Modification of Takaishi-Sensui formula for a diaphragm gauge system connected by an arbitrary length pipe

The thermal transpiration effect in a vacuum system, where a circular pipe connects a capacitance diaphragm gauge (CDG) and a vacuum vessel, was numerically investigated using the direct simulation Monte Carlo (DSMC) method. The simulated pressure ratios were plotted versus the Knudsen number K, over the range 10−3 ≤ K ≤ 103, for a fixed diameter and various pipe lengths. The curve obtained here was compared with that obtained using the Takaishi-Sensui formula (T-S curve). For a long pipe, with λ ≥ 10, (λ: aspect ratio of length to diameter), the simulated curve agreed well with the T-S curve over the entire examined range of K. For a shorter pipe (λ < 10), the simulated curve seemed to shift in the low K (high pressure) direction, with respect to the T-S curve, and the distance between the curves abruptly increased with decreasing λ. The discrepancy for a short pipe was found to be removable by rescaling the Knudsen number. The discrepancy that originally existed for a long pipe could also be reduced, if the reflection on the pipe wall obeyed an incompletely accommodated Maxwell model.