Measurement of Diffusional Time Constants

In a chromatographic experiment a small packed adsorption column is subjected to a perturbation in the inlet concentration of an adsorbable species and the dynamic response at the column outlet is measured. Such measurements provide, in principle, a simple and rapid means of studying adsorption kinetics and equilibria. This method has been widely applied to gaseous sorbates but similar techniques are in principle applicable with liquids. In practice it is usual to employ either a pulse or a step input although other types of perturbation may also be used. The choice between step or pulse depends entirely on practical convenience since exactly the same information may be obtained from either experiment. 

In the interpretation and analysis of chromatographic data it is assumed that the system is linear. Kinetic and equilibrium parameters are determined by matching the experimental response curve to the dimensionless theoretical curve calculated from a suitable dynamic model for the system. The assumption of linearity is a valid approximation provided that the concentration change over which the response is measured is sufficiently small. In the linear regime the normalized response is independent of the magnitude of the perturbation, and variation of the pulse (or step) size therefore provides a simple and direct test of system linearity. 

The ease with which the individual mass transfer parameters and the axial dispersion coefficient can be determined depends on the relative magnitude of the various resistances. If mass transfer is rapid the dispersion of the chro matogram will be caused mainly by axial dispersion, jand under these conditions it is not possible to derive any information coiicerning the diffusional time constants. In the low Reynolds number regime Sh = D , w2.0 so 

It is evident that in this regime both the external mass transfer and macropore resistances are directly proportional to the square of Ihe particle radius. The contribution of these terms may therefore be reduced to an insignificant level by using sufficiently small particles. Furthermore, in he low Reynolds number regime, the axial dispersion coefficient becomes independent of particle size so variation of the particle size provides a convenient experimental test for the significance of external film and macropore diffusion resistances. 

It follows from Eq. (8.43) that within the low Reynolds number regime a plot of (a /2ju XT/c) versus /v should be linear with slope D and intercept corresponding to the total mass transfer resistance  

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