Diffusion and flow of gases and vapours through micropores I. Slip flow and molecular streaming

Abstract

It has been shown that the slight minimum found by Knudsen in the plot of G against p for circular capillaries is very much exaggerated for non-circular cross-sections. Since the pore-system in a porous medium must correspond to non-circular sections, a similar minimum might be expected. Such a possibility would give rise to considerable uncertainty in applying gas permeabilities to the determination of specific surfaces of very fine powders, when flow takes place mainly by molecular streaming. The minimum should appear when d e = λ (transition region). By using a number of powders of different particle size and four different gases, a very wide range of values of d e /λ on both sides of unity has been covered. It has been established clearly that, while the plot of G against p sometimes undergoes a small and very gradual change of gradient in the transition region, no sign of a minimum has been detected. For all practical purposes, it is sufficient to assume that G against p is linear for all values of p . For a powder of Pyrex glass microspheres, the value of δ/k´ = 0·46, which agrees in magnitude with theoretical expectations. For different plugs, and also for the same plug, when G against p is curved, δ/k´ has different values, but the total range of variation is not large. The foregoing conclusions are not dependent on porosity or pore texture. The pore texture of fine powders at high porosities is so non-uniform that the surface calculated from permeability is 50% or less of its true value, but the transition from slip flow to streaming is unaffected and values of δ/k´ are normal.