H. Flow of Rarefied Gases

Schaaf, S. A.; Chambre, P.L.

doi:10.1515/9781400877539-010

Cited by 162 publications

(88 citation statements)

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“…In the case of perfect slip, the drag force is due exclusively to the form drag due to the pressure. In rarified gases, the slip coefficient, β p , and slip length, λ p , can be rigorously related to the mean free path, λ f , by the Maxwell relation λ f /λ = β p K n = σ/(2 − σ ), where K n ≡ λ f /a is the Knudsen number, and σ is the tangential momentum accommodation coefficient (TMAC) expressing the fraction of molecules that undergo diffusive instead of specular reflection (e.g., [7,8]). The limit σ = 2 yields the no-slip boundary condition, β p → ∞, whereas the limit σ = 0 yields the perfect-slip boundary condition, β p → 0.…”

Section: Linear Flow Past a Spherical Particle In An Infinite Domainmentioning

confidence: 99%

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Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall

Luo

Pozrikidis

2007

J Eng Math

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The motion of a spherical particle in infinite linear flow and near a plane wall, subject to the slip boundary condition on both the particle surface and the wall, is studied in the limit of zero Reynolds number. In the case of infinite flow, an exact solution is derived using the singularity representation, and analytical expressions for the force, torque, and stresslet are derived in terms of slip coefficients generalizing the Stokes-Basset-Einstein law. The slip velocity reduces the drag force, torque, and the effective viscosity of a dilute suspension. In the case of wall-bounded flow, advantage is taken of the axial symmetry of the boundaries of the flow with respect to the axis that is normal to the wall and passes through the particle center to formulate the problem in terms of a system of one-dimensional integral equations for the first sine and cosine Fourier coefficients of the unknown traction and velocity along the boundary contour in a meridional plane. Numerical solutions furnish accurate predictions for (a) the force and torque exerted on a particle translating parallel to the wall in a quiescent fluid, (b) the force and torque exerted on a particle rotating about an axis that is parallel to the wall in a quiescent fluid, and (c) the translational and angular velocities of a freely suspended particle in simple shear flow parallel to the wall. For certain combinations of the wall and particle slip coefficients, a particle moving under the influence of a tangential force translates parallel to the wall without rotation, and a particle moving under the influence of a tangential torque rotates about an axis that is parallel to the wall without translation. For a particle convected in simple shear flow, minimum translational velocity is observed for no-slip surfaces. However, allowing for slip may either increase or decrease the particle angular velocity, and the dependence on the wall and particle slip coefficients is not necessarily monotonic.

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Section: Linear Flow Past a Spherical Particle In An Infinite Domainmentioning

confidence: 99%

“…The slip boundary condition was first proposed by Navier [5] and further discussed by Maxwell [6] in the context of gas flow [7,8]. Basset [9] derived an analytical solution for the flow due to a solid sphere translating in infinite fluid at low Reynolds numbers, and generalized the Stokes law for the drag force.…”

Section: Introductionmentioning

confidence: 99%

Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall

Luo

Pozrikidis

2007

J Eng Math

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“…An expression for the Knudsen number in terms of the Mach number and Reynolds number is provided by 1.26Öc(M Du /Re d ) (Schaaf and Chambre 1958), where c is the ratio of specific heats, taken as c = 1.4 for air. The Mach number M Du is based upon Du, the maximum particle slip velocity, which occurs downstream of the shock wave.…”

Section: Particle Response Assessmentmentioning

confidence: 99%

Particle image velocimetry measurements of a shock wave/turbulent boundary layer interaction

2007

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Particle image velocimetry is used to investigate the interaction between an incident shock wave and a turbulent boundary layer at Mach 2.1. A particle response assessment establishes the fidelity of the tracer particles.The undisturbed boundary layer is characterized in detail. The mean velocity field of the interaction shows the incident and reflected shock wave pattern, as well as the boundary layer distortion. Significant reversed flow is measured instantaneously, although, on average no reversed flow is observed. The interaction instantaneously exhibits a multi-layered structure, namely, a high-velocity outer region and a low-velocity inner region. Flow turbulence shows the highest intensity in the region beneath the impingement of the incident shock wave. The turbulent fluctuations are found to be highly anisotropic, with the streamwise component dominating. A distinct streamwiseoriented region of relatively large kinematic Reynolds shear stress magnitude appears within the lower half of the redeveloping boundary layer. Boundary layer recovery towards initial equilibrium conditions appears to be a gradual process.

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“…However, it has been suggested by Gad-el-Hak [4] that rarefaction effects are discernible at Knudsen numbers as low as Kn = 0.001. Following ideas proposed by Maxwell, the Navier-Stokes equations can be extended into the slip-flow regime provided the Knudsen number, Kn, is less than 0.1 (Schaaf and Chambré [5]). However, improvements in micro-fabrication techniques are enabling systems to be constructed with sub-micron feature dimensions.…”

Section: Knmentioning

confidence: 99%

A Critical Review Of The Drag Force On A Sphere In The Transition Flow Regime

Bailey¹,

Barber

Emerson

et al. 2005

AIP Conference Proceedings

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Abstract. Improvements in micro-fabrication techniques are enabling Micro-Electro-Mechanical-Systems to be constructed with sub-micron feature sizes. At this scale, even at standard atmospheric conditions, the flow is in the transition regime. This paper considers the range 0.1 < Kn < 1, where non-equilibrium effects can be appreciable, and specifically illustrates problems involving non-planar surfaces by analyzing the drag force for low speed, incompressible flow past an unconfined microsphere. A critical comparison is made between experimental data, analytical solutions derived from kinetic theory, Grad's thirteen-moment equations, and the Navier-Stokes equations with first-and secondorder treatment of the slip boundary. The results, even for this simple geometry, highlight major problems in predicting the drag in the transition flow regime for non-kinetic schemes.

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H. Flow of Rarefied Gases

Cited by 162 publications

References 0 publications

Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall

Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall

Particle image velocimetry measurements of a shock wave/turbulent boundary layer interaction

A Critical Review Of The Drag Force On A Sphere In The Transition Flow Regime

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