Environmental Engineering Reference
In-Depth Information
Wastewater treatment pond
(submerged aerator)
Air
Water
Water
Air
Water
Air
Air
Air
Water
Water
Bubble air stripper tower
Packed tower air stripper
FIGURE 4.2
Examples of air-water contact and equilibrium in separation processes. In each
of the three cases, contact between air and water is important.
where
C
i
w
is the concentration of
i
in water that would be in equilibrium with air.
This is given by the air-water distribution constant
C
i
a
K
aw
.
C
i
w
=
(4.4)
The maximum overall flux from water to air will be attained when
C
i
a
=
0. Thus,
N
max
i
0, then the flux will be from air to water. Thus, if the sign
is positive the flux is from water to air, and if negative it is from air to water. If
the bulk air and water phases are in equilibrium, then
C
i
w
=
=
K
w
C
i
w
.If
C
i
w
=
C
i
a
/K
aw
and the net
overall flux
N
i
=
0. Thus, the flow of material between the two phases will continue
until the concentrations of the two bulk phases reach their equilibrium values as
determined by the air-water equilibrium constant.At equilibrium, the
net overall flux
is zero, and the water-to-air and air-to-water diffusion rates are equal but opposite
in direction.
The flux expression given in Equation 4.3 above is predicated upon the assumption
that compound
i
diffuses through a stagnant water film to a stagnant air film across an
interface of zero volume (Figure 4.3). Equilibrium is assumed to exist at the interface,
butthetwobulkphasesarenotinequilibriumandhaveuniformconcentrationsbeyond
the film thickness,
δ
C
i
a
/K
aw
)
is called the
concentration driving
force
for mass transfer. The
overall mass transfer coefficient K
w
includes the value
of the equilibrium constant in the following form (see Section 6.1.4.1 in Chapter 6):
. The term (
C
i
w
−
1
K
w
=
1
k
w
+
1
k
a
K
aw
,
(4.5)
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