Conductance measurement of a conical tube and calculation of the pressure distribution

In recent articles [J. Gomez-Goni, and P. J. Lobo J. Vac. Sci. Technol. A 21, 1452 (2003); P. Swemin and M. Niewinski, Vacuum 67, 359 (2002)] the conductance of conical tube in the molecular flow regime has been calculated using the Monte Carlo method or by the resolution of the Clausing integral equation, reformulated by Iczkowski et al. [J. Phys. Chem. 67, 229 (1963)], for the case of a cone. The comparison between the analytical values and different simulations allows one to determine a correction factor k to apply to the intrinsic conductance of the cones. This coefficient depends on the propagation direction of flow and increases considerably for larger conic angles. For a cone half-angle of 40° and a length ten times greater than smallest entrance radii, the correction factor is approximately 5.3 for a circulating flow from the smallest to the largest orifice. Our experimental device measured the conical conductance by a dynamic method. In order to do this, it was necessary to determine the surface pressure distribution. The extension of the Oatley method, with the addition of several components of various transmission probabilities, permits one to establish this distribution for a vacuum system and thus to give the pressure measured by a gauge situated along the wall of the duct. This method provides a good approximation for tubes and cones and can be used for engineering practice. The determination of this distribution is all the more critical when the conductance and the pumping speed are large and can thus have a great influence on the vacuum metrology.