Diffusion through an orifice

A good example of translational fractionation is one-way diffusion through an orifice that is smaller than the mean-free path of the gas. Related, but somewhat more complex velocity-dependent fractionations occur during diffusion through a host gas, liquid, or solid. In these fractionations the isotopic masses in the translational fractionation factor are often replaced by some kind of effective reduced mass. For instance, in diffusion of a trace gas JiR through a medium, Y, consisting of molecules with mass ttiy. 

The value of T from Eq. 29 is 0.575 for y = 1.4 and doesn t vary by more than 10% for values of y from 1.1 to 1.67. At very large Kn the value of T is 0.399, the value for free molecular diffusion through an orifice [46]. In between the high and low Kn number limits the value of T assumes intermediate values [45]. Thus, it can be seen that using the low Kn limit expression in the transition regime is a conservative assumption when calculating gas flows for the purpose of sizing vacuum pumps. 

The mass transfer is the product of the flux times the orifice cross-sectional area. Thus it is proportional to the square of the orifice radius and to the difference in concentration. Let us take the case of helium diffusing through an orifice of diameter 25 micron and the pressure on one side is 1 Ton and that on the other side is at vacuum condition. The mass transfer through the orifice at ambient temperature is ... 

Fig. 3.5-2. Diffusion through an orifice. The diffusing solute necks down to pass through a circular hole.

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