Generalized hydrodynamics, normal-stress effects, and velocity slips in the cylindrical Couette flow of Lennard-Jones fluids

In this paper we extend the previous study of flow profiles in cylindrical Couette flow of a Lennard-Jones fluid so as to include the effects of normal stresses neglected in the previous work. The flow is subject to a temperature gradient and thermoviscous effects are taken into consideration. We apply the generalized hydrodynamic equations which are provided by the modified moment method for the Boltzmann equation reported previously. The results of calculation are in good agreement with the Monte Carlo direct simulation results of K. Nanbu [Phys. Fluids 27, 2632 (1984)] and experimental data for all Knudsen numbers. The inclusion of normal stresses also brings about a new aspect to the flow properties which has not been seen before, since the flow profiles exhibit a phase-transition-like behavior as the Knudsen number increases beyond a critical value. There also appear slips in velocity at the inner cylinder wall in the supercritical regime of Knudsen number. At the critical Knudsen number the entropy production for the flow process also exhibits a singular behavior which is reminiscent of a second-order phase transition in thermodynamic systems.