Flow of Rarefied Gases

Schaaf, S. A.; Chambre, Paul A.

doi:10.1515/9781400885800

Cited by 120 publications

(27 citation statements)

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“…The velocity of the incident molecule is obtained by collision with a fluid molecule located at a distance away from the wall. Using the mean free path method [31,33], the incident velocity can be calculated by performing a spatial discretization of the fluid velocity about the wall. Here, Maxwell and other researchers make an implicit assumption that the fluid velocity can only vary in the wall normal direction.…”

Section: The Generalized Velocity Boundary Conditionmentioning

confidence: 99%

Unified slip boundary condition for fluid flows

Thalakkottor

Mohseni

2016

Phys. Rev. E

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Determining the correct matching boundary condition is fundamental to our understanding of several everyday problems. Despite over a century of scientific work, existing velocity boundary conditions are unable to consistently explain and capture the complete physics associated with certain common but complex problems such as moving contact lines and corner flows. The widely used Maxwell and Navier slip boundary conditions make an implicit assumption that velocity varies only in the wall normal direction. This makes their boundary condition inapplicable in the vicinity of contact lines and corner points where, velocity gradient exists both in the wall normal and wall tangential directions. In this paper, by identifying this implicit assumption we are able to extend Maxwell's slip model. Here, we present a generalized velocity boundary condition that shows that slip velocity is a function of not only the shear rate but also the linear strain rate. In addition, we present a universal relation for slip length which shows that, for a general flow, slip length is a function of the principal strain rate. The universal relation for slip length along with the generalized velocity boundary condition provides a unified slip boundary condition to model a wide range of steady Newtonian fluid flows. We validate the unified slip boundary for simple Newtonian liquids, by using molecular dynamics simulations and studying both, the moving contact line and corner flow problems.

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Section: The Generalized Velocity Boundary Conditionmentioning

confidence: 99%

Unified slip boundary condition for fluid flows

Thalakkottor

Mohseni

2016

Phys. Rev. E

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“…42 If K n is greater than 1, diffusion of vapor is mainly due to molecule/wall interactions and therefore is in the Knudsen diffusion regime. 43 For water vapor circulation inside the pores whose average radius is 2 nm, K n »1. The calculated Knudsen diffusion coefficient 42,44,45 of the water vapor inside the altered layer is equal to 7.8 × 10 -7 m 2 s -1 (Eq.…”

Section: Resultsmentioning

confidence: 99%

Long-term weathering rate of stained-glass windows using H and O isotopes

et al. 2018

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The understanding of glass alteration is a biogeochemical, industrial, societal (radioactive waste confinement), and cultural heritage issue. Studies have been mainly performed in aqueous conditions. However, glass reactivity under hydraulically unsaturated conditions may be more important than previously recognized. In this context, we evaluate here the role of the alteration layer formed on medieval stained-glass windows on the ongoing alteration in unsaturated conditions. H 2 O adsorption isotherms were measured to study the relation between the vapor sorption and the relative humidity inside the alteration layer. From it, the average pore radius was calculated, yielding a water vapor diffusion coefficient of 7.8 × 10 -7 m² s -1 inside the pore network. Experiments using doped water vapor (D 2 18 O) confirm the vapor transport up to the alteration front via fractures and pore network. They also demonstrate that the alteration mainly progresses via an interdiffusion mechanism. The calculated interdiffusion coefficients at 20°C are 3.6 × 10 -20 m 2 s -1 at 70% RH and 4.9 × 10 -20 m 2 s -1 at 90% RH, which is similar to the values measured on model stained-glass samples altered in short durations (1-4 years). Therefore, this study highlights that, given its morphology, the alteration layer is not protective against vapor transport and interdiffusion.

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“…These transmissibility multipliers were used to ''mimic'' slip flow in ECLIPSE and therefore verify the correct implementation of our code with slip flow. To enable ECLIPSE to Table 1 Flow regimes classified by Chambre and Schaaf (1961). ''mimic'' slip flow, we simplified the multicomponent problem to a single component problem with 100% methane.…”

Section: Model Validationmentioning

confidence: 99%

Effect of distinguishing apparent permeability for different components on BHP and produced gas composition in tight- and shale-gas reservoir

Zhang

2015

Journal of Unconventional Oil and Gas Resources

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Flow of Rarefied Gases

Cited by 120 publications

References 0 publications

Unified slip boundary condition for fluid flows

Unified slip boundary condition for fluid flows

Long-term weathering rate of stained-glass windows using H and O isotopes

Effect of distinguishing apparent permeability for different components on BHP and produced gas composition in tight- and shale-gas reservoir

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