Kinetic Theory of a Simple Dense Fluid
In Chap. 5 , we have glimpsed into the possibility that the Boltzmann equation may be an archetype, but only in a special form, of irreversible kinetic equation for fluids, after which the kinetic equation for dense fluids of correlated particles may be
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Kinetic Theory of a Simple Dense Fluid
In Chap. 5, we have glimpsed into the possibility that the Boltzmann equation may be an archetype, but only in a special form, of irreversible kinetic equation for fluids, after which the kinetic equation for dense fluids of correlated particles may be fashioned and therewith the Gibbs ensemble theory can be formulated for time-dependent irreversible processes in dense fluids. As a first step to realize this goal, we would like to make an attempt to extend the Boltzmann-like kinetic equation for moderately dense gases, which we have formulated in Chap. 5, to dense correlated gases and liquids. We will thereby acquire a class of irreversible kinetic equations in the form of generalized Boltzmann equation (BGE), which will enable us to derive various evolution equations for macroscopic variables in the thermodynamic manifold necessary to describe macroscopic evolution of a fluid. Then, on the basis of them, we hope to comprehend the phenomenological thermodynamic theory of irreversible (transport) processes discussed in Chap. 2 from the molecular theory standpoint. The kinetic theory foundations of irreversible thermodynamics and generalized hydrodynamics will be hopefully laid thereby. We will begin with the system consisting of a single-component simple fluid. The set of macroscopic evolution equations for variables spanning the thermodynamic manifold will turn out to be the dense fluid versions of generalized hydrodynamic equations of gases, which consist of the balance equations for conserved variables—the conservation laws—and the evolution equations of nonconserved variables. Unlike the dilute uncorrelated gases discussed in Chap. 3 the distribution functions, however, are no longer made up of singlet distribution functions only, but fully involve effects of spatial correlations which would be indispensable in describing the fluid behaviors in the dense fluid regime. Therefore the macroscopic variables for the fluid must be computed with spatial correlations explicitly taken to account. Nevertheless, their evolution equations still consist of the equation of continuity or the mass balance equation, momentum balance equation, and internal energy balance equation for the conserved variables, and various constitutive equations for the © Springer International Publishing Switzerland 2016 B.C. Eu, Kinetic Theory of Nonequilibrium Ensembles, Irreversible Thermodynamics, and Generalized Hydrodynamics, DOI 10.1007/978-3-319-41147-7_6
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shear stress, excess normal stress, heat flux, etc., plus the volume transport equation in the case when volume transport phenomena are non-negligible in the dense fluid regime. By including a variable characterizing the representative volume of the fluid—the Voronoi volume, more specifically—among the nonconserved variables in the thermodynamic manifold, we are able to explicitly extend the thermodynamic manifold. The structure of generalized hydrodynamic equations obtained thereby broadens the s
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