Atmospheric diffusion equation errors

According to measurements made in the atmosphere, the Lagrangian time scale is of the order of 100 sec (Csanady, 1973). Using a characteristic particle velocity of 5 m sec", the above conditions are 100 sec and L > 500 m. Since one primary concern is to examine diffusion from point sources such as industrial stacks, which are generally characterized by small T and L, it is apparent that either one (but particularly the second one) or both of the above constraints cannot be satisfied, at least locally, in the vicinity of the point-like source. Therefore, in these situations, it is important to assess the error incurred by the use of the atmospheric diffusion equation. 

In summary, we conclude that the application of the atmospheric diffusion equation to point sources will introduce an error of the order of 10% into predictions at points reasonably well removed (on the order of 1 km) from the source. 

Of course, both of the two coefficients, C and Klo are some combination of the processes considered when equation (8.87) through (8.102) were developed, and are a function of liquid film coefficient across both the bubbles and the free surface, bubble and water surface interfacial area, hydrostatic pressure, the mole ratio of gas in the bubbles, and equilibrium with the atmosphere. These two coefficients, however, can be valuable in the design of an aeration system, as long as (1) the arrangement of diffusers in the water body or tank is similar to the application and (2) the depth of the test is the same as the application. Significant deviations from these two criteria will cause errors in the application of the tests to the field. 

Interpretation of available data is frustrated by lack of knowledge of certain fundamental quantities such as Interfacial area, mass transfer coefficients, solubility data, diffusion coefficients, bubble sizes, etc.. Existing equations for almost all of these variables have been developed on the basis of experiments conducted at atmospheric pressure and around room temperature. Use of such predictive equations at the reacting conditions involves large extrapolation, and the combined errors would make the analysis of kinetic data very suspect. In spite of this, most work reported in the literature does use such correlations. 

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