Diffusion piston like

The units on A are mol/(m s). This is the convective flux. The student of mass transfer will recognize that a diffusion term like —3>Adaldz is usually included in the flux. This term is the diffusive flux and is zero for piston flow. The design equation for the variable-density, variable-cross-section PFR can be written as... 

We know the order of affinity of these ions is Na < K < Ca. Without calculation, we expect that Na will be flushed out earlier than K, followed by Ca. We assume that the displacement Is piston like, and the diffusion and dispersion are not included. Initially, Na and K "stick" to the rock based on their exchangeable fractions. The injected Ca will replace Na and K. We want to find out how long it takes to flush out Na and K. To do that, we need to know how much Na and K stick to the rock initially. 

Electroosmotic flow variance. As the flow profile of the EOF is flat, almost like a piston, its contribution to dispersion of the migrating zones is small. The EOF positively contributes to the axial diffusion variance, as can be derived from Eq. 17.26, when it moves in the similar direction as the analytes. However, when the wall of the capillary is not uniformly charged, local turbulence can occur and cause irreproducible dispersion [27]. 

Two main types of models are in common use for describing axial mixing in bubble columns. The most commonly used model is the Dispersion Model. Here, a diffusion-like process is superimposed on piston or plug flow. The stirred tanks-in-series model has also been used to describe flow of liquids in bubble columns. Levenspiel (1 ) presents a number of models incorporating various combinations of mixed tanks to model stagnant regions and backflow. 

The surface renewal model, like the thin him model, yields a piston, or gas exchange, velocity that can be used to calculate chemical fluxes as previously described. In contrast with the thin him model, however, the surface renewal model predicts that the ratio of piston velocities for two different volatile chemicals depends on the square root of the ratio of their molecular diffusion coefficients (and thus approximately the fourth root of the inverse ratio of their molecular weights). Schwarzenbach et al. (1993) discuss molecular diffusion coefficients in more detail. 

As shown in the previous section, scaling with geometric similarity, Sr = Sl = gives constant pressure drop when the flow is laminar and remains laminar upon scaleup. This is true for both liquids and gases. The Reynolds number and the external area increase as. Piston flow is a poor assumption for laminar flow in anyfhing but small tubes. Conversion and selectivity of the reaction is likely to worsen upon scaleup unless the pilot reactor is already so large that molecular and thermal diffusion are negligible on the pilot scale. Ways to avoid unpleasant surprises are discussed in Chapter 8... 

It is known that the diffusion and dispersion coefficients are different in z = 0+ and z = 0 . Similarly z = L in another part of the reactor. If there is no difference, the reactor behaves like a piston, i.e., ideal behavior. Therefore, the above equation is simplified as ... 

In fact the piston flow model, as well as the diffusion model, gives too ideal picture of the structure of the flows. They take into account neither the diffusion boundary layer nor the real movement of the phases. These models are especially far from the real situation in flie apparatus in respect to the liquid phase which moves not like a piston flow but in the form of film, drops and jets which are not only separate in space but have also different and continuously changing velocities. Nevertheless, not only the diffusion model but in some cases also its simpler variant, the piston flow model, gives oflxm very good description of the mass transfer processes in industrial apparatuses. This can be explained with the comparatively weak influence of the real structure of the flows on the mass transfer. On the other side using in the model such experimentally obtained values as mass transfer coefficient, effective surface, and Peclet number, it is possible to take into account the important for the mass transfer rate characteristics of the flows structures. In Chaptra 8 the cases when it is possible to use the simpler piston flow model, and when it is necessary to use the diffusion model are considered and specified. 

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