Moderately dense gas quantum kinetic theory: Aspects of pair correlations (original) (raw)
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Moderately dense gas quantum kinetic theory: Transport coefficient expressions
The Journal of Chemical Physics, 1996
Expressions for the transport coefficients of a moderately dense gas are obtained, based on a recently derived density corrected quantum Boltzmann equation. Linearization of the equations determining the pair correlation and the ''free'' singlet density operators about local equilibrium is discussed first. The rate of change of the pair correlations is treated as dynamic effects for pairs of particles relaxing to local equilibrium via a relaxation time model arising from interactions with ''third particles.'' In contrast, the singlet density operator satisfies a Boltzmann equation with binary collisions. Spatially inhomogeneous corrections to the collision superoperator are included. Contributions to the transport coefficients arise from the perturbation from local equilibrium through fluxes associated with kinetic, collisional and, for the thermal conductivity, potential energy mechanisms. A comparison is made between the classical limit of the transport coefficient expressions obtained here and the classical expressions previously derived from the Boltzmann equation with the nonlocal collision corrections of Green and Bogoliubov.
Kinetic theory of dense fluids. III. Density dependence of transport coefficients for dense gases
Annals of Physics, 1979
The viscosity coefficient obtained in a previous paper of this series is calculated as a function of density by developing the N-particle collision operator into a dynamic cluster expansion. The excess transport coefficient A7 is given in an exponential form, where TJ~ is the two-body Chapman-Enskog result for the transport coefficient, n is the density, and fir is a density-independent quantity consisting of connected cluster contributions of (I + 2) particles. Therefore, the leading term p1 consists of connected three-body cluster contributions. The excess shear viscosity coefficient is calculated for a monatomic hard-sphere fluid by computing ,8L up to the three-body contributions and the result is compared with the molecular dynamics result by Ashurst and Hoover and also with the experimental data on Ar at 75°C. In spite of the crudity of the potential model used and the approximations made the agreement is good. The result can be improved if l-body clusters (I > 4) are included in the calculation. The thermal conductivity coefficient can be obtained in a similar form by using exactly the same procedure used for the viscosity coefficient.
Kinetic theory of correlated fluids: From dynamic density functional to Lattice Boltzmann methods
The Journal of Chemical Physics, 2009
Using methods of kinetic theory and liquid state theory we propose a description of the nonequilibrium behavior of molecular fluids, which takes into account their microscopic structure and thermodynamic properties. The present work represents an alternative to the recent dynamic density functional theory, which can only deal with colloidal fluids and is not apt to describe the hydrodynamic behavior of a molecular fluid. The method is based on a suitable modification of the Boltzmann transport equation for the phase space distribution and provides a detailed description of the local structure of the fluid and its transport coefficients. Finally, we propose a practical scheme to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the Lattice Boltzmann method. 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964
Kinetic theory of a normal quantum fluid. II. Transport properties
Physical Review B, 1978
Renormalized expressions for the transport coefficients of a normal quantum fluid are derived from a nonlocal kinetic equation. As was shown in the classical case by Forster and Martin and by Resiboie, the expressions for the transport coefficients separate naturally into "kinetic" and "direct" parts. The kinetic terms are proportional to matrix elements of the inverse of the kinetic kernel, and have the same general structure as the "bare" transport coefficients obtained from a local Boltzmann equation. The direct terms are proportional to matrix elements of the kernel itself, and have no counterpart in calculations based on a local kinetic equation, as in the kinetic theory of gases. %'e evaluate the transport coef5cients using the weak- coupling approximation to the kernel derived in a previous paper. Results are given, first, for both Bose and Fermi Auids at arbitrary temperature, and then for the Fermi fluid near T = 0, where complete solutions are obtained. It is found that the direct parts of the shear viscosity and thermal conductivity are of higher order in T than the kinetic parts, and are therefore negligible at very low temperature. The kinetic parts have the same leading temperature dependence as the predictions of the Landau theory, For the bulk viscosity, however, the direct and kinetic contributions begin at the same order (T ) in the temperature.
AIP Conference Proceedings, 2008
In this paper we discuss the mass-density of gas media as represented in kinetic theory. It is argued that conventional representations of this variable in gas kinetic theory contradict a macroscopic field variable and thermodynamic property in classical thermodynamics. We show that in cases where mass-density variations exist throughout the medium, introducing the mass-density as a macroscopic field variable leads to a restructuring of the diffusive/convective fluxes and implies some modifications to the hydrodynamic equations describing gas flows and heat transfer. As an illustration, we consider the prediction of mass-density profiles in a simple heat conduction problem between parallel plates maintained at different temperatures.
Unified Theory of Lattice Boltzmann Models for Nonideal Gases
Physical Review Letters, 1998
A nonideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for nonideal gases. The existing lattice Boltzmann models for nonideal gases are analyzed and compared with the model derived here. [S0031-9007(98)06759-3] PACS numbers: 47.11. + j, 05.20.Dd, 47.55.Kf, 51.30. + i In recent years, there has been significant progress in the development of the lattice Boltzmann equation (LBE) method [1-4], a novel technique developed for modeling complex systems. One particular application of the lattice Boltzmann method which has attracted considerable attention is the modeling of inhomogeneous fluids, such as multiphase or multicomponent fluids . These flows are important, but are difficult to simulate by conventional techniques of solving the Navier-Stokes equations. The main difficulty conventional techniques face is the existence of interfaces in inhomogeneous flow. There is ample evidence that the lattice Boltzmann models based on mesoscopic theory are particularly suitable for these systems . There are fundamental reasons for the success of the LBE models. Besides their broad applicability, the LBE models can also serve as new paradigms in nonequilibrium statistical mechanics, much like the Ising model in equilibrium statistical mechanics. Many hydrodynamic systems far from equilibrium are difficult to simulate by using the Boltzmann equation directly. The LBE method provides a novel and efficient means to simulate systems far from equilibrium. The LBE models do not start at the macroscopic level; instead, they start at the mesoscopic level at which one can freely use a "potential" to model interactions in the system. Macroscopic or hydrodynamic effects naturally emerge from mesoscopic dynamics, provided that the mesoscopic dynamics possess the correct and necessary conservation laws and associated symmetries.
Research Square (Research Square), 2023
The quantum corrections related to the ideal gas model that are often considered are those which are related to the particles nature: bosons or fermions. These corrections lead respectively to the Bose-Einstein and Fermi-Dirac statistics. However, in this work, other kinds of corrections which are related to the quantum nature of phase space are considered. These corrections are introduced as improvement in the expression of the partition function of an ideal gas. Then corrected thermodynamics properties of the gas are deduced. Both the nonrelativistic quantum and relativistic quantum cases are considered. It is shown that the corrections in the non-relativistic quantum case may be particularly useful to describe the deviation from classical behavior of a Maxwell-Boltzmann gas at low temperature and in confined space. These corrections can be considered as including the description of quantum size and shape effects. For the relativistic quantum case, the corrections could be relevant for confined space and when the thermal energy of each particle is comparable to their rest energy. The corrections appear mainly as modifications in the thermodynamic equation of state and in the expressions of the partition function and thermodynamic functions like entropy, internal energy, and free energy. Classical expressions are obtained as asymptotic limits.
Physica A: Statistical Mechanics and its Applications, 2006
We propose a ''mixed'' integral equation for the pair correlation function of molecular fluids which interpolates between the hypernetted-chain and Percus-Yevick approximations. Thermodynamic consistency between the virial and compressibility equation of state is achieved by varying a single parameter in a suitably chosen mixing function. The integral equation proposed here generalizes the suggestion by Rogers and Young ͓Phys. Rev. A 30, 999 ͑1984͔͒ to an angle-dependent pair potential. When compared to available computer simulation data, the equation is found to yield excellent results for both the thermodynamic properties and the pair-correlation functions. ͓S1063-651X͑96͒02507-X͔