A model of the wall boundary condition in kinetic theory.

Epstein, Melvin

doi:10.2514/3.4307

Cited by 78 publications

(31 citation statements)

References 6 publications

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“…The accommodation coefficient approaches Θ 1 at the high-energy asymptote. This simple expression gives good agreement of the thermal accommodation coefficient (that relates the temperature jump to the heat passing through the wall) between the theory and experimental data, for various kinds of gases interacting with tungsten, over a wide range of temperature (Epstein 1967). In addition to the Maxwell model, the BC developed by Cercignani & Lampis (1971) has also been widely used.…”

Section: Gas Kinetic Boundary Conditionsmentioning

confidence: 98%

“…In the Maxwell model, the TMAC is independent of the velocities (or energies) of the impinging molecules, which contradicts both theoretical and experimental investigations. To remove the deficiency in the Maxwell model, Epstein (1967) proposed the generalized scattering kernel 9) where the probability of a gas molecules being reflected diffusely is given by Θ(v), which is a function of the molecular velocity. For Θ(v) = α M , the Epstein model (2.9) reduces to the Maxwell model (2.8).…”

Section: Gas Kinetic Boundary Conditionsmentioning

confidence: 99%

“…Later, Klinc & Kuěčer (1972) introduced an isotropic scattering to account for the influence of the roughness of the wall surface. Recently, Struchtrup (2013) combined the models of Epstein (1967) and Klinc & Kuěčer (1972), which has more flexibility to fit the experimental data. The gas-surface interaction plays an important role in internal rarefied gas flows, especially in gas micro-electro-mechanical systems with large surface area to volume ratios; sometimes it is more important to get the BC correct than solving the Boltzmann equation with the realistic intermolecular potential accurately.…”

Section: Introductionmentioning

confidence: 99%

“…The Maxwell model employs only one parameter, the tangential momentum accommodation coefficient (TMAC), which describes the proportion of diffusely reflected molecules at the wall, while the remaining gas molecules are assumed to be specularly reflected. This model has been improved by Epstein (1967) by introducing a molecular velocity-dependent TMAC. Unfortunately, the Epstein model is rarely used by (or even known to) the community of rarefied gas dynamics, although it has successfully described the temperature-dependence of the thermal accommodation coefficient for various gases interacting with tungsten.…”

Section: Introductionmentioning

confidence: 99%

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Assessment and development of the gas kinetic boundary condition for the Boltzmann equation

Struchtrup

2017

J. Fluid Mech.

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Gas-surface interactions play important roles in internal rarefied gas flows, especially in micro-electro-mechanical systems with large surface area to volume ratios. Although great progresses have been made to solve the Boltzmann equation, the gas kinetic bound- ary condition (BC) has not been well studied. Here we assess the accuracy the Maxwell, Epstein, and Cercignani-Lampis BCs, by comparing numerical results of the Boltzmann equation for the Lennard-Jones potential to experimental data on Poiseuille and thermal transpiration flows. The four experiments considered are: Ewart et al. [J. Fluid Mech. 584, 337-356 (2007)], Rojas-C ́ardenas et al. [Phys. Fluids, 25, 072002 (2013)], and Yam- aguchi et al. [J. Fluid Mech. 744, 169-182 (2014); 795, 690-707 (2016)], where the mass flow rates in Poiseuille and thermal transpiration flows are measured. This requires the BC has the ability to tune the effective viscous and thermal slip coefficients to match the experimental data. Among the three BCs, the Epstein BC has more flexibility to adjust the two slip coefficients, and hence in most of the time it gives good agreement with the experimental measurement. However, like the Maxwell BC, the viscous slip coefficient in the Epstein BC cannot be smaller than unity but the Cercignani-Lampis BC can. Therefore, we propose to combine the Epstein and Cercignani-Lampis BCs to describe gas-surface interaction. Although the new BC contains six free parameters, our approxi- mate analytical expressions for the viscous and thermal slip coefficients provide a useful guidance to choose these parameters

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Section: Gas Kinetic Boundary Conditionsmentioning

confidence: 98%

Section: Gas Kinetic Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Assessment and development of the gas kinetic boundary condition for the Boltzmann equation

Struchtrup

2017

J. Fluid Mech.

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“…The existing phenomenological structures, such as scattering kernels proposed by Maxwell [5], Cercignani-Lampis [6] and Epstein [7], have a mathematical basis and are artificial to a certain extent. Therefore, each given model has some limitations caused by the complexity of description of the processes occurring at the phase interface.…”

Section: Introductionmentioning

confidence: 99%

Simulation of the influence of surface chemical composition on internal gas flow at large Knudsen numbers

Ukhov

Borisov

Porodnov

2013

International Journal of Heat and Mass Transfer

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a b s t r a c tOn the basis of the developed model, an attempt to describe a rarefied gas flow in the cylindrical channel, whose surface chemical composition conforms with the real experimental conditions, has been made. During the modeling two cases are considered: the atomically clean silver channel surface and the surface fully covered with the adsorbate, which is simulated by oxygen according to the data of the Augerspectroscopic analysis. The gas-surface interaction process is based on the molecular dynamic principle. Thermal vibrations of the surface atoms are also considered. The obtained results of calculation are compared with experimental data.Crown

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The Monte Carlo and Molecular Dynamics Simulation of Gas-Surface Interaction

Borisov¹,

Sazhin²,

Gerasimova³

2005

Lecture Notes in Computer Science

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A testing procedure and a program product for modeling gas-surface scattering process have been developed. Using the developed product the numerical simulation of the thermal transpiration phenomenon at free molecular conditions of the gas flow in channels with the use of different scattering kernels has been carried out. The surface structure influence on energy and momentum exchange in a gas-surface system has been studied by the use of Molecular Dynamics method.

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A model of the wall boundary condition in kinetic theory.

Cited by 78 publications

References 6 publications

Assessment and development of the gas kinetic boundary condition for the Boltzmann equation

Assessment and development of the gas kinetic boundary condition for the Boltzmann equation

Simulation of the influence of surface chemical composition on internal gas flow at large Knudsen numbers

The Monte Carlo and Molecular Dynamics Simulation of Gas-Surface Interaction

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