Einstein-Kubo-Helfand and McQuarrie relations for transport coefficients

Journal Article · Mon May 01 04:00:00 EDT 1995 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.51.4296· OSTI ID:44825

Erpenbeck, J J ^[1]

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1. Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

Monte Carlo molecular dynamics calculations of {eta}{sub {ital E}}{sup ({ital C})}({ital t};{ital N}) for an equimolar binary mixture of hard spheres (diameter ratio of 0.4 and mass ratio of 0.03) confirm these large differences at a few mean free times, but suggest a long-time plateau value having the magnitude of the Green-Kubo result, but the values at 70 mean free times do not approach {eta}({ital t};{ital N}) with increasing {ital N}. Finally, we consider the one-particle, EKH-like, McQuarrie expression for shear viscosity, showing that the Chialvo-Cummings-Evans [Phys. Rev. E 47, 1702 (1993)] ``proof`` is defective. Moreover, we demonstrate through molecular dynamics calculations for the same hard-sphere mixture that the two-particle contribution to the time-dependent viscosity, which must vanish at long times for the McQuarrie formula to be valid, in fact contributes roughly 40% of the shear viscosity at a volume of (5 {radical}2 /2){ital tsum}{sub {ital a}}{ital N}{sub {ital a}}{sigma}{sub {ital a}}{sup 3}, where {ital N}{sub {ital a}} is the number of particles of species {ital a} having diameter {sigma}{sub {ital a}}.

• OSTI ID: 44825
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 5 Vol. 51; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOUNDARY CONDITIONS
DIFFUSION
HARD-SPHERE MODEL
KUBO FORMULA
MONTE CARLO METHOD
SHEAR
TRANSPORT THEORY
VISCOSITY