Environmental Engineering Reference
In-Depth Information
Assume that adsorption on aerosols is governed by a BET isotherm
Γ
i
Γ
K
BET
i
=
y
i
)
1
1
) y
i
.
(4.40)
m
(
1
−
+
(K
BET
−
Since
y
i
1,
i
K
BET
P
i
m
Γ
i
= Γ
.
(4.41)
P
i
Using the ideal gas law and
M
i
the molar mass of compound
i
, we obtain
i
K
BET
C
i
a
RT
m
Γ
i
= Γ
.
(4.42)
M
i
P
i
Consider a total suspended particle concentration in air,
C
s
; then the fraction of
i
in
the solids is
Γ
i
C
s
Γ
i
C
s
+
φ
i
P
=
C
i
a
.
(4.43)
Now,
C
s
=
A
v
/A
m
, where
A
v
is the total surface area per unit volume of air and
A
m
is the surface area of one particle. Hence,
ρ
i
A
v
ρ
i
A
v
+
φ
i
P
=
,
(4.44)
P
i
ρ
i
is given by
A
ι
K
BET
RT/M
ι
A
μ
. It is characteristic of the compound and
depends on the compound molar mass and the surface concentration for monolayer
coverage of the compound (Pankow, 1987).
P
i
is the subcooled liquid vapor pressure
for compounds that are solids at room temperature. Compounds that have large vapor
pressurestendtohavesmallvaluesof
φ
where
p
i
,whereascompoundsofsmallvaporpressures
are predominantly associated with the aerosols.
p
i
is small for
P
i
>
10
−
6
mm Hg.
In a clean atmosphere, therefore, many of the hydrophobic compounds such as PCB
congeners, DDT, and Hg should exist in the vapor phase. A range of vapor pressures
from 10
−
4
to 10
−
8
mm Hg are observed for environmentally significant compounds,
and those with
P
i
>
10
−
4
mm Hg must be predominantly in the vapor phase whereas
those with
P
i
<
10
−
8
mm Hg must exist almost entirely in the particulate phase. The
fraction occurring in the aerosol phase generally increases with increasing molecular
weight and decreasing
P
i
for a homologous series of compounds (e.g.,
n
-alkanes).
For a compound that is removed by both gas and aerosol scavenging by rain, cloud,
or fog droplets, the following is the overall expression for washout ratio:
φ
W
T
=
− φ
i
P
)
+
W
P
φ
i
P
.
W
g
(
1
(4.45)
W
P
is the aerosol washout ratio, which is a function of meteorological factors and
particle size.A raindrop reaches equilibrium with the surrounding atmosphere within
a 10-m fall, and hence the washout of vapors may be viewed as an equilibrium
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