Effusion. VII. The Failure of Isotropy of a Gas in an Effusion Cell and the Transition Region

Abstract

A theory with a molecular model is presented for the transition region between the molecular flow region and the hydrodynamic flow region for the effusion of gases through orifices. The theory has as its basis a parameter which is associated with the failure of isotropy of the gas within the effusion container and which is calculated from the solid angle subtended by the vacuum opening of the orifice at the collision site of gaseous molecules within the effusion cell. This leads to modification of the kinetic theory equations for the ideal orifice for both the angular number distributions and the orifice transmission factors; these modified equations agree well with available experimental data. For orifices with orifice walls, the solid angle subtended by the orifice wall becomes an important parameter because the probability that a molecule has its trajectory such that it collides with the orifice wall depends upon that solid angle. A modification of the Clausing theory for nonideal orifices appears to agree well with experimental angular distributions for the cylindrical orifice case. It should be possible to extend these calculations to other nonideal orifice shapes.