Overall air-water exchange velocity

Box 20.2 Temperature Dependence of Air-Water Exchange Velocity v(w of Volatile Compounds Calculated with Different Models Overall Air-Water Exchange Velocities... 

All the physics is hidden in the coefficient via/w which, because it has the dimension of a velocity (LT-1), is called the (overall) air-water exchange velocity. Air-water exchange occurs due to random motion of molecules. Equation 20-1 is a particular version of Eq. 18-4 in which the air-water exchange velocity adopts the role of the mass transfer velocity, vA/B. 

Let us now combine these results to estimate the overall air-water exchange velocity viaAv. 

Figure 20.1 Schematic view of the overall air-water exchange velo-city, via/w, as a function of the air-water partition coefficient, Ku/w, calculated from Eq. 20-3 with typical single-phase transfer velocities v,a = 1 cm s"1, vM = 10 3 cm s1. The broken line shows the exchange velocity v a/w (air chosen as the reference system). The upper scale gives the Henry s Law coefficient at 25°C, Km = 24.7 (Lbar mol"1) x Ku/W.

For compounds with Kii/Vl larger than about 10 2 the overall air-water transfer velocity is approximately equal to the water-phase exchange velocity viw The latter is related to wind speed uw by a nonlinear relation (Table 20.2, Eq. 20-16). The annual mean of viw calculated from Eq. 20-16 with the annual mean wind speed ul0 would underestimate the real mean air-water exchange velocity. Thus, we need information not only on the average wind speed, but also on the wind-speed probability distribution. 

In the preceding discussion, we presented experimental information on the singlephase air-water exchange velocities. Water vapor served as the test substance for the air-phase velocity v,a, while 02, C02 or other compounds yielded information on v,w. Now, we need to develop a model with which these data can be extrapolated to other chemicals which either belong also to the single-phase group or are intermediate cases in which both via and vlw affect the overall exchange velocity v,a/w (Eq. 20-3). 

At first sight, there seems to be a basic difference between the two regimes with respect to the influence of Kia/Vl. In the water-phase-controlled regime, the overall exchange velocity, via/w, is independent of Kia/v/, whereas in the air-phase controlled regime v(a/w is linearly related to Ga/w. Yet, this asymmetry is just a consequence of our decision to relate all concentrations to the water phase. In fact, for substances with small Kia/v/ values, the aqueous phase is not the ideal reference system to describe air-water exchange. This can be best demonstrated for the case of exchange of water itself (Kia/V1 = 2.3 x 10 5 at 25°C), that is, for the evaporation of water. 

Before we discuss these models, we note that, in contrast to v,w, the air-phase exchange velocity, via, is not strongly affected by the flow. Thus, the following considerations are not relevant for compounds with very small Henry s law coefficients. This is no longer true when the air-water interface is broken up by bubbles and droplets. Some models attempt to incorporate the effect of air bubbles into the exchange velocity v,w (see Eq. 20-38 below), yet air bubbles also lead to a modification of Eq. 20-3 describing the overall exchange velocity, via/w. In the context of river flow, this situation will be treated in Section 24.4. 

Because the diffusivity ratio, Dia/Dja, is not exactly identical for air and water and since Eq. 20-3 also contains Kia,w, Eq. 20-19 does not hold for the composite (overall) exchange velocity v,Ww. It can be applied to classes of substances which are either solely water-phase- or air-phase-controlled. 

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