Environmental Engineering Reference
In-Depth Information
f
i
w
Fugacity profile
f
i
f
i
a
C
i
w
Concentration profile
C
i
eq
C
i
eq
C
i
a
Air
film
Water
film
Bulk water
Bulk air
Interface
FIGURE 4.3
Film theory of mass transfer of solutes between air and water. The above dia-
gram is for the volatilization of a compound from water. The concentration profile shows a
discontinuity at the interface, whereas the fugacity profile does not. The overall resistance to
mass transfer is composed of four individual resistances to diffusion of chemical from water
to air. For more details, see also Section 6.1.4.1.
where
k
w
and
k
a
are the individual film mass transfer coefficients on the water and
air side, respectively. Each term in the above equation corresponds to a resistance to
mass transfer. 1
/K
w
is the total resistance, whereas 1
/k
w
is the resistance to diffusion
through the water film
(
δ
w
)
.1
/k
a
K
aw
is the resistance provided by the air film
(
δ
a
)
.
E
XAMPLE
4.2 O
VERALL AND
I
NDIVIDUAL
M
ASS
T
RANSFER
C
OEFFICIENTS
For evaporation of benzene from water,
k
w
=
7.5
×
10
−
5
m/s and
k
a
=
6
×
10
−
3
m/s.
Estimate the overall mass transfer coefficient
K
w
. What is the percent resistance in the
air side of the interface?
At 298 K,
K
aw
=
0.23 (from Appendix 1). Hence 1
/K
w
=
1
/k
w
+
1
/(k
a
K
aw
)
=
1.4
×
10
4
and
K
w
=
7.1
×
10
−
5
m/s. Percent resistance in the air film
=
(K
w
/k
a
K
aw
)
×
100
=
5.1%.Benzenevolatilizationisthereforewaterphasecontrolled.
Note that if
K
aw
is small, percent air-side resistance will increase.
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