Effusion. III. Angular Number Distributions of Gaseous CsCl from Right-Circular Cylindrical Orifices into Vacuum

Abstract

Angular number distribution in effusion is of concern to users of the Knudsen effusion cell, who frequently assume the validity of the Clausing theory. In this study a stationary surface-ionization detector in a high vacuum measured the angular number distribution of CsCl molecules effusing from a saturated vapor through a right-circular cylindrical orifice in the wall of a rotatable copper effusion cell. The variables were θ, the off-orifice-axis angle; D, the orifice diameter; L / D, the length-to-diameter ratio; and T, the effusion-cell temperature. Two orifices having D ≅ 0.28 mm were used, with respective L / D values of 0.49 and 1.3. For the short orifice, the range of p, the saturated vapor pressure, was 0.006–0.99 mm Hg, and that of T was 820°–1017°K; for the long orifice, p was 0.006–0.86 mm Hg and T was 820°–1010°K. At low T, where the Clausing theory was expected to be valid, the probability density P(θ), defined as the fraction steradian−1 effusing in direction θ, was in fair agreement with theory for θ > 35° for the short orifice and for θ > 20° for the long orifice. At θ near 0°, the largest deviations from the Clausing theory were observed. An unexpected deviation from theory was observed, namely, P(θ) at fixed θ showed fluctuation with the state of the gas. This fluctuation (1) had an L / D dependence, (2) was greatest at θ near 0°, (3) was least at θ near 45°, (4) was small but appreciable at θ near 90°, and (5) was reproducible upon cycling T and θ. High-pressure limits for molecular flow were found to be 2.1 > K (Knudsen number, ratio of mean free path to orifice diameter) >1.7 for the short orifice and 1.6 > K > 1.3 for the long orifice. In the transition region beyond the high-pressure limit of molecular flow, P(0°) decreased with increasing pressure for the long orifice, whereas P(0°) increased with increasing pressure for the short orifice, as did P(0°) for a near-ideal orifice.