Particular solutions of the linearized Boltzmann equation for a binary mixture of rigid spheres

Garcia, R. D. M.; Siewert, C. E.

doi:10.1007/s00033-007-6106-y

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…Following our previous work as reported in [9,11], we express our solution (evaluated at the N pairs of discrete ordinates ±μ i ) of (2.47) in the form…”

Section: Solutionsmentioning

confidence: 99%

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Channel Flow of a Binary Mixture of Rigid Spheres Described by the Linearized Boltzmann Equation and Driven by Temperature, Pressure, and Concentration Gradients

Garcia¹,

Siewert²

2007

SIAM J. Appl. Math.

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An analytical version of the discrete-ordinates method (the ADO method) is used with recently established analytical expressions for the rigid-sphere scattering kernels in a study devoted to the flow of a binary gas mixture in a plane channel. In particular, concise and accurate solutions to basic flow problems in a plane channel driven by temperature, pressure, and concentration gradients and described by the linearized Boltzmann equation are established for the case of Maxwell boundary conditions for each of the two species. The velocity, heat-flow, and shear-stress profiles, as well as the mass-and heat-flow rates, are established for each species of particles, and numerical results are reported for two binary mixtures (Ne-Ar and He-Xe). Introduction.While the classical problems of Poiseuille flow and thermalcreep flow in a plane channel in the general field of rarefied gas dynamics [24,3,5,4] have been extensively studied for the case of a single-species gas (see, for example, [1,25,20,22,21,14,17] and the references therein), there are relatively few works (for example, [23, 16, 13]) devoted to these problems for gas mixtures. While [23] and [16] are based on the McCormack kinetic model [15], the work of Kosuge et al. [13] is carried out in terms of the linearized Boltzmann equation (LBE). It can be noted that the paper by Siewert and Valougeorgis [23] reports (in terms of the McCormack model) concise and accurate solutions to the problems of channel flow driven by pressure, temperature, and concentration gradients. While the approach used in [16], also based on the McCormack model, is purely numerical, that work does investigate flow in a two-dimensional channel. Most closely related to this work is [13], where purely numerical methods are used to establish some results for channel-flow problems based on the LBE.In this work, we develop and evaluate concise and accurate solutions for flow problems in a plane-parallel channel driven by pressure, temperature, and concentration gradients. We make use of an analytical discrete-ordinates method (ADO method, [2]), and we use (in the LBE) explicit forms of the rigid-sphere collision kernels for binary gas mixtures [12,6,8]. The developed solutions depend (aside from some normalizations) only on the mass and diameter ratios and the relative equilibrium concentration of the two species of particles. We allow a free choice of the accommodation coefficients for each species at the confining surfaces of the channel. Our

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“…Following our previous work as reported in [9,11], we express our solution (evaluated at the N pairs of discrete ordinates ±μ i ) of (2.47) in the form…”

Section: Solutionsmentioning

confidence: 99%

“…In [8] and [11], we have defined and computed, for selected cases, the generalized Chapman-Enskog and Burnett (vector-valued) functions A (1) (c), A (2) (c), B(c), D(c), and E(c) that appear in (3.7)-(3.9). In addition, the constant ε p is expressed in [11] as…”

Section: Solutionsmentioning

confidence: 99%

Channel Flow of a Binary Mixture of Rigid Spheres Described by the Linearized Boltzmann Equation and Driven by Temperature, Pressure, and Concentration Gradients

Garcia¹,

Siewert²

2007

SIAM J. Appl. Math.

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Comparison of Solution Methods for some Classical Flow Problems in Rarified Gas Dynamics

Njoseh¹,

Musa²

2013

JAMP

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A comparison of two methods of solution to classical flow problem in rarefied gas dynamics was presented. The two methods were chosen to examine the effect of the following transport phenomena (pressure gradient and temperature difference) viz Poiseuille and Thermal creep respectively on the flow of rarefied gas. The governing equations were approximated using BGK model. It was shown that while the Discrete Ordinate Method could consider more values of the accommodation coefficients, the Finite Difference Method can only take accommodation coefficient of one. It was also shown that the flow rate has its minimum in both solution methods at K n = 0.1 in the transition regime and that as the channels get wider, the Thermal creep volume flow rates get smaller.

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Particular solutions of the linearized Boltzmann equation for a binary mixture of rigid spheres

Cited by 2 publications

References 13 publications

Channel Flow of a Binary Mixture of Rigid Spheres Described by the Linearized Boltzmann Equation and Driven by Temperature, Pressure, and Concentration Gradients

Channel Flow of a Binary Mixture of Rigid Spheres Described by the Linearized Boltzmann Equation and Driven by Temperature, Pressure, and Concentration Gradients

Comparison of Solution Methods for some Classical Flow Problems in Rarified Gas Dynamics

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