Effusion from Spherical Orifices. I. Transmission by Molecular Flow

Abstract

Molecular flow through orifices which are spherical segments is treated by a method analogous to that which previously has been applied to cylindrical and conical orifices. The integral equation which expresses the rate at which molecules impinge on a unit area is shown to possess a simple, closed-form solution for spherical orifices, and the transmission probability for such orifices is derived in closed form. Transmission probabilities are presented for several spherical orifices and are shown to be always larger than those for conical or cylindrical orifices of the same dimensions. For very short and very long divergent spherical orifices the transmission probability approaches unity, and at intermediate lengths it passes through a minimum. For very short spherical orifices with equal and parallel plane entrance and exit, the transmission probability approaches unity, and it decreases to a limiting value of one-half for very great length.