Low-Temperature Viscosity Cross Sections Measured in a Supersonic Argon Beam

An exact translational-relaxation equation is derived from the Boltzmann equation for the special case in which (a) the flow is spherically symmetric source flow, (b) the velocity distribution is ellipsoidal, and (c) the atoms are hard spheres. It is shown that, at least for small temperature differences, the appropriate cross section is the thermal-conductivity (or viscosity) transport cross section. This relaxation equation is used then to calculate values of argon cross sections from velocity distributions near the centerline of a free jet measured by molecular-beam techniques. These values (a) agree with the values obtained from viscosity measurements in the temperature range in which the two sets of data overlap, (b) continue to increase as the temperature decreases to about 25°K, and (c) decrease as the temperature decreases to about 10°K. The observed decrease in values as the temperature decreases from about 25°K was not expected and has not been explained.