The Enskog theory for multicomponent mixtures. I. Linear transport theory

Haro, M. López de; Cohen, E. G. D.; Kincaid, J. M.

doi:10.1063/1.444985

Cited by 121 publications

(91 citation statements)

References 27 publications

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“…The explicit construction of solutions to those equations by the CE expansion to first order in the gradients was given more that twenty years ago in Ref. [49]. These solutions, together with the macroscopic balance equations obtained from the kinetic equations, provide a self-consistent derivation of Navier-Stokes hydrodynamics for mixtures and the identification of expressions for all the Navier-Stokes parameters (equations of state, transport coefficients).…”

Section: (420)-(422) To Zeroth Order In the Gradients One Gets Thmentioning

confidence: 99%

“…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%

“…To be specific, and for comparison with Ref. [49] it is assumed here to be of first order in the gradients.…”

Section: Appendix B: Balance Equations and Fluxesmentioning

confidence: 99%

“…In the elastic limit, α ij → 1, these equations become the Enskog theory for mixtures of dense molecular gases studied in Ref. [49].…”

Section: Revised Enskog Kinetic Theorymentioning

confidence: 99%

“…[49] to inelastic hard sphere granular mixtures. Modification of the collisions to account for inelasticity leads to significant differences from ordinary fluids in detail, but the formal structure of the CE expansion remains the same.…”

Section: (420)-(422) To Zeroth Order In the Gradients One Gets Thmentioning

confidence: 99%

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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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Section: (420)-(422) To Zeroth Order In the Gradients One Gets Thmentioning

confidence: 99%

Section: Overview Of Derivationmentioning

confidence: 99%

“…To be specific, and for comparison with Ref. [49] it is assumed here to be of first order in the gradients.…”

Section: Appendix B: Balance Equations and Fluxesmentioning

confidence: 99%

“…In the elastic limit, α ij → 1, these equations become the Enskog theory for mixtures of dense molecular gases studied in Ref. [49].…”

Section: Revised Enskog Kinetic Theorymentioning

confidence: 99%

Section: (420)-(422) To Zeroth Order In the Gradients One Gets Thmentioning

confidence: 99%

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

2007

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CFD modeling of gas‐fluidized beds with a bimodal particle mixture

Wachem¹,

Schouten²,

Bleek³

et al. 2001

AIChE Journal

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Calculation of High Pressure Counterflow Diffusion Flames up to 3000 bar

Saur

Behrendt

Franck

1993

Ber Bunsenges Phys Chem

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The combustion of methane, hydrogen and carbon monoxide at atmospheric pressure in one‐dimensional diffusion flames was quantitatively described with computer simulations by Warnatz et al. and others. The present paper extends the one‐dimensional flame description from dilute gas regions to pressures of 3000 bar, where particles are mostly in contact with each other. A realistic equation of state with repulsion and attraction terms is used. Transport phenomena are modelled with a modified Enskog equation. A special problem arises from the stiffness of the systems of differential equations. Integration uses methods developed by Deuflhard et al. Flames of methane and hydrogen burning in mixtures with argon or supercritical water with injected oxygen are simulated and discussed. Profiles of temperature and other functions at high pressures through the reaction coordinate are shown. The width of the reaction zone is narrowed to less than 5% if pressure is increased from 1 to 1000 bar. Maximum temperatures of 3500 K are attained with CH4/Ar‐O2‐flames. Maximum flame temperatures decrease with pressure above about 500 bar. Several concentration profiles including those of H‐ and O‐radicals and H2O2 are presented. Comparison with recently measured high pressure flame temperatures is made.

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The Enskog theory for multicomponent mixtures. I. Linear transport theory

Cited by 121 publications

References 27 publications

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

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

CFD modeling of gas‐fluidized beds with a bimodal particle mixture

Calculation of High Pressure Counterflow Diffusion Flames up to 3000 bar

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