Integral equation for nonequilibrium chemical potential and the Kirkwood diffusion equation: derivation from the generalized Boltzmann equation

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Abstract
In this paper the kinetic equation for dense simple fluids reported previously is generalized and applied to derive an integral equation for nonequilibrium chemical potential and the Kirkwood diffusion equation for dense polyatomic fluids (e.g., polymers). The derivation requires a generalization of the Kirkwood integral equation for configuration distribution function, the integral equation for local chemical potential to the case of nonequilibrium polyatomic fluids, and a set of evolution equations for macroscopic variables. The evolution equations for macroscopic variables and irreversible thermodynamics are found to have the same mathematical structures as for dense simple fluids. The simple and nonsimple fluids are distinguished in the present theory by the different collision bracket integrals appearing in the evolution equations (constitutive equations) for various fluxes such as stress tensors, heat fluxes and diffusion fluxes. The Kirkwood diffusion equation is obtained for the configuration distribution function of a polyatomic molecule by using a set of approximations on the distribution function and the mass flux diffusion equations. As an illustration of application of the evolution equations for macroscopic variables, the viscosity of a binary solution of polyatomic and monatomic fluids is considered and an intrinsic viscosity formula is obtained for it in terms of collision bracket integrals. This formula provides a statistical mechanical formula for intrinsic viscosity

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