Chemistry Reference
In-Depth Information
face,
w'
(
z
), which bring fresh fluid from the bulk to the interface for diffu-
sion, contribute to gas-transfer enhancement. Assuming incompressibility,
these velocity fluctuations can be expressed in terms of the surface diver-
gence as
|c to first order, where the subscript '
o
' indi-
cates evaluation at the interface,
z
= 0. Expressing
w'
(
z
) in such manner
suggests a strong connection between the surface divergence,
w
(
z
)
(
v
c
)
z
h
o
v
c
,
and gas transport. Some models (e.g., Lamont and Scott 1970, Brumley
and Jirka 1988) attempt to predict gas-transfer rates by considering surface
renewal by turbulent eddies. Such a process is sketched conceptually in
Fig. 2, which shows how upwelling eddies bring about a horizontal surface
divergence that renews the near-surface region with bulk fluid from below.
This figure also makes clear how the presence of a surfactant can influence
surface renewal and divergence. A common difficulty with many gas-
transfer models has been relating the model inputs (velocity, length, and/or
time scales) to relevant, measurable hydrodynamic parameters. Therefore,
a direct experimental measurement of the surface divergence could prove
very useful. In addition, such a measurement could be used to explore the
model results of Ledwell (1984) and Csanady (1990), which provide direct
relationships between surface divergence and the gas-transfer rate.
(
)
h
o
Fig. 2.
Conceptualisation of surface renewal by a turbulent eddy in the presence of
a surfactant. The eddy upwells fresh fluid to the surface, while the differential
spreading pressure, '3, opposes the transport of new fluid to the interface.
Adapted from Davies and Rideal (1963)
In order to gain insight into the impact of an interfacial film on surface
divergence, the case of linear, monochromatic capillary-gravity waves was
studied. Although it is generally believed that the mechanical straining of
the surface due to orbital wave motions is not sufficiently large enough to
bring about significant gas-transfer enhancement, this simple case provides
a useful and illustrative result.
