The modified Enskog equation

Beijeren, H. van; Ernst, M. H.

doi:10.1016/0031-8914(73)90372-8

Cited by 350 publications

(230 citation statements)

References 12 publications

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“…The revised Enskog theory (RET) [10,11] provides a closed approximate expression for the collision term as a function of the single-particle distribution function:…”

Section: Theorymentioning

confidence: 99%

Beyond dynamic density functional theory: the role of inertia

Marconi

Tarazona

Cecconi

et al. 2008

J. Phys.: Condens. Matter

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We discuss the recent attempts to generalize dynamical density functional (DDF) theory to situations where the momentum and energy transport, not necessarily associated with mass diffusion, play a role. We consider an assembly of particles described by inertial dynamics and subjected to the influence of a heat-bath. By means of a time multiple timescale analysis we derive the evolution equation for the noise-averaged density field. Remarkably, for large values of the friction parameter and/or the mass of the particles we obtain the same governing equation of DDF, and in addition we are able to compute higher-order corrections.

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“…The revised Enskog theory (RET) [10,11] provides a closed approximate expression for the collision term as a function of the single-particle distribution function:…”

Section: Theorymentioning

confidence: 99%

Beyond dynamic density functional theory: the role of inertia

Marconi

Tarazona

Cecconi

et al. 2008

J. Phys.: Condens. Matter

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“…The derivation of hydrodynamics and evaluation of transport coefficients based on the Enskog kinetic equation leads to an accurate and unique description of moderately dense gases. The generalization to mixtures requires a revision of the original Enskog theory for thermodynamic consistency (revised Enskog theory, or RET) [48], and its application to hydrodynamics and mixture transport coefficients was accomplished twenty years ago [49]. As noted above, for granular (dissipative) gases, there remains an open problem of predicting transport properties at moderate densities, as occur in current experiments and simulations.…”

Section: Overview Of Derivationmentioning

confidence: 99%

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport

2007

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A hydrodynamic description for an s-component mixture of inelastic, smooth hard disks (two dimensions) or spheres (three dimensions) is derived based on the revised Enskog theory for the single-particle velocity distribution functions. In this first portion of the two-part series, the macroscopic balance equations for mass, momentum, and energy are derived. Constitutive equations are calculated from exact expressions for the fluxes by a Chapman-Enskog expansion carried out to first order in spatial gradients, thereby resulting in a Navier-Stokes order theory. Within this context of small gradients, the theory is applicable to a wide range of restitution coefficients and densities. The resulting integral-differential equations for the zeroth-and first-order approximations of the distribution functions are given in exact form. An approximate solution to these equations is required for practical purposes in order to cast the constitutive quantities as algebraic functions of the macroscopic variables; this task is described in the companion paper.

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“…The derivation of Ref. 10 employs standard tools of kinetic theory and in particular the revised Enskog equation 12,13 . In this paper we generalize such an approach to fluids of inelastic hard core particles subject to a stochastic forcing.…”

Section: Introductionmentioning

confidence: 99%

Theory of thermostatted inhomogeneous granular fluids: A self-consistent density functional description

Marconi

Tarazona

Cecconi

2007

The Journal of Chemical Physics

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The authors present a study of the non equilibrium statistical properties of a one dimensional hard-rod fluid dissipating energy via inelastic collisions and subject to the action of a Gaussian heat bath, simulating an external driving mechanism. They show that the description of the fluid based on the one-particle phase-space reduced distribution function, in principle necessary because of the presence of velocity dependent collisional dissipation, can be contracted to a simpler description in configurational space. Indeed, by means of a multiple-time scale method the authors derive a self-consistent governing equation for the particle density distribution function. This equation is similar to the dynamic density functional equation employed in the study of colloids, but contains additional terms taking into account the inelastic nature of the fluid. Such terms cannot be derived from a Liapunov generating functional and contribute not only to the relaxational properties, but also to the non equilibrium steady state properties. A validation of the theory against molecular dynamics simulations is presented in a series of cases, and good agreement is found.

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The modified Enskog equation

Cited by 350 publications

References 12 publications

Beyond dynamic density functional theory: the role of inertia

Beyond dynamic density functional theory: the role of inertia

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport

Theory of thermostatted inhomogeneous granular fluids: A self-consistent density functional description

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