McKay, Donald. "Front matter" Multimedia Environmental Models ...

1/k 2 versus K OW to obtain quantities containing k M and k W. Such a plot was compiled
by Mackay and Hughes (1984), yielding estimates of the two-resistances expressed
as characteristic uptake times.
Another example is the penetration of chemicals through the waxy cuticles of
leaves in which there are air and wax resistances in series. Kerler and Schonherr
(1988) have measured such penetration rates for a variety of chemicals, and Schramm
et al. (1987) have attempted to model chemical uptake by trees using this tworesistance
approach. A plant’s principal problem in life is to manage its water budget
and avoid excessive loss of water through leaves. It accomplishes this by forming
a waxy layer through which water has only a very slow diffusion rate. Diffusivities
are very low, leading to very low MTCs and D values for water. The plant thus
exploits this two-resistance approach to conserve water. If only governments could
manage their budgets with the same efficiency!
7.9 COMBINING SERIES AND PARALLEL D VALUES
Having introduced these transport D values and shown how they combine when
describing resistances in series, it is useful to set out the general flux equation for
any combination of transport processes in series or parallel.
Each transport process is quantified by a D value (deduced as GZ, kAZ, or
BAZ/Y) that applies between two points in space such as a bulk phase and an
interface, or between two bulk phases. It is helpful to prepare an arrow diagram of
the processes showing the connections, as illustrated in Figure 7.9. Diffusive processes
are reversible, so they actually consist of two arrows in opposing directions
with the same D value but driven by different source fugacities.
When processes apply in parallel between common points, the D values add. An
example is wet and dry deposition from bulk air to bulk water.
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D TOTAL = D 1 + D 2 + D 3, etc.
When processes apply in series, the resistances add or, correspondingly, the reciprocal
D values add to give a reciprocal total.
1/D TOTAL = 1/D 1 + 1/D 2 + 1/D 3, etc.
An example is the addition of air and water boundary layer resistances, which in
total control the rate of volatilization from water.
It is possible to assemble numerous combinations of series and parallel processes
linking bulk phases and interfaces. These situations can be viewed as electrical
analogs, with voltage being equivalent to fugacity, resistance equivalent to 1/D, and
current equivalent to flux (mol/h). Figure 7.9 gives some examples.
In air-water exchange, there can be deposition by the parallel processes of (1)
dry particle deposition, (2) wet particle deposition, (3) rain dissolution, and (4)
diffusive absorption-volatilization.