Study of Some of the Parameters Affecting Knudsen Effusion. V. Free-Path Considerations in Small Knudsen Cells

Monte Carlo methods have been used to calculate distributions describing the behavior of particles in a typical, small Kundsen cell. For pressure conditions corresponding to free-molecule flow, three distributions were obtained: (1) the wall collisions per particle, (2) the path lengths of the particles between collisions, and (3) the total path lengths of the particles. Knowledge of these distributions provides considerable insight into the behavior of particles at the beginning of the transition region. In particular, the relationship between gaseous collisions and the Knudsen number is clarified. Also, it is shown that the population of free paths depends on the geometry of the cell but is independent of the condensation coefficient αc. The lifetime of a given particle, however, is strongly dependent on αc. The analysis, which can be applied to any vapor species, is described for gold.