Axial dispersion and model development

The dispersed plug-flow model can be regarded as the first stage of development from the simple idea of plug flow along a pipe. The fluid velocity and the concentrations of any dissolved species are assumed to be uniform across any section of the pipe, but here mixing or dispersion in the direction of flow (i.e. in the axial z-direction) is taken into account (Fig. 2.10). The axial mixing is described by 

Investigations into the underlying flow mechanisms that actually cause axial mixing in a pipe have shown that, in both laminar and turbulent flow, the non-uniform velocity profiles (see Fig. 2.11 and Volume 1, Fig. 3.11.) are primarily 

If the radial diffusion or radial eddy transport mechanisms considered above are insufficient to smear out any radial concentration differences, then the simple dispersed plug-flow model becomes inadequate to describe the system. It is then necessary to develop a mathematical model for simultaneous radial and axial dispersion incorporating both radial and axial dispersion coefficients. This is especially important for fixed bed catalytic reactors and packed beds generally (see Volume 2, Chapter 4). 

The model developed below is for dispersion in the axial direction only. Because the underlying mechanisms producing axial dispersion are complex as the discussion above shows, equation 2.12 is best regarded as essentially a mathematical definition 

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