Fundamental equations eddy diffusivity

Equation 10.115 has a considerable fundamental and practical importance. It combines parameters of fimdamentally different origins, the plate number at infinite dilution, N, which characterizes the intensity of axial dispersion taking place in the column and two parameters of thermod5mamic origin, the retention factor at infinite dilution, ICg, related to the initial slope of the isotherm, and the loading factor, proportional to the sample size and related to the saturation capacity of the isotherm. Accordingly, Eq. 10.115 indicates the extent to which the self-sharpening effect on the band profile due to the nonlinear thermodynamics is balanced by the dispersive effect of axial and eddy diffusion and of the mass transfer resistances. 

The sections of this chapter deal with the following elements of atmospheric dynamics vertical structure of the atmosphere (Section 3.2), fundamental equations of atmospheric motions (Section 3.3), transport of chemical constituents and the relative importance of dynamical and chemical effects on photochemical species (Section 3.4), atmospheric waves (Section 3.5), the mean meridional circulation and the use of the transformed Eulerian formalism to illustrate the roles of mean meridional and eddy transports (Section 3.6), the important role of wave transience and dissipation (Section 3.7), vertical transport by molecular diffusion in the thermosphere (Section 3.8), and finally, models of the middle atmosphere (Section 3.9). 

The eddy diffusivity depends on the fluid properties but also on the velocity and position in the flowing stream. Therefore Eq, (21.30) cannot be directly integrated to determine the flux for a given concentration difference. This equation is used with theoretical or empirical relationships for e f in fundamental studies of mass transfer, and similar equations are used for heat or momentum transfer in developing analogies between the transfer processes. Such studies are beyond the scope of this text, but Eq. (21.30) is useful in helping to understand the form of some empirical correlations for mass transfer. 

Equation 21.8 is a slightly modified version of the Van Deem ter equation, Equation 22.10, used in gas chromatography. Because of the so-called coupling between the A term (eddy diffusion) and the Cu, term of Equation 22.10, a different relationship between H and v is observed in LC than in GC. The fundamental difference between GC and LC is the great difference in sample diffusion rates in liquids and in gases Dm is 10 -10 times greater in GC. Thus, the contribution in LC is much smaller than in GC, whereas the /fmp term is larger. 

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