Asymptotic Behavior for Rayleigh Problem Based on Kinetic Theory

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We investigate the dynamics of the gas bounded by an infinite flat plate which is initially in equilibrium and set at some instant impulsively into uniform motion in its own plane. We use the Boltzmann equation to describe intermolecular collisions and assume the diffuse reflection to describe the interaction of the gas with the boundary. The Mach number of the plate is assumed to be small so that we can linearize the Boltzmann equation as well as the boundary condition. We show that the asymptotic behavior of the gas represents a perturbation to the free molecular gas when the time is much less than the mean free time. On the other hand, if the time is much greater than the mean free time, we show that the gas dynamics is governed by the linearized Navier–Stokes equation with a slip flow on the boundary and establish a boundary layer correction with thickness of the order of the mean free path. We also establish the singularity of velocity distribution function along the particle trajectory near the boundary.

Original languageEnglish
Pages (from-to)1247-1275
Number of pages29
JournalJournal of Statistical Physics
Volume166
Issue number5
DOIs
Publication statusPublished - 2017 Mar 1

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Kinetic Theory
kinetic theory
Rayleigh
Asymptotic Behavior
Boltzmann Equation
gases
Slip Flow
slip flow
Particle Trajectory
particle trajectories
gas dynamics
Flat Plate
Gas Dynamics
Velocity Distribution
molecular gases
flat plates
Mach number
Instant
mean free path
Boundary Layer

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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abstract = "We investigate the dynamics of the gas bounded by an infinite flat plate which is initially in equilibrium and set at some instant impulsively into uniform motion in its own plane. We use the Boltzmann equation to describe intermolecular collisions and assume the diffuse reflection to describe the interaction of the gas with the boundary. The Mach number of the plate is assumed to be small so that we can linearize the Boltzmann equation as well as the boundary condition. We show that the asymptotic behavior of the gas represents a perturbation to the free molecular gas when the time is much less than the mean free time. On the other hand, if the time is much greater than the mean free time, we show that the gas dynamics is governed by the linearized Navier–Stokes equation with a slip flow on the boundary and establish a boundary layer correction with thickness of the order of the mean free path. We also establish the singularity of velocity distribution function along the particle trajectory near the boundary.",
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Asymptotic Behavior for Rayleigh Problem Based on Kinetic Theory. / Kuo, Hung Wen.

In: Journal of Statistical Physics, Vol. 166, No. 5, 01.03.2017, p. 1247-1275.

Research output: Contribution to journalArticle

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