Knudsen Diffusion Through Cylindrical Tubes of Varying Radii: Theory and Monte Carlo Simulations

摘要

In this study, Knudsen diffusion of low-pressure gases of infinite mean free path through various tubes is studied using the integral equation theory (IET), standard diffusion theory, and Monte Carlo (MC) simulations. We investigated the transmission probabilities (TPs) of linearly diverging-converging, sinusoidally bulging, and periodic tubes as compared with TPs of conventional straight cylinders. An exact analytic solution for the TP through the straight cylindrical tube was developed using the standard diffusion theory with a linear concentration approximation. IET for the TPs through the diverging-converging and bulging tubes were developed. MC simulation techniques were applied to calculate TPs through all the tube types azimuthal symmetry of which was held with tube radius changing only along the axial coordinate (z). The linearly diverging-converging and sinusoidally bulging tubes provide noticeably higher TPs than those of the equivalent straight tubes. Periodic tubes show that if the tube length scaled by the equivalent diameter is of an order of or greater than the periodicity coefficient (equal to the number of peaks on the tube wall), then the TP of the periodic tube is larger than that of the equivalent straight tube.