Nonlinear transport processes and fluid dynamics: Effects of thermoviscous coupling and nonlinear transport coefficients on plane Couette flow of Lennard-Jones fluids

Abstract

To examine the effects of nonlinear transport processes on the flow properties of a real fluid, we study the plane Couette flow under a temperature gradient in a Lennard-Jones fluid over a range of gas pressure. The analysis is based on the nonlinear transport coefficients derived in the modified moment method. The linear transport coefficients appearing in the theory are those constructed by Ashurst and Hoover from the nonequilibrium molecular-dynamics simulations, while for the equation of state for the Lennard-Jones fluid we use the empirical form proposed by Ree. Examples for the flow characteristics at two extreme conditions when either the gas is very dilute, or when it is very dense, are presented. It is shown that the temperature and velocity profiles for nonlinear transport processes are significantly different from the ones obtained with the linear transport coefficients. In the dilute-gas limit, slip boundary conditions are used which are derived by applying the Langmuir theory of gas-surface interaction. Flow profiles show pronounced boundary-layer structures near the wall when the product of the Knudsen number and the Mach number is sufficiently large.