Fick’s second diffusion

This is Fick s second diffusion equation [242], an adaptation to diffusion of the heat transfer equation of Fourier [253]. Technically, it is a second-order parabolic partial differential equation (pde). In fact, it will mostly be only the skeleton of the actual equation one needs to solve there will usually be such complications as convection (solution moving) and chemical reactions taking place in the solution, which will cause concentration changes in addition to diffusion itself. Numerical solution may then be the only way we can get numbers from such equations - hence digital simulation. 

A new method for measuring diffusion coefficients by IR spectroscopy was developed by Karge and Niessen [158],Niessen [132] and Karge et al. [939]. The change in the intensities of bands typical of molecules migrating inside a zeolite structure during their uptake or desorption were measured by FTIR spectroscopy under high time-resolution as a fimction of small partial pressure jumps and at various temperatures. An appropriate method of evaluation of the time-resolved spectra was developed on the basis of solutions of Fick s second diffusion law provided by Crank [940]. As an example,Fig. 53 illustrates an uptake experiment with benzene (B) as the adsorbate and H-ZSM-5 as the adsorbent. 

The three points thus give us a new point at the next time. Compare this with the box-method expression, Eq. 3.5 they are identical. In fact, one might say that the box-method derives Fick s second diffusion equation in discrete form. Although Eqs. 3.5 and 3.26 are identical, it is clear that the point method derivation is much faster with only a little practice, the discretisation formulae 3.10 to 3.13 are easily memorised and expressions like Eq. 3.26 can be written down straight from the diffusion equation. Furthermore, it will be seen that if the... 

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