Nird2

and y nm

For example, for N2 at a pressure of 1 atm, at 300 K the number density is 2.4x1019 molecules cm-3 and for a typical molecular diameter of 2x10~8 cm we get l = 3 x 10~5 cm. From Avogadro's number, the mass is equal to 28/(6 x 1023) g, and so the mean speed is 5x104 cm s-1. Thus, the diffusion coefficient is 0.5 cm2 s-1 and the collision frequency is 5x109 s-1.

In the atmosphere if we consider diffusion of a molecule i in the vertical direction and define the flux to be positive in the direction of the decreasing atmospheric density with altitude z. We can then write dn -

where Dij (cm2 s-1) is the molecular diffusion coefficient of molecule i in a bath molecule j, which can be expressed as Dij = bij/n, where bij is the binary collision parameter (cm-1 s-1) and n is the total number density. For a gas mixture

Table 7.1 Bimolecular diffusion coefficients, at To = 273 K and po = 1 atm. (see Notes)

System

Do

m

h-co2

0.96

1

70

H-N2

1.23

1

.70

He-co 2

0.494

1

.80

He-N2

0.621

1

.73

H2-co2

0.575

1

.76

H2-N2

0.689

1

.72

H2o-co2

0.146

1

.84

H2o-N2

0.260

1

.84

o-N2

0.248

1

.77

N-N2

0.251

1

.77

the binary collision parameter will correspond to the two types of colliding molecules . As we saw from simple kinetic theory, the bimolecular diffusion coefficient has a pressure and temperature dependence of the form where Doj is the diffusion coefficient of molecule i in a bath molecule j at standard conditions To = 273 K, po = 1 atm, with values usually in the range 0 . 1 and 1 . 0 cm2 s_1, and mij is usually about 1 . 70 as shown in Table 7 . 1 .

Similarly, we can define a turbulent or eddy diffusion coefficient, K, for the gas mixture, which needs to be determined empirically (usually based on inert or tracer species in the atmosphere). In the troposphere K(z) has a constant value of about 1.0 x 105, as shown in Fig. 7.1. From the pressure dependence of the molecular diffusion coefficient, we see that the eddy diffusion coefficient is larger for pressures below about po/p < 106, that is below about 100 km altitude.

7.3.3 Diffusive flux

In a 1D stratified atmosphere where the density decreases with altitude z, the diffusive flux equation needs to be corrected for apparent diffusion due to the density gradient that arises from gravitational stratification in the number density (see chapter 2). In the absence of any diffusion, we would still have an apparent component of Brownian diffusive flux implicitly included through the stratification density gradient, even if the atmosphere was in diffusive equilibrium. The corrected Brownian diffusive flux is then where for the correction term

FIg. 7.1. Semiempirical eddy-diffusion coefficient profile and the bimolecular diffusion coefficient for helium in nitrogen. (Based on data from Brasseur and Solomon 1986, Strobel 1989)

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