Theoretical studies of highly expanded free jets: Influence of quantum effects and a realistic intermolecular potential

TLDR

The authors extend an approximate Boltzmann‑equation theory to include quantum effects and realistic intermolecular potentials in the collision integrals for calculating speed ratios and temperatures in free jet expansions. The extended theory predicts that quantum effects substantially raise helium speed ratios—sensitive to potential shape—yielding agreement with experiments and suggesting that, absent condensation, the highest observed ratio of 225 could reach 700, corresponding to a quasiequilibrium gas temperature near 10⁻³ K.

Abstract

An earlier approximate theory proposed by Knuth and Fisher and Miller and Andres for solving the Boltzmann equation to calculate speed ratios and temperatures in free jet expansions has been extended to take account of quantum effects and realistic potentials in the collision integrals. The calculations show that quantum effects lead to a substantial increase in terminal speed ratios in helium but not in heavier gases. For He the speed ratios depend sensitively on the shape of the potential. Despite the approximate nature of the theory the predictions are in reasonable agreement with recent experiments. The theory predicts that the presently highest achieved speed ratio in He of 225 can be increased to 700 if condensation does not occur. At this speed ratio the quasiequilibrium gas phase temperature is roughly 10−3 K.