Wicke-Kallenbach method

FIGURE 5.2. Schematic diagram showing essential features of the Wicke-Kallenbach apparatus for measuring intraparticle diffusivities. 

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The customary way of measuring intraparticle macropore diffusivities is the Wicke-Kallenbach method, which depends on measuring the flux through a pellet under steady-state conditions when the two faces are maintained at... 

This limitation is overcome in the Wicke-Kallenbach method [11]. This method differs from the original permeability experiment in that, by applying a carrier gas, the flux is measured under constant pressure conditions with a known concentration difference maintained across the membrane or pellet. In this way, any nondiffusive contribution (Poiseuille flow) to the observed fluxes may be excluded. 

Procedures to remove the restrictions of the permeation technique, also inherent in the time lag method, have been described by Grachev et al. [13] and Gibilaro et al. [14], As with the Wicke-Kallenbach method, they are based on the application of a carrier gas. Details of these methods may be found in Ref. 1. 

A diffusion cell method was introduced by Wicke and Kallenbach [3] and therefore is called the Wicke-Kallenbach method. The experimental set up (Figure 5.1) is called the Wicke-Kallenbach cell. It is the most popular method for different diffusion measurements. 

Figure 4.4 Wicke-Kallenbach method for measuring effective diffusivity.

Since (D,. (g/O, ) = otP , measurements at various pressure levels permits determination of both D, ab nd D Ky,. This experimental approach is usually termed the Wicke-Kallenbach method (Wicke and Kallenbach [52] or Weisz [53] also see Satterfield [40]) and has been widely used to measure effective diffusivities. Transient methods are also available (e.g., Etogu and Smith [54]). 

Deff can be measured, either directly by the flux through a catalyst pellet (Wicke-Kallenbach diffusion cell [60]), or by transient pulse method [61]. It is easier, but less accurate, to relate Deff to molecular diffusivity. 

The second method is called the Wicke-Kallenbach (WK) method as these researchers first described this technique for diffiision experiments. In this method the membrane is flushed with gas at both sides. At the feed side the components that are being investigated are fed, while at the permeate side an inert sweep gas is being used that sweeps away the permeated components. The resulting mixture ( the permeate ) is being analysed by mass spectrometry or gas chromatography. Also the gas... 

The method has the advantage that it depends on a steady-state measurement and it is not affected by finite heat transfer. Effective intraparticle diffusivities determined in this way are commonly somewhat smaller than the values derived for the same adsorbent under simitar conditions from transient uptake rate measurements. This is because blind pores, which contribute to the flux in a transient measurement, make no contribution in a Wicke-Kallenbach system. 

The effective diffusivity of a porous adsorbent may be determined as the adsorption process proceeds by passing the gas for which the diffusion coefficient is being measured, diluted and carried by an inert gas, such as helium, across one face of the adsorbent pellet and the inert gas alone across the obverse face of the pellet. The fabricated adsorbent pellet is compressed into a cylindrical shape and sealed within a cell known as a Wicke-Kallenbach cell (shown in Figure 4.9) after the first publication of the method originated by Wicke and Kallenbach (1941). The measurement procedure has since been modified by Henry et al. (1961) and Suzuki and Smith (1972). The method adopted by Suzuki and Smith is to allow a pulse of the adsorbate under investigation to be injected into an inert gas stream... 

The classical method of measuring intraparticle or macropore diffusivities is due to Wicke and Kallenbach. The apparatus is shown schematically in Figure 5.2. Knowing the thickness of the pellet and the concentrations and... 

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