Page 271 - Soil and water contamination, 2nd edition

258 Soil and Water Contamination

14.2 THIN FILM MODEL
If the system is not in equilibrium, a gas flux across the water–air interface occurs to
counteract the non-equilibrium state. For surface water bodies, this process of gas exchange
is often modelled according to the thin film model (or stagnant layer model). This model is

based on the assumption that a dissolved chemical has a uniform concentration throughout
both the surface water body and the overlying atmosphere, except in two very thin layers –
one in the water and one in the air – at the water’s surface (Figure 14.1). Within these very
thin layers, it is assumed that the eddies responsible for turbulent diffusion are suppressed
and that the chemical transport is solely through molecular diffusion , governed by Fick’s first
law (Equation 11.16):
dC D
J D C (14.4)
dx
-3
-2
-1
where J = the flux density [M L T ], C = the chemical concentration [M L ], D = the
-1
2
molecular diffusion coefficient [L T ], and δ = the film thickness [L]. At steady state , the
flux through the water film is equal to the flux through the air film, so:
J k C C k C C (14.5)
a sa a w w sw
D
k a a (14.6)
a
D
k w (14.7)
w
w
-1
where k = the gas exchange coefficient for air [L T ], k = the gas exchange coefficient for
a w
-1
-1
2
water [L T ], D = the molecular diffusion coefficient in air [L T ], D = the molecular
a w
2
-1
diffusion coefficient in water [L T ], δ = the air film thickness [L], δ = the water film
a w
-3
thickness [L], C = the chemical concentration in air [M L ] (Note the difference in
a
dimensions compared to C in Equation (14.2)!), C = the chemical concentration in air at
air sa
C a
Air Turbulent diffusion
C sa
Gas film Molecular diffusion
Water film Molecular diffusion
C sw
Water Turbulent diffusion
6642 6642 6642 C w Concentration

Figure 14.1 Concept of the thin film model : The resistance of gas exchange across the air–water interface
is assumed to lie in two thin stagnant layers – one in the air and the other in the water. Within the thin layer,
molecular diffusion occurs, driven by the concentration gradients. Outside the layers, turbulent diffusion occurs,
which causes the concentration gradients to be negligible. Adapted from Hemond and Fechner-Levy (2000).

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