Geoscience Reference
In-Depth Information
During condensation, latent heat is released, warm-
ing the surface of a drop. This warming immediately
increases the SVP over the drop surface, as illustrated
in Figure 5.12. The warming also creates a temperature
gradient between the drop surface and the air around
it, causing energy to flow from the surface back to the
cooler air, slightly reducing the warming of the drop sur-
face. Nevertheless, the SVP increase due to the warmer
surface slows the rate of vapor transfer to the surface.
Vapor transfer is also slowed by the fact that drop growth
depletes vapor away from the drop, decreasing the par-
tial pressure over time.
These physical processes are described by Equation
5.3, which gives the rate of change in volume (
rate because heat released during condensation trans-
fers away from the drop surface faster, diminish-
ing the warming upon condensation and the increase
in SVP.
Example 5.3
Calculate the percent increase in the growth rate
of single-particle volume from Equation 5.3 if the
radius doubles, p s =
1hPa,thepartial pressure
( p )increases from 1.01 p s to 1.02 p s ,andall other
parameters stay constant.
Solution
The ratio of the final to initial pressure gradient
from the example is (1.02 p s
,cm 3
per particle) of a single liquid drop due to condensation
or evaporation as
d
=
2. Multiplying this by a factor of 2 to account
for the doubling of particle radius gives a final
growth rate 4 times the initial value, for an
increase of 300 percent. Thus, the growth rate of
asingleparticle increases with increasing particle
size and with increasing difference between the
partial pressure and saturation vapor pressure.
p s )
/
(1.01 p s
p s )
d t =
4
rD ( p
p s )
L e m
R T
1
(5.3)
R T
DL e
p s
+
T
m
where r is drop radius (cm), D is the diffusion coeffi-
cient of vapor through the air (cm 2 s 1 ), p is the partial
pressure of vapor away from the surface (hPa), p s is
the SVP over the surface (hPa), L e is the latent heat of
evaporation (J g 1
10 4
cm 3
hPa g 1 ),
=
is the liquid
The relative humidity (RH) is the partial pres-
sure of water vapor ( p )divided by the SVP of water
over a flat, pure liquid water surface ( p s ), all mul-
tiplied by 100 percent. When the relative humidity
exceeds 100 percent, p
density of the drop (g cm 3 ),
is the thermal conductiv-
ity of air (J cm 1 s 1 K 1 ; Section 3.2.1), T is the drop
surface temperature, m is the molecular weight of the
vapor (g mol 1 ), and R is the universal gas constant
(cm 3 hPa mol 1 K 1 ). A diffusion coefficient is the rate
of transfer of a gas through a bath of air molecules aris-
ing from random motion and redirection upon collision
with the air molecules. The latent heat of evaporation
is the energy added to a liquid to evaporate it and equals
the energy released to the air by a vapor to condense it.
Forwater vapor, D
p s , and water vapor con-
denses onto CCN to form cloud drops .When the RH
drops below 100 percent, p
>
<
p s , and liquid water on
a CCN surface evaporates, leaving the residual aerosol
particle.
0.211 cm 2 s 1 , L e =
2,501 J g 1 ,
=
Example 5.4
If the partial pressure of water vapor is 20 hPa
and the temperature is 30 C, what is the relative
humidity?
1gcm 3 .
Equation 5.3 indicates that the rate of change of drop
volume is proportional to the gradient between the par-
tial pressure and SVP, and to the diffusion coefficient of
the vapor through air. Thus, the greater the partial pres-
sure relative to the SVP, the faster the growth rate of the
drop. Similarly, the greater the diffusion coefficient, the
greater the growth rate. If the SVP exceeds the partial
pressure, the drop shrinks (liquid evaporates).
Equation 5.3 also shows that the greater the latent
heat of evaporation, the slower the drop growth rate.
In other words, if more heat is released during con-
densation, less vapor can condense because the heat
feeds back to increase the SVP. Conversely, the greater
the thermal conductivity of air, the faster the growth
18.015 g mol 1 , and
m
=
=
Solution
From Figure 5.12a, the SVP is 42.5 hPa. There-
fore, the relative humidity is 100 percent
×
20 hPa/42.5 hPa
=
47 percent.
Sulfuric acid gas, which has a low SVP, also con-
denses onto particles. Once condensed, sulfuric acid
rarely evaporates because its SVP is so low. Sulfu-
ric acid condenses primarily onto accumulation mode
particles because the accumulation mode has a larger
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