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

partition coefficient. The significance of the addition of reciprocal k terms is perhaps
best understood by viewing the process in terms of resistances rather than conductivities,
where the resistance, R, is 1/k in the same sense that the electrical resistance
(ohms) is the reciprocal of conductivity (siemens or mhos). The overall resistance,
R O, is then the sum of the water phase resistance R W and the air phase resistance R A.
Thus,
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R W = 1/(k W A)
R A = RT/(H k A A) = 1/(K AW A k A)
R O = R W + R A = 1/(k OW A)
which is equivalent to the equation for 1/k OW above.
Because the resistances are in series, they add, and the total reciprocal conductivity
is the sum of the individual reciprocal conductivities. The reason that K AW
enters the summation of resistances is that it controls the relative values of the
concentrations in air and water. If K AW is large, C WI is small compared to C AI, thus
the concentration difference (C W – C WI) will be constrained to be small compared
to (C AI – C A), and the flux N will be constrained by the small value of k W(C W –
C WI). In general, diffusive resistances tend to be largest in phases where the concentrations
are lowest, and thus the concentration gradients are lowest.
Typical values of k A and k W are, respectively, 10 and 0.1 m/h; thus, the resistances
become equal when K AW is 0.01 or H is approximately 25 Pa m 3 /mol. If H exceeds
250 Pa m 3 /mol, the concentration in the air is relatively large, and the air resistance,
R A, is probably less than one-tenth of R W and may be ignored. Conversely, if H is
less than 2.5 Pa m 3 /mol, the water resistance R W is less than one-tenth of R A, and
it can be ignored.
Interestingly, when H is large, k W tends to equal k OW, and if C A or P/H is small,
the flux N becomes simply k WAC W. This group does not contain H, thus the evaporation
rate becomes independent of H or of vapor pressure. At first sight, this is
puzzling. The reason is that, if H or vapor pressure is high enough, its value ceases
to matter, because the overall rate is limited only by the diffusion resistance in the
water phase.
An overall mass transfer coefficient k OA can also be defined as
and
It follows that
1/k OA = 1/k A + H/RTk W = 1/k A + K AW/k W
N = k OA(C wK AW – C A) = k OA(C wH – P)/RT
k OW = k OAK AW = k OAH/RT