Kinetic Model for Binary Gas Mixtures

Hamel, B.B.

doi:10.1063/1.1761239

Cited by 229 publications

(114 citation statements)

References 4 publications

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“…Exactly the same result is obtained for other BGK-type models [8] with a proper choice of parameters, because these models give the same transport coefficients and the same linearized equation as the GSB model. The extension to the Boltzmann equation for Maxwell's molecules is straightforward.…”

Section: Discussionsupporting

confidence: 64%

Half-space problem of weak evaporation and condensation of a binary mixture of vapors

Takata¹

2005

AIP Conference Proceedings

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Abstract. Half-space problem of weak evaporation and condensation of a binary mixture of vapors is investigated on the basis of the BGK-type Boltzmann model. By a systematic asymptotic analysis, it is shown that the steady evaporation and condensation takes place only if the parameters that characterize the state of the condensed phase and that of the vapors at a far distance satisfy one relation for the condensation case and three relations for the evaporation case. As an application, the resulting relations are used as the boundary conditions of the Euler system in the study of the two-surface problem of a vapor mixture for small Knudsen numbers. This system has two branches of solutions, which causes two different solutions for the same physical situation in the continuum limit. This result is discussed in connection with the ghost effect.

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Section: Discussionsupporting

confidence: 64%

Half-space problem of weak evaporation and condensation of a binary mixture of vapors

Takata¹

2005

AIP Conference Proceedings

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“…Therefore, evaporation or condensation of gas A (vapor) may take place on the surface of the particle. We investigate the steady behavior of the vapor (gas A) and the noncondensable gas (gas B) around the particle and obtain the force acting on the particle (diffusiophoretic force) for a wide range of the Knudsen (i) The behavior of the mixture is described by the model Boltzmann equation proposed by Hamel [9] or that by Garzó et al [10]. [Once the linearization around an equilibrium state at rest is made, these two models give the same equation.…”

Section: Problem and Assumptionsmentioning

confidence: 99%

“…In this situation, evaporation and condensation of the vapor taking place on the surface of the particle may have an important effect on the flows of both components around the particle. We will analyze such flows for a wide range of the Knudsen number numerically on the basis of the linearized version of a model Boltzmann equation [9,10] and obtain the force acting on the particle (diffusiophoretic force) accurately.…”

Section: Introductionmentioning

confidence: 99%

Diffusiophoresis of a Spherical Volatile Particle

Aoki¹,

Hatano²,

Kosuge³

et al. 2005

AIP Conference Proceedings

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Abstract.A spherical condensed phase (volatile particle) is placed in an infinite expanse of a binary mixture consisting of the vapor of the condensed phase and another noncondensable gas. The mixture is assumed to be at rest with uniform pressure and temperature at infinity. However, the vapor and the noncondensable gas have small uniform density (or concentration) gradients of the same magnitude but in the opposite direction. The flows of both components around the particle are analyzed numerically by a finite-difference method on the basis of a model Boltzmann equation for gas mixtures, and the force acting on the particle (diffusiophoretic force) is obtained accurately for a wide range of the Knudsen number.

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“…The binary Couette flow problem has been solved in Refs. [16][17][18], by using the Hamel model 19 and very recently by applying the McCormack model. 20 The micro cavity problem has been studied only for a single gas, 2 21 22 while for a binary gas mixture, as far as the authors are aware of, there are no available results in the literature.…”

Section: Introductionmentioning

confidence: 99%

Shear Driven Micro-Flows of Gaseous Mixtures

Naris¹,

Valougeorgis

2006

Sen Lett

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A mesoscale kinetic-type approach is proposed to solve shear driven micro flows of binary gas mixtures in MEMS. The coupled linear integro-differential equations, which formally describe the flow, are solved using the discrete velocity method. The complicated collision integral term is approximated by the McCormack model. The proposed approach is applied in one and two dimensions, solving the Couette and the driven cavity problems respectively, for two binary gas mixtures (Ne-Ar and He-Xe). Numerical results are presented for a wide range of the rarefaction and for various molar concentrations. It is demonstrated that the formulation is very efficient and can be implemented as an alternative to classical approaches, such as Navier Stokes solvers with slip boundary conditions.

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Kinetic Model for Binary Gas Mixtures

Cited by 229 publications

References 4 publications

Half-space problem of weak evaporation and condensation of a binary mixture of vapors

Half-space problem of weak evaporation and condensation of a binary mixture of vapors

Diffusiophoresis of a Spherical Volatile Particle

Shear Driven Micro-Flows of Gaseous Mixtures

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