Atmospheric diffusion equation constraints

To arrive at the atmospheric diffusion equation (3.17), a number of constraints must be imposed (Seinfeld, 1975). The deviation between reality and these constraints will thus represent a measure of the inaccuracies associated with the atmospheric diffusion equation. Among these constraints, the following two are most pertinent ... 

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. 

The ideal partial molar enthalpy equation (47) was derived from Eq. (45) under the constraint that in an ideal solution, k = 0. The interpretation of this Ar con-straint is that the thickness of the Debye—Hiickel diffuse ion atmosphere, has become infinite, indicative of the absence of electrostatic screening among solute ions. While K is required to be zero for ideal solutions and real solutions as they approach... 

Na ions bound to the polyion per charged group. One could even get carried away and interpret the dependence of Equation (25) on + as a decrease in the number of bound Na" due to the competition of the Mg " ions with the Na" for sites on the polyion. Such an interpretation, however, is completely wrong the effects are due to the diffuse Debye-Hiickel atmosphere. Actually, in this case, the effect persists even if ( = 0, that is, even when all activity coefficients are unity the electroneutrality constraint given by Equation (12) is sufficient to cause an asymmetric distribution of small ions. 

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