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

diffuse from the water to the octanol until it reaches a concentration in octanol that
is K OW, or 135, times that in the water. We could rephrase this by stating that, initially,
the fugacity of benzene in the water was (say) 500 Pa, and the fugacity in the octanol
was zero. The benzene then migrates from water to octanol until both fugacities
reach a common value of (say) 200 Pa. At this common fugacity, the ratio C O/C W
is, of course, Z O/Z W or K OW. We argue that diffusion will always occur from high
fugacity (for example, f W in water) to low fugacity (f O in octanol). Therefore, it is
tempting to write the transfer rate equation from water to octanol as
©2001 CRC Press LLC
N = D(f W
– fO)
mol/h
This equation has the correct property that, when f
W
and fO
are equal, there is no
net diffusion. It also correctly describes the direction of diffusion.
In reality, when the fugacities are equal, there is still active diffusion between
octanol and water. Benzene molecules in the water phase do not know the fugacity
in the octanol phase. At equilibrium, they diffuse at a rate, DfW,
from water to
benzene, and this is balanced by an equal rate, DfO,
from octanol to water. The
escaping tendencies have become equal, and N is zero. The term (fW
– fO)
is termed
a departure from equilibrium group, just as a temperature difference represents a
departure from thermal equilibrium. It quantifies the diffusive driving force.
Other areas of science provide good precedents for using this approach. Ohm’s
law states that current flows at a rate proportional to voltage difference times
electrical conductivity. Electricians prefer to use resistance, which is simply the
reciprocal of conductivity. The rate of heat transfer is expressed by Fourier’s law as
a thermal conductivity times a difference in temperature. Again, it is occasionally
convenient to think in terms of a thermal resistance (the reciprocal of thermal
conductivity), especially when buying insulation. These equations have the general
form
or
rate = (conductivity) ¥ (departure from equilibrium)
rate = (departure from equilibrium)/(resistance)
Our task is to devise recipes for calculating D as an expression of conductivity or
reciprocal resistance for a number of processes involving diffusive interphase transfer.
These include the following:
1. Evaporation of chemical from water to air and the reverse process of absorption.
Note that we consider the chemical to be in solution in water and not present as
a film or oil slick, or in sorbed form.
2. Sorption from water to suspended matter in the water column, and the reverse
desorption.
3. Sorption from the atmosphere to aerosol particles, and the reverse desorption.
4. Sorption of chemical from water to bottom sediment, and the reverse desorption.