Kinetic Theory of Sound Propagation in Rarefied Gases

Kahn, Donald R.; Mintzer, David

doi:10.1063/1.1761358

Cited by 45 publications

(10 citation statements)

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“…Predicting sound wave phase speed and damping is a challenge both for kinetic models derived from the Boltzmann dilute gas equation and for continuum fluid hydrodynamics [4]. The few kinetic models [7,10,12] that agree with the experimental data over the entire range of Knudsen number suffer three major criticisms. First, questions often arise about the compatibility of kinetic boundary value problems with experimental measurement [3,4].…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, researchers have argued on the basis of spectral analysis that continuum models based on a finite set of partial differential equations cannot capture this branch of the graph [11]. In any case, interpreting sound waves in terms of pressure waves and momentum exchanges between (only) molecules during collisions should be expected to lead to vanishing damping as intermolecular collisions are no longer the dominant phenomena in the very high Knudsen number regime [7,9].…”

Section: A Prediction Of the Damping Coefficient In The High Frequmentioning

confidence: 99%

“…Regarding the specific problem of predicting sound wave propagation in monatomic gases in the high Knudsen number regime, many of these Boltzmann based approximations fail, as does Navier-Stokes-Fourier [4,5,6,7,8]. While a few have shown some agreement with experiments [9,10], detailed analysis makes any conclusion far from clear-cut [4,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

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A volume-based hydrodynamic approach to sound wave propagation in a monatomic gas

Dadzie

Reese

2010

Physics of Fluids

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A volume-based hydrodynamic approach to sound wave propagation in a monatomic gas Citation for published version: Dadzie, SK & Reese, JM 2010, 'A volume-based hydrodynamic approach to sound wave propagation in a monatomic gas' Physics of Fluids, vol. 22, no General rightsCopyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policyThe University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately and investigate your claim. We investigate sound wave propagation in a monatomic gas using a volume-based hydrodynamic model. In Dadzie et al. ͓Physica A 387, 6079 ͑2008͔͒, a microscopic volume-based kinetic approach was proposed by analyzing molecular spatial distributions; this led to a set of hydrodynamic equations incorporating a mass-density diffusion component. Here we find that these new mass-density diffusive flux and volume terms mean that our hydrodynamic model, uniquely, reproduces sound wave phase speed and damping measurements with excellent agreement over the full range of Knudsen number. In the high Knudsen number ͑high frequency͒ regime, our volume-based model predictions agree with the plane standing waves observed in the experiments, which existing kinetic and continuum models have great difficulty in capturing. In that regime, our results indicate that the "sound waves" presumed in the experiments may be better thought of as "mass-density waves," rather than pressure waves.

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Section: Discussionmentioning

confidence: 99%

Section: A Prediction Of the Damping Coefficient In The High Frequmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A volume-based hydrodynamic approach to sound wave propagation in a monatomic gas

Dadzie

Reese

2010

Physics of Fluids

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“…The zeroth-order distribution function and the orthogonal set of polynomials are generally chosen so that the series converges rapidly, and therefore only a few terms in the series ex, pansion are needed to describe the distribution function. The actual truncation procedure is that all expansion coefficients of order higher than some value are set equal to zero, and the equations for the remaining expansion coefficients (the transport equations) are then solved simultaneously [Grad, 1949[Grad, , 1958Mintzer, 1965].…”

Section: A Useful Technique For Obtaining Approximate Expressions Formentioning

confidence: 99%

Mathematical structure of transport equations for multispecies flows

Schunk¹

1977

Reviews of Geophysics

339

326

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In this review we attempt to present a unified picture of transport in multispecies gas mixtures. To accomplish this task, it is necessary to outline the mathematical structure of the transport equations. Starting from Boltzmann's equation, we derive a general system of transport equations using an approach that is valid for flow situations in which there are large temperature and drift velocity differences between the interacting species. However, this system of equations, which is obtained by taking velocity moments of the Boltzmann equation, does not constitute a closed set, since the equation governing the velocity moment of order r contains the velocity moment of order r + 1. To close the system of transport equations, it is therefore necessary to adopt an approximate expression for the species velocity distribution function. For near‐equilibrium flows, various levels of approximation are considered, including the 5‐, 8‐, 10‐, 13‐, and 20‐moment approximations. The procedure for obtaining closed sets of transport equations for far‐from‐equilibrium flows is also discussed. When the transport equations are ordered with respect to the collisional mean free path, the result is the Euler, Navier‐Stokes, or extended Navier‐Stokes equations depending upon whether terms proportional to the zeroth, first, or second power of the mean free path are retained. For a collisionless plasma the analogous expansion using the Larmor radius yields the Chew‐Goldberger‐Low (CGL) equations to zeroth order and the extended CGL equations to first order.

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“…These sound propagation measurements were made at a temperature of 300 K in a 11 MHz double-crystal interferometer for different values of the gas pressure. The sound wave absorption factor was obtained by a determination of the logarithmic decrement in the sound level of the signal as a function of the traveled sound path, whereas the reciprocal speed ratio was determined by measuring the phase difference between a direct signal from the driving oscillator and the signal received at the receiver ditto as a function of the sound path [6,20]. For the numerical calculations we used the following material parameters:…”

Section: Comparison With Experimentsmentioning

confidence: 99%