based.on.the.area.of.a.
given.passage.as.follows:
r
a
dn
dt
∫
dc
dx
.
=
DA
⋅
4
π
.
(9.9)
x
=
0
Substituting.the.Stokes-Einstein.equation,.the.relation.can.be.expressed.as.a.solvable.
expression.as.follows:
r
dn
dt
2
3
kT
r
∫
dc
dx
=
⋅
A
⋅
.
.
(9.10)
η
p
x
=
0
where.
k
.is.the.Boltzmann.constant,.
T
.is.the.absolute.temperature,.η.is.the.viscosity.
of.the.aerosol,.and.
r
p
.is.the.radius.of.the.nanoparticle.
The. diffusion. of. a. nanomaterial. from. gaseous. suspension. to. the. epithelium.
involves. not. only. a. change. in. location,. but. also. a. change. in. state. from. aerosol. to.
hydrosol.within.the.mucous.layer.of.the.pulmonary.airways..Usually,.the.concentra-
tion. gradient,.
dc/dx
,. needs. to. be. modiied. to. account. for. the. differential. fugacity.
between. the. two. states.. However,. nanoparticles. have. a. low. escaping. tendency.
because.of.their.high.relative.masses..Because.nanomaterials.contacting.the.muco-
sal.layer.will.not.signiicantly.return.to.the.gaseous.aerosol,.diffusion.transport.is,.in.
effect,.one.way,.such.that.the.integral.of.
dc/dx
.=.1..Furthermore,.because.of.the.rate.
of.ventilation.and.turbulence,.the.cross-sectional.gradient.within.the.airway.can,.for.
the.most.part,.be.ignored..With.these.two.assumptions,.the.concentration.gradient.
can.be.simpliied.to.the.differential.concentration.between.that.suspended.in.the.air.
stream.and.that.suspended.in.the.mucosal.layer.
The.linear.nature.of.the.airway.means.that.at.any.point.(
y
),.the.concentration.is.
equivalent.to.the.initial.concentration.([
C
0
]),.minus.the.integral.of.the.material.lost.
in.the.previous.airway.as.follows:
Y
dn
dt
2
3
kT
r
∫
dn
dy
.
=
⋅
A
⋅
C
−
.
(9.11)
Y
0
η
p
y
=
0
Note. that. the. integral. is. based. on. the. linear. transport. of. air. and. will. differ. based.
on.whether.the.ventilation.is.in.inhalation.or.exhalation..Furthermore,.the.air.low.
velocity.(
v-
).places.a.constraint.on.
dy
,.and.by.implication.
A
Y
.
,.by.the.amount.of.sur-
face.area.exposed.per.unit.time.as.follows: