Theory of Second-Order Stress in a Dense Gas

Abstract

The phenomenological coefficients associated with stress tensor terms proportional to the square of the velocity gradient have been computed for dense gases composed of rigid spheres and of particles interacting with a square-well potential. Most of the calculations reported here were obtained from a generalization of the moment method which is appropriate to a dense gas. A detailed comparison between theory and experiment leads to the following conclusions: (i) Reiner's torsional flow observations for gases and for liquid toluene are not attributable to second-order stress. At low densities kinetic theory predicts an effect with the opposite algebraic sign from that observed experimentally. At high densities the theory predicts a reversal of sign. At all densities the magnitudes of the theoretical and experimental effects differ by several orders of magnitude. (ii) Oliver and MacSporran's measurements of jet thrust due to liquids issuing from circular orifices differ by many orders of magnitude from the predictions of kinetic theory. However, at high densities there is agreement with regard to the algebraic sign of the effect. (iii) Oliver and MacSporran also studied jet thrust from a slot, but were unable to observe any effect with gases. Kinetic theory is in agreement with this.