Flux Relationships for Diffusion in Microcapillaries

Abstract

IT is well known that flux ratios in small capillaries, that is in capillaries where the Knudsen number (N_k, defined as the ratio of capillary diameter to the mean free path of the diffusing molecule) is much less than one, vary as the square root of the inverse molecular weight ratio for binary systems. It has been shown¹ that for counter-diffusion in an ‘open’ system, corresponding to the physical situation in most transport experiments of the Wicke–Kallenbach type², flux ratio may vary from dependence on the square root to the first power of the inverse molecular weight ratio for the bulk diffusion mechanism alone. For capillaries of a fixed length, the progression from square root to first power dependence is associated with increasing Knudsen numbers, the latter mechanism corresponding to N_k≫1. It is clear, then, that at N_k≪1 the predominant mechanism of transport is that of Knudsen diffusion, and flux ratios are equal to the square root of inverse molecular weight ratios, and at N_k≫1 the predominant mechanism of transport is that of bulk diffusion. Flux ratios for sufficiently large N_k will then be equal to the first power of the inverse molecular weight ratios (provided capillary length–diameter ratios do not approach the order of unity).