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Title: Transport theory for the Lennard-Jones dense fluid

Abstract

A kinetic theory for a fluid of particles interacting via a pair potential with hard-core plus truncated tail is described and used to derive a transport theory for the Lennard-Jones fluid as well as the square-well fluid. Numerical results for shear viscosity, thermal conductivity, and the self-diffusion coefficient are given for the Lennard-Jones fluid and compared with simulation and experimental results. Our Lennard-Jones theory proves quantitatively useful over a wide range of states.

Authors:
; ;
Publication Date:
Research Org.:
Department of Science and Mathematics, GMI Engineering and Management Institute, Flint, Michigan 48504-4898
OSTI Identifier:
6930557
Resource Type:
Journal Article
Resource Relation:
Journal Name: J. Chem. Phys.; (United States); Journal Volume: 89:9
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; LIQUIDS; SELF-DIFFUSION; THERMAL CONDUCTIVITY; VISCOSITY; RARE GASES; STRUCTURE FACTORS; COMPUTERIZED SIMULATION; LENNARD-JONES POTENTIAL; SQUARE-WELL POTENTIAL; TRANSPORT THEORY; DIFFUSION; ELEMENTS; FLUIDS; GASES; NONMETALS; NUCLEAR POTENTIAL; PHYSICAL PROPERTIES; POTENTIALS; SIMULATION; THERMODYNAMIC PROPERTIES 400201* -- Chemical & Physicochemical Properties

Citation Formats

Karkheck, J., Stell, G., and Xu, J. Transport theory for the Lennard-Jones dense fluid. United States: N. p., 1988. Web. doi:10.1063/1.455533.
Karkheck, J., Stell, G., & Xu, J. Transport theory for the Lennard-Jones dense fluid. United States. doi:10.1063/1.455533.
Karkheck, J., Stell, G., and Xu, J. 1988. "Transport theory for the Lennard-Jones dense fluid". United States. doi:10.1063/1.455533.
@article{osti_6930557,
title = {Transport theory for the Lennard-Jones dense fluid},
author = {Karkheck, J. and Stell, G. and Xu, J.},
abstractNote = {A kinetic theory for a fluid of particles interacting via a pair potential with hard-core plus truncated tail is described and used to derive a transport theory for the Lennard-Jones fluid as well as the square-well fluid. Numerical results for shear viscosity, thermal conductivity, and the self-diffusion coefficient are given for the Lennard-Jones fluid and compared with simulation and experimental results. Our Lennard-Jones theory proves quantitatively useful over a wide range of states.},
doi = {10.1063/1.455533},
journal = {J. Chem. Phys.; (United States)},
number = ,
volume = 89:9,
place = {United States},
year = 1988,
month =
}
  • For a large region of dense fluid states of a Lennard-Jones system, they have calculated the friction coefficient by the force autocorrelation function of a Brownian-type particle by molecular dynamics (MD). The time integral over the force autocorrelation function showed an interesting behavior and the expected plateau value when the mass of the Brownian particle was chosen to be about a factor of 100 larger than the mass of the fluid particle. Sufficient agreement was found for the friction coefficient calculated by this way and that obtained by calculations of the self-diffusion coefficient using the common relation between these coefficients.more » Furthermore, a modified friction coefficient was determined by integration of the force autocorrelation function up to the first maximum. This coefficient can successfully be used to derive a reasonable soft part of the friction coefficient necessary for the Rice-Allnatt approximation for the shear velocity and simple liquids.« less
  • In this paper we report on calculations of flow profiles for cylindrical Couette flow of a Lennard-Jones fluid. The flow is subjected to a temperature gradient and thermoviscous effects are taken into consideration. We apply the generalized fluid dynamic equations which are provided by the modified moment method for the Boltzmann equation reported previously. The results of calculations are in good agreement with the Monte Carlo direct simulation method by K. Nanbu (Phys. Fluids 27, 2632 (1984)) for most of Knudsen numbers for which the simulation data are available.
  • We consider the application of the cell theory to single component and binary Lennard-Jones solids. We calculate solid phase properties and solid{endash}fluid equilibrium using the cell theory for the solid phase and an equation of state for the fluid phase. In the single component case the thermodynamic properties as well as the solid{endash}fluid phase diagram predicted by the theory are in quite good agreement with Monte Carlo simulation results. The introduction of correlations between the motions of nearest neighbor particles into the cell theory in a fashion suggested by Barker significantly improves the agreement. For binary Lennard-Jones 12-6 mixtures themore » predictions of the theory are compared with experimental data for mixtures forming substitutionally disordered solid solutions involving argon, krypton and methane. The theory correctly predicts the form of the phase diagram but the quantitative predictions are quite sensitive to the choice of potential parameters. The shape of the phase diagram is similar to that for a hard sphere mixture with the same diameter ratio. {copyright} {ital 1996 American Institute of Physics.}« less
  • We present calculations of the full spectra of Lyapunov exponents for 8- and 32-particle systems in three dimensions with periodic boundary conditions and interacting with the repulsive part of a Lennard-Jones potential. A new algorithm is discussed which incorporates ideas from control theory and constrained nonequilibrium molecular dynamics. Equilibrium and nonequilibrium steady states are examined. The latter are generated by the application of an external field F/sub e/ through which equal numbers of particles are accelerated in opposite directions, and by thermostatting the system using Nose-Hoover or Gauss mechanics. In equilibrium (F/sub e/ = 0) the Lyapunov spectra are symmetricalmore » and may be understood in terms of a simple Debye model for vibrational modes in solids. For nonequilibrium steady states (F/sub e/not =0) the Lyapunov spectra are not symmetrical and indicate a collapse of the phase-space density onto an attracting fractal subspace with an associated loss in dimensionality proportional to the square of the applied field. Because of this attractor's vanishing volume in phase space and the instability of the corresponding repellor it is not possible to observe trajectories violating the second law of thermodynamics in spite of the time-reversal invariance of the equations of motion. Thus Nose-Hoover mechanics, of which Gauss's isokinetic mechanics is a special case, resolves the reversibility paradox first stated by J. Loschmidt (Sitzungsber. kais. Akad. Wiss. Wien 2. Abt. 73, 128 (1876)) for nonequilibrium steady-state systems.« less
  • The vapor–liquid nucleation in a dense Lennard-Jones system is studied analytically and numerically. A solution of the nucleation kinetic equations, which includes the elementary processes of condensation/evaporation involving the lightest clusters, is obtained, and the nucleation rate is calculated. Based on the equation of state for the cluster vapor, the pre-exponential factor is obtained. The latter diverges as a spinodal is reached, which results in the nucleation enhancement. The work of critical cluster formation is calculated using the previously developed two-parameter model (TPM) of small clusters. A simple expression for the nucleation rate is deduced and it is shown thatmore » the work of cluster formation is reduced for a dense vapor. This results in the nucleation enhancement as well. To verify the TPM, a simulation is performed that mimics a steady-state nucleation experiments in the thermal diffusion cloud chamber. The nucleating vapor with and without a carrier gas is simulated using two different thermostats for the monomers and clusters. The TPM proves to match the simulation results of this work and of other studies.« less