Analysis of the transport coefficients for simple dense fluid: Application of the modified Enskog theory

Hanley, H. J. M.; McCarty, R.D.; Cohen, E. G. D.

doi:10.1016/0031-8914(72)90108-5

Cited by 169 publications

(67 citation statements)

References 39 publications

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“…These contributions are known from the Enskog theory of dense fluids, see Ref. [51]. They take into account the transfer of energy and momentum via the intermolecular potential and arise because the size of colliding molecules is not neglected anymore.…”

Section: Moments Of the Distribution Functions And The Collision Opermentioning

confidence: 99%

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Chapman–Enskog expansion for the Vicsek model of self-propelled particles

Ihle¹

2016

J. Stat. Mech.

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Abstract. Using the standard Vicsek model, I show how the macroscopic transport equations can be systematically derived from microscopic collision rules. The approach starts with the exact evolution equation for the N-particle probability distribution, and after making the mean-field assumption of Molecular Chaos leads to a multi-particle Enskog-type equation. This equation is treated by a non-standard Chapman-Enskog expansion to extract the macroscopic behavior. The expansion includes terms up to third order in a formal expansion parameter ǫ, and involves a fast time scale. A selfconsistent closure of the moment equations is presented that leads to a continuity equation for the particle density and a Navier-Stokes-like equation for the momentum density. Expressions for all transport coefficients in these macroscopic equations are given explicitly in terms of microscopic parameters of the model. The transport coefficients depend on specific angular integrals which are evaluated asymptotically in the limit of infinitely many collision partners, using an analogy to a random walk. The consistency of the Chapman-Enskog approach is checked by an independent calculation of the shear viscosity using a Green-Kubo relation.

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Section: Moments Of the Distribution Functions And The Collision Opermentioning

confidence: 99%

“…4.3 was done in the limit of large mean free path r 0 ≪ v 0 τ . It can be shown, [55], that similar to dense fluids [51] and other particle-based models [52,53], there is an additional collisional contribution, ν coll , due to collisional momentum transfer,…”

Section: Momentum Density Evolution For Time Scale Tmentioning

confidence: 99%

Chapman–Enskog expansion for the Vicsek model of self-propelled particles

Ihle¹

2016

J. Stat. Mech.

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“…Though this theory properly describes density dependence of the kinetic coefficients, at the same time the suppositions about the structure of the collision integral remain sufficiently rough and phenomenological. Despite approximate assumptions on the collision integral in the kinetic equation for a one-particle distribution function of hard spheres, the Enskog theory very well describes a set of properties for real dense gases [25,31].…”

Section: Overviewmentioning

confidence: 99%

A Consistent Description of Kinetics and Hydrodynamics of Systems of Interacting Particles by Means of the Nonequilibrium Statistical Operator Method

Tokarchuk¹,

Omelyan²,

Kobryn³

1998

Condens. Matter Phys.

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A statistical approach to a self-consistent description of kinetic and hydrodynamic processes in systems of interacting particles is formulated on the basis of the nonequilibrium statistical operator method by D.N.Zubarev. It is shown how to obtain the kinetic equation of the revised Enskog theory for a hard sphere model, the kinetic equations for multistep potentials of interaction and the Enskog-Landau kinetic equation for a system of charged hard spheres. The BBGKY hierarchy is analyzed on the basis of modified group expansions. Generalized transport equations are obtained in view of a self-consistent description of kinetics and hydrodynamics. Time correlation functions, spectra of collective excitations and generalized transport coefficients are investigated in the case of weakly nonequilibrium systems of interacting particles.

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“…Neither the standard Enskog theory (SET) [1] nor its modifications (MET) [2,3] and (RET) [4,5] solve the problem as far as they are valid for hard spheres. The Enskog-type kinetic theories [6,7] suggested for a "hard spheres + smooth tail" potential treat the long-range interactions by a non-dissipative mean-field term.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic equations for dense fluid mixtures with multistep interaction between particles

Токарчук¹,

Humenyuk²

2007

Condens. Matter Phys.

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Generalization of the kinetic equation for a dense fluid with a multistep interaction potential to the case of a dense mixture is presented. Derivation of hydrodynamic equations is performed starting with the kinetic equation for the one-particle distribution function and the transport equation for the potential energy density. Expressions for momentum and heat fluxes are obtained. The transport equation for the kinetic energy density is shown to contain a new term of the "source" type, which describes fast exchange processes between kinetic and potential energies of the system.

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Analysis of the transport coefficients for simple dense fluid: Application of the modified Enskog theory

Cited by 169 publications

References 39 publications

Chapman–Enskog expansion for the Vicsek model of self-propelled particles

Chapman–Enskog expansion for the Vicsek model of self-propelled particles

A Consistent Description of Kinetics and Hydrodynamics of Systems of Interacting Particles by Means of the Nonequilibrium Statistical Operator Method

Hydrodynamic equations for dense fluid mixtures with multistep interaction between particles

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