Transport Properties of Polyatomic Fluids, a Dilute Gas of Perfectly Rough Spheres

Condiff, Duane W.; Lu, Wei‐Kao; Dahler, John S.

doi:10.1063/1.1695749

Cited by 95 publications

(19 citation statements)

References 9 publications

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“…where g5 < 1 and is the local equilibrium distribution function. The presentf'O) differs slightly from the equilibrium distribution functions used for the case of perfectly elastic and perfectly rough spheres by Chapman & Cowling (1970), Condiff et al (1965 and Theodosopulu & Dahler (1974a, b). In those cases, energy is conserved and there is equipartition of the mean translational and rotational fluctuation kinetic energies.…”

Section: Moment Methodsmentioning

confidence: 68%

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Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres

1991

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A general set of conservation equations and constitutive integrals for the dynamic properties of the rapid flow of a granular material consisting of slightly inelastic and slightly rough spherical particles is derived by following an approach used in the kinetic theory of dense gases. By taking moments of the translational and rotational particle velocities in the general transport moment equation and making the Enskog approximation, the singlet velocity distribution function is determined. As a result, the constitutive relations and coefficients such as stresses, energy fluxes, rates of translational and rotational energy interchanges, shear viscosity, spin viscosity, bulk viscosity and ‘thermal’ conductivities are obtained. The present theory incorporates the kinetic as well as the collisional contributions for stresses and energy fluxes. Thus, it is appropriate for dilute as well as dense concentrations of solids. For the case of simple shear flow, there is favourable agreement between the theoretical predictions of stresses and both the experimental measurements and the results from computer simulations.

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Section: Moment Methodsmentioning

confidence: 68%

“…For the case of uniform solid sphere treated here, K = Q. where n is the local number density of the particles and f ( l ) ( r , c, w ; t) is the usual single-particle velocity distribution function. The rate of change of ( y i ) can be expressed as (Condiff, Lu & Dahler 1965;Lun et al 1984;Lun & Savage 1987)…”

mentioning

confidence: 99%

Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres

1991

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“…2,[26][27][28][29] The most complete solution, at the level of the Chapman-Enskog approximation, was given by Condiff, Lu, and Dahler 2 who compared the contributions to transport coefficients from different terms in a basis of Sonine polynomials. At the lowest order of approximation, Pidduck's formulae for the transport coefficients are obtained, namely…”

Section: Transport Coefficientsmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] Given such importance, it is valuable to have a set of well-converged benchmark calculations against which comparisons with theory can be made. In fact, Condiff, Lu, and Dahler 2 examined in some detail the effect of different basis sets on the values of transport coefficients using the Chapman-Enskog approximation to the Boltzmann equation.…”

Section: Introductionmentioning

confidence: 99%

Transport properties of the rough hard sphere fluid

Kravchenko

Thachuk

2012

The Journal of Chemical Physics

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Results are presented of a systematic study of the transport properties of the rough hard sphere fluid. The rough hard sphere fluid is a simple model consisting of spherical particles that exchange linear and angular momenta, and energy upon collision. This allows a study of the sole effect of particle rotation upon fluid properties. Molecular dynamics simulations have been used to conduct extensive benchmark calculations of self-diffusion, shear and bulk viscosity, and thermal conductivity coefficients. As well, the validity of several kinetic theory equations have been examined at various levels of approximation as a function of density and translational-rotational coupling. In particular, expressions from Enskog theory using different numbers of basis sets in the representation of the distribution function were tested. Generally Enskog theory performs well at low density but deviates at larger densities, as expected. The dependence of these expressions upon translational-rotational coupling was also examined. Interestingly, even at low densities, the agreement with simulation results was sometimes not even qualitatively correct. Compared with smooth hard sphere behaviour, the transport coefficients can change significantly due to translational-rotational coupling and this effect becomes stronger the greater the coupling. Overall, the rough hard sphere fluid provides an excellent model for understanding the effects of translational-rotational coupling upon transport coefficients.

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“…Since A is a vector, it can be expressed as a sum of projections along the three polar vectors V, (V · ω)ω, and V × ω [57], namely…”

Section: Navier-stokes-fourier Transport Coefficients a Exact Formentioning

confidence: 99%

Transport coefficients of a granular gas of inelastic rough hard spheres

Kremer¹,

Santos

Garzó

2014

Phys. Rev. E

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The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution and hence the translational and rotational degrees of freedom are coupled. A normal solution to the Boltzmann equation is obtained by means of the Chapman-Enskog method for states near the homogeneous cooling state. The analysis is carried out to first order in the spatial gradients of the number density, the flow velocity, and the granular temperature. The constitutive equations for the momentum and heat fluxes and for the cooling rate are derived, and the associated transport coefficients are expressed in terms of the solutions of linear integral equations. For practical purposes, a first Sonine approximation is used to obtain explicit expressions of the transport coefficients as nonlinear functions of both coefficients of restitution and the moment of inertia. Known results for purely smooth inelastic spheres and perfectly elastic and rough spheres are recovered in the appropriate limits.

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Transport Properties of Polyatomic Fluids, a Dilute Gas of Perfectly Rough Spheres

Cited by 95 publications

References 9 publications

Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres

Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres

Transport properties of the rough hard sphere fluid

Transport coefficients of a granular gas of inelastic rough hard spheres

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