Abstract
A stochastic model of the revised Enskog equation is considered. A choice of the smearing function suggested by the work of Leegwater is used to apply the model to the repulsive part of the Lennard-Jones potential and the inverse-power soft-sphere potential. The virial coefficients obtained from the equilibrium properties of the models are in excellent agreement with the known exact coefficients for these models. The transport coefficients for the repulsive Lennard-Jones (RLP) model are also computed and appear to be of comparable accuracy to the Enskog-theory coefficients applied directly to a hard-sphere system, although exact results for the RLP with which to make an extensive comparison are not yet available. The pressure and the transport coefficients obtained from the model (shear viscosity, thermal conductivity, and self-diffusion) are compared with the pressure and the corresponding transport coefficients predicted by the Enskog and square-well kinetic theories.
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REFERENCES
J. A. Leegwater, Velocity autocorrelation function of Lennard-Jones fluids, J. Chem. Phys. 94:7402–7410 (1991).
D. Enskog, Kinetische Theorie, Kgl. Svenska Vetenskaps Akademiens Handl 63, no. 4 (1921) [English translation in S. Brush, Kinetic Theory, Vol. 3 (Pergamon Press, New York, 1972)].
H. van Beijeren and M. H. Ernst, The modified Enskog equation, Physica 68:437–456 (1973).
P. Résibois and M. De Leener, Classical Kinetic Theory of Fluids (Wiley, New York, 1977).
H. T. Davis, Stuart A. Rice, and J. V. Sengers, On the kinetic theory of dense fluids. IX. The fluid of rigid spheres with a square-well attraction, J. Chem. Phys. 35:2210–2233 (1961).
J. Karkheck and G. Stell, Maximization of entropy, kinetic equations, and irreversible thermodynamics, Phys. Rev. A 25:3302–3327 (1982).
G. Stell, J. Karkheck, and H. van Beijeren, Kinetic mean field theories: Results of energy constraint in maximizing entropy, J. Chem. Phys. 79:3166–3167 (1983).
J. Karkheck, H. van Beijeren, I. de Schepper, and G. Stell, Kinetic theory and H theorem for a dense square-well fluid, Phys. Rev. A 32:2517–2520 (1985).
J. Blawzdziewicz and G. Stell, Local H-theorem for a kinetic variational theory, J. Stat. Phys. 56:821–840 (1989).
H. vanBeijeren, Kinetic theory of dense gases and liquids, inFundamental Problems in Statistical Mechanics VII, H. van Beijren, ed. (Elsevier, 1990), pp.357–380.
J. Karkheck, G. Stell, and J. Xu, Transport theory for the Lennard-Jones dense fluid, J. Chem. Phys. 89:5829–5833 (1988).
A. Ya. Povzner, The Boltzmann equation in the kinetic theory of gases, Amer. Math. Soc. Transl. 47:193–216 (1962).
M. Lachowicz and M. Pulvirenti, A stochastic system of particles modeling the Euler equation, Arch. Rat. Mech. Anal. 109:81–93 (1990).
M. Pulvirenti, Kinetic limits for stochastic particle systems, in Lecture Notes in Mathematics, Vol. 1627, D. Talay and L. Tubaro, eds. (Springer-Verlag, 1995), pp. 96–126.
N. Bellomo and J. Polewczak, The generalized Boltzmann equation existence and exponential trend to equilibrium, C. R. Acad. Sci. Paris, Série I 319:893–898 (1994).
D. Ruelle, Statistical Mechanics (Benjamin, London, 1969).
J. Polewczak and G. Stell, New properties of a class of generalized kinetic equations, J. Stat. Phys. 64:437–464 (1991).
M. Mareschal, J. Blawzdziewicz, and J. Piasecki, Local entropy production from the revised Enskog equation: General formulation for inhomogeneous fluids, Phys. Rev. Lett. 52:1169–1172 (1984).
J. Jeans, Dynamical Theory of Gases (Cambridge University Press, Cambridge, 1925).
T. Kihara and T. Hikita, in Fourth Symposium on Combustion (Williams and Wilkins Co., Baltimore, 1953), 458.
J. S. Rowlinson, An equation of state of gases at high temperatures and densities, Molecular Phys. 7:349 (1964).
J. S. Rowlinson, The statistical mechanics of systems with steep intermolecular potentials, Molecular Phys. 8:107 (1964).
N. F. Carnahan and K. E. Starling, J. Chem. Phys. 51:635 (1969).
W. Sung and G. Stell, J. Chem. Phys. 80:3350 (1984).
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Polewczak, J., Stell, G. Transport Coefficients in Some Stochastic Models of the Revised Enskog Equation. Journal of Statistical Physics 109, 569–590 (2002). https://doi.org/10.1023/A:1020406413636
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DOI: https://doi.org/10.1023/A:1020406413636