Kinetic mean-field theories

Journal Article · Sat Aug 01 04:00:00 EDT 1981 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.442154· OSTI ID:6449236

Karkheck, J; Stell, G

A kinetic mean-field theory for the evolution of the one-particle distribution function is derived from maximizing the entropy. For a potential with a hard-sphere core plus tail, the resulting theory treats the hard-core part as in the revised Enskog theory. The tail, weighted by the hard-sphere pair distribution function, appears linearly in a mean-field term. The kinetic equation is accompanied by an entropy functional for which an H theorem was proven earlier. The revised Enskog theory is obtained by setting the potential tail to zero, the Vlasov equation is obtained by setting the hard-sphere diameter to zero, and an equation of the Enskog--Vlasov type is obtained by effecting the Kac limit on the potential tail. At equilibrium, the theory yields a radial distribution function that is given by the hard-sphere reference system and thus furnishes through the internal energy a thermodynamic description which is exact to first order in inverse temperature. A second natural route to thermodynamics (from the momentum flux which yields an approximate equation of state) gives somewhat different results; both routes coincide and become exact in the Kac limit. Our theory furnishes a conceptual basis for the association in the heuristically based modified Enskog theory (MET) of the contact value of the radial distribution function with the ''thermal pressure'' since this association follows from our theory (using either route to thermodynamics) and moreover becomes exact in the Kac limit. Our transport theory is readily extended to the general case of a soft repulsive core, e.g., as exhibited by the Lennard-Jones potential, via by-now-standard statistical--mechanical methods involving an effective hard-core potential, thus providing a self-contained statistical--mechanical basis for application to such potentials that is lacking in the standard versions of the MET. Thermal conductivity and shear viscosity of several saturated simple liquids agree with experiment.

• Research Organization: Department of Mechanical Engineering, State University of New York at Stony Brook, Long Island, New York 11794
• OSTI ID: 6449236
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 75:3; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640420* -- Fluid Physics-- Properties & Structure of Fluids-- (-1987)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
DISTRIBUTION FUNCTIONS
ENTROPY
EQUATIONS
FLUIDS
FUNCTIONS
HARD-SPHERE MODEL
KINETIC EQUATIONS
LIQUIDS
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES
TRANSPORT THEORY