Nonequilibrium statistical thermodynamics: Nonequilibrium grand ensemble method for sheared dilute gases

Abstract

The nonequilibrium grand ensemble method previously reported is rigorously implemented for a nonequilibrium dilute gas mixture sheared in plane Couette flow geometry and analytic results are presented for the nonequilibrium thermodynamic quantities of the sheared gas. The calortropy is shown to contain all the constitutive information of the system. The notions of temperature and pressure for the nonequilibrium gas are examined on the basis of the calortropy calculated from the nonequilibrium grand partition function. The shear rate dependence of the nonlinear shear and first normal stress coefficients is calculated numerically and also by means of an iterative method. The first iterative solutions are found to give a qualitatively correct behavior for all Peclet numbers.

Thermodynamics of Fluids Under Flow

“…Farhat and Eu (1998), who also included normal-pressure effects in a non-equilibrium ensemble method proposed by Eu (1998). Note that (2.32) could also be written as M = (k B T ) −1 U + λ , with the component of λ defined accordingly.…”

Generalized hydrodynamics in the transient regime and irreversible thermodynamics

“…There are a number of ways to close the open hierarchy. We have found that the following closure gives rise to a structure of generalized hydrodynamics consistent with irreversible thermodynamics and at the same time a divergence free non-equilibrium statistical mechanics which enables us to calculate the non-equilibrium partition function (Al-Ghoul & Eu 2001a;Farhat & Eu 1998). Such a closure is (Al-Ghoul & Eu 1997, 2001b)…”