A modified numerical method for the accurate calculation of molecular flow transmission probabilities and density distributions of cylindrical tubes

•Accurate calculations of molecular flow rates of tubes are important.•We report a modified numerical method with accuracies as high as 10−11–10−13.•They're better than the results reported by Mohan et al. and Gómez-Goñi et al.

Accurate numerical calculations of molecular flow transmission probabilities and density distributions of tubes are important to the benchmark problems of Monte Carlo solutions, dynamic expansion vacuum gauge calibration systems, and molecular beam formation studies. Although Nawyn and Meyer [published by van Essen and Heerens. J Vac Sci Technol 1976; 13:1183] have solved cylindrical tube problems by using the numerical method based on Clausing's equations, perhaps the calculated results still lack sufficient accuracy. In this paper, we propose a modified method that could achieve calculation accuracies of transmission probabilities as high as 10−11–10−13 in the range of L′/R ≤ 100 (where L′ is the tube length, R is the tube radius), which are more accurate than the results recently reported by Mohan et al. [J Vac Sci Technol A 2007; 25:758] and Gómez-Goñi et al. [J Vac Sci Technol A 2003; 21:1452].