Molecular drag model based on differential reduction of the Kruger–Shapiro equations

Abstract

The history of the method of differential probability in molecular flow is reviewed, beginning with the little known derivation by D. Santeler (5th Annual Symposium on Space Environmental Simulation, Arnold Air Force Station, TN, May, 1964), based on the equation of C. W. Oatley [Br. J. Appl. Phys. 8, 15 (1957)]. This method contains the aperture correction within the theory, without phenomenological assumptions. A new equation of this type, for molecular pumping, is derived by differential reduction of the Kruger–Shapiro equations. A simple solution of the differential equations yields results of good accuracy for engineering use. The physical characteristics of molecular pumping are clarified by describing the pressure distribution within the pumping tube as if it were a conductance. By this method the calculated performance of a model pump is shown to be in satisfactory agreement with a Clausing-type solution from a previous publication.