Abstract
A calculation is made of the rate of diffusion of "tagged" molecules in a pure gas at uniform pressure in a long capillary tube of half-length and radius . At pressures for which the mean free path , the result in the limit reduces to that already obtained by M. Knudsen, the diffusion coefficient being given by , where is the mean molecular speed. For a capillary of finite length the diffusion coefficient is, to first order in , smaller than this by a factor . In the opposite limit of high pressures, for which , the result reduces to the elementary kinetic theory expression for the self diffusion coefficient, . One of the most significant features of the result is that in a long tube the diffusion coefficient drops very rapidly with increasing pressure from its initial value for . Thus the initial slope of as a function of pressure is given by . It is shown that these results account for the anomalous low pressure minima observed by several investigators who have measured the specific flow through long capillary tubes as a function of mean pressure . The failure to observe such minima with porous media, for which effectively in each pore, is also explained by these results. The formulae obtained here represent a rigorous solution to the long capillary diffusion problem, valid at all pressures and subject only to the limitations of the mean free path type of treatment.
- Received 22 December 1947
DOI:https://doi.org/10.1103/PhysRev.73.762
©1948 American Physical Society