Agriculture Reference
In-Depth Information
turbulent bulk air
d
z
G
still air layer
d
z
L
still water layer
turbulent bulk water
Figure 3.4
The air-water interface
Two main approaches have been taken to modelling the air-water interface
in natural systems so as to calculate rates of volatilization and dissolution (Liss
and Slater, 1974; Frost and Upstill-Goddard, 1999; McGillis
et al
., 2001). In the
simpler the interface is viewed as two thin still layers, one in the air and one in
the water, separating well-mixed bulk phases (Figure 3.4). Transport across the
still layers is by diffusion. The still layers arise because of the increased viscosity
of the air and water near the interface. Their thicknesses depend on such factors
as wind speed and surface roughness. Under turbulent conditions, the thickness of
the still layers is reduced and rates of gas transport correspondingly increased. At
steady state the fluxes across the layers are equal. Therefore, if the gas undergoes
no reactions, we have from Fick's first law
D
G
δz
G
(C
G0
−
C
G
)
=−
D
L
δz
L
(C
L
−
C
L0
)
F
=−
(
3
.
27
)
where subscripts G and L indicate the gas and liquid phases, respectively, and
subscript 0 indicates the interface.
The alternative approach considers that turbulent eddies periodically mix the
surface layers with the bulk fluids. The flux across the interface is related to
the concentration difference by a transfer coefficient equal to the square root
of the diffusion coefficient divided by a characteristic time,
τ
, representing the
frequency of mixing. Thus
D
G
τ
G
(C
G0
−
C
G
)
=−
D
L
τ
L
(C
L
−
C
L0
)
F
=−
(
3
.
28
)
Neither model accounts completely for the processes operating in the interface,
and they provide similar fits to empirical data (Frost and Upstill-Goddard, 1999).
However the first model has the advantage of conceptual simplicity and I use it
in the following sections.
