Relaxation Effects in the Transport Properties of a Gas of Rough Spheres

Monchick, L.; Yun, K. S.; Mason, Edward A.

doi:10.1063/1.1733846

Cited by 23 publications

(4 citation statements)

References 4 publications

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“…(1) wherein the relaxation time T is described in terms of collision dynamics through the expression 23 ,24 (10) The quantity <t.f2), which reflects the total energy change in a bimolecular collision, is an integral expression which takes into account the dynamics of an encounter; a detailed description is adequately presented elsewhere. 23 A theoretical evaluation of T can therefore be made either through the use of Eq. (10), by computing the collision integral <t.f2), or through the use of Eq.…”

Section: Discussionmentioning

confidence: 99%

Temperature Dependence of Rotational Collision Numbers from Thermal Transpiration

Annis

Malinauskas

1971

The Journal of Chemical Physics

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The temperature dependence of the rotational collision numbers for O2, N2, CO, and CO2 was investigated in the range 47S-676°K by the thermal transpiration technique with the use of a novel apparatus design. In all cases the collision number was found to increase with temperature. For O2 and N2, where some comparison with theory is possible, the experimental rate of increase with temperature was found to be faster than the predicted behavior. The results for CO and CO2 are in general agreement with other transpiration measurements and with acoustic absorption results which were obtained at lower temperatures.

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Section: Discussionmentioning

confidence: 99%

Temperature Dependence of Rotational Collision Numbers from Thermal Transpiration

Annis

Malinauskas

1971

The Journal of Chemical Physics

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“…One notable result from these studies is that the neglect of anisotropy in the intermolecular potential has only a small effect on the computed diffusion coefficients. Monchick et al 20 provided formal arguments that the effects of anisotropy and inelasticity on transport properties such as diffusion should be expected to be small in general, but the error associated with the neglect of these details has not been quantified for systems with more than a few atoms.…”

Section: Introductionmentioning

confidence: 99%

First-principles binary diffusion coefficients for H, H2, and four normal alkanes + N2

et al. 2014

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Collision integrals related to binary (dilute gas) diffusion are calculated classically for six species colliding with N 2 . The most detailed calculations make no assumptions regarding the complexity of the potential energy surface, and the resulting classical collision integrals are in excellent agreement with previous semiclassical results for H + N 2 and H 2 + N 2 and with recent experimental results for C n H 2n+2 + N 2 , n = 2-4. The detailed classical results are used to test the accuracy of three simplifying assumptions typically made when calculating collision integrals: (1) approximating the intermolecular potential as isotropic, (2) neglecting the internal structure of the colliders (i.e., neglecting inelasticity), and (3) employing unphysical R −12 repulsive interactions. The effect of anisotropy is found to be negligible for H + N 2 and H 2 + N 2 (in agreement with previous quantum mechanical and semiclassical results for systems involving atomic and diatomic species) but is more significant for larger species at low temperatures. For example, the neglect of anisotropy decreases the diffusion coefficient for butane + N 2 by 15% at 300 K. The neglect of inelasticity, in contrast, introduces only very small errors. Approximating the repulsive wall as an unphysical R −12 interaction is a significant source of error at all temperatures for the weakly interacting systems H + N 2 and H 2 + N 2 , with errors as large as 40%. For the normal alkanes in N 2 , which feature stronger interactions, the 12/6 Lennard-Jones approximation is found to be accurate, particularly at temperatures above ∼700 K where it predicts the full-dimensional result to within 5% (although with somewhat different temperature dependence). Overall, the typical practical approach of assuming isotropic 12/6 Lennard-Jones interactions is confirmed to be suitable for combustion applications except for weakly interacting systems, such as H + N 2 . For these systems, anisotropy and inelasticity can safely be neglected but a more detailed description of the repulsive wall is required for quantitative predictions. A straightforward approach for calculating effective isotropic potentials with realistic repulsive walls is described. An analytic expression for the calculated diffusion coefficient for H + N 2 is presented and is estimated to have a 2-sigma error bar of only 0.7%. © 2014 AIP Publishing LLC. [http://dx.

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“…First attempts to deal with the Wang Chang and Uhlenbeck equation were made using the Chapman-Enskog method. Monchick et al [33][34][35] and Morse et al 36,37 obtained the relations for shear and bulk viscosity and heat conductivity as functions of the relaxation times. Recently, Kustova, Nagnibeda, and co-workers 38 studied the strong vibrational non-equilibrium in reacting mixtures of polyatomic gases for different cases with regards to the characteristic time of the microscopic processes.…”

Section: Kinetic Modelmentioning

confidence: 99%

Capturing non-equilibrium phenomena in rarefied polyatomic gases: A high-order macroscopic model

Rahimi

Struchtrup

2014

Physics of Fluids

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A high-order macroscopic model for the accurate description of rarefied polyatomic gas flows is introduced based on a kinetic equation of Bhatnagar-Gross-Krook (BGK)type, where the different energy exchange processes are accounted for by two collision terms. The order of magnitude method is applied to the primary moment equations to acquire the optimized moment definitions and the final scaled set of Grad's 36 moment equations for polyatomic gases. The two Knudsen numbers of the system are used for model reduction in terms of their powers, which yields a wide range of different reduced systems, a total of 13 different orders. These include, at lower order, a modification of the Navier-Stokes-Fourier (NSF) equations which shows considerable extended range of validity in comparison to the classical NSF equations. The highest order of accuracy considered gives a set of 18 regularized partial differential equations (PDEs) (R18). Attenuation and speed of linear waves are studied as the first application of the many sets of equations. For frequencies where the internal degrees of freedom are effectively frozen, the equations reproduce the behavior of monatomic gases. C 2014 AIP Publishing LLC. [http://dx.

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Relaxation Effects in the Transport Properties of a Gas of Rough Spheres

Cited by 23 publications

References 4 publications

Temperature Dependence of Rotational Collision Numbers from Thermal Transpiration

Temperature Dependence of Rotational Collision Numbers from Thermal Transpiration

First-principles binary diffusion coefficients for H, H2, and four normal alkanes + N2

Capturing non-equilibrium phenomena in rarefied polyatomic gases: A high-order macroscopic model

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