Velocity profile in the Knudsen layer according to the Boltzmann equation

Lilley, Charles R.; Sader, John E.

doi:10.1098/rspa.2008.0071

Cited by 60 publications

(40 citation statements)

References 36 publications

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“…Lilley and Sader 46,47 , drawing on Boltzmann theoretical solutions for hard-sphere molecules, propose a power-law structure to the inner part of the momentum Knudsen layer, with the consequence that the viscosity of the gas closest to the solid surface is effectively zero. The PEH model of Lockerby and Reese 12 adopts a similar power-law structure, viz.…”

Section: Near-wall Constitutive Scaling ('Phenomenological Extended Hmentioning

confidence: 99%

Simulating Fluid Flows in Micro and Nano Devices: The Challenge of Non-Equilibrium Behaviour

Reese¹,

Zhang²

2009

Jnl of Comp & Theo Nano

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We review some recent developments in the modelling of non-equilibrium (rarefied) gas flows at the micro-and nano-scale, concentrating on two different but promising approaches: extended hydrodynamic models, and lattice Boltzmann methods.Following a brief exposition of the challenges that non-equilibrium poses in micro-and nano-scale gas flows, we turn first to extended hydrodynamics, outlining the effective abandonment of Burnett-type models in favour of high-order regularised moment equations. We show that the latter models, with properly-constituted boundary conditions, can capture critical non-equilibrium flow phenomena quite well. We then review the boundary conditions required if the conventional Navier-Stokes-Fourier (NSF) fluid dynamic model is applied at the micro scale, describing how 2 nd -order Maxwell-type conditions can be used to compensate for some of the non-equilibrium flow behaviour near solid surfaces. While extended hydrodynamics is not yet widely-used for real flow problems because of its inherent complexity, we finish this section with an outline of recent 'phenomenological extended hydrodynamics' (PEH) techniques -essentially the NSF equations scaled to incorporate nonequilibrium behaviour close to solid surfaces -which offer promise as engineering models.Understanding non-equilibrium within the lattice Boltzmann (LB) framework is not as advanced as in the hydrodynamic framework, although LB can borrow some of the techniques which are being developed in the latter -in particular, the near-wall scaling of certain fluid properties that has proven effective in PEH. We describe how, with this modification, the standard 2 nd -order LB method is showing promise in predicting some rarefaction phenomena, indicating that instead of developing higher-order off-lattice LB methods with a large number of discrete velocities, a simplified high-order LB method with near-wall scaling may prove to be just as effective as a simulation tool.

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Section: Near-wall Constitutive Scaling ('Phenomenological Extended Hmentioning

confidence: 99%

Simulating Fluid Flows in Micro and Nano Devices: The Challenge of Non-Equilibrium Behaviour

Reese¹,

Zhang²

2009

Jnl of Comp & Theo Nano

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“…Since Maxwell, many refinements of Eq. (1) have been suggested [5,10]; it is important to note that in this Letter, these refinements will affect our measured values of , but not our conclusions [11].…”

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confidence: 99%

In SituControl of Gas Flow by Modification of Gas-Solid Interactions

Seo

2013

Phys. Rev. Lett.

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The boundary condition for gas flow at the solid-gas interface can be altered by in situ control of the state of a thin film adsorbed to the solid. A monolayer of ocatadecyltrichlorosilane (OTS) reversibly undergoes a meltinglike transition. When the temperature of an OTS-coated particle and plate is moved through the range of OTS ''melting'' temperatures, there is a change in the lubrication force between the particle and plate in 1 atm of nitrogen gas. This change is interpreted in terms of a change in the flow of gas mediated by the slip length and tangential momentum accommodation coefficient (TMAC). There is a minimum in slip length (290 nm) at 18 C, which corresponds to a maximum in TMAC (0.44). The slip length increases to 590 nm at 40 C which corresponds to a TMAC of 0.25. We attribute the decrease in TMAC with increasing temperature to a decrease in roughness of the monolayer on melting, which allows a higher fraction of specular gas reflections, thereby conserving tangential gas momentum. The importance of this work is that it demonstrates the ability to control gas flow simply by altering the interface for fixed geometry and gas properties.

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“…Then the slip lengths on the mica and the graphite surfaces can be calculated with the measured value of the slip length on the glass surface as 110 ± 21 and 234 ± 29 nm, respectively. On the basis of the measured values of the slip length, the accommodation coefficients σ of the three surfaces can be calculated by 13,20 …”

Section: Resultsmentioning

confidence: 99%

Slip Length Measurement of Confined Air Flow on Three Smooth Surfaces

2013

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An experimental measurement of the slip length of air flow close to three different solid surfaces is presented. The substrate was driven by a nanopositioner moving toward an oscillating glass sphere glued to an atomic force microscopy (AFM) cantilever. A large separation distance was used to get more effective data. The slip length value was obtained by analyzing the amplitude and phase data of the cantilever. The measurements show that the slip length does not depend on the oscillation amplitude of the cantilever. Because of the small difference among the slip lengths of the three surfaces, a simplified analysis method was used. The results show that on glass, graphite, and mica surfaces the slip lengths are 98, 234, and 110 nm, respectively.

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Velocity profile in the Knudsen layer according to the Boltzmann equation

Cited by 60 publications

References 36 publications

Simulating Fluid Flows in Micro and Nano Devices: The Challenge of Non-Equilibrium Behaviour

Simulating Fluid Flows in Micro and Nano Devices: The Challenge of Non-Equilibrium Behaviour

In SituControl of Gas Flow by Modification of Gas-Solid Interactions

Slip Length Measurement of Confined Air Flow on Three Smooth Surfaces

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