TY - JOUR

T1 - Asymptotic Behavior for Rayleigh Problem Based on Kinetic Theory

AU - Kuo, Hung Wen

N1 - Funding Information:
We thank Professor Tai-Ping Liu for his interest and discussions. We also thank Professor Kazuo Aoki for his insightful suggestions. This work was supported by MOST Grant 104-2115-M-006-010-MY2. It was also in part supported by the Ministry of Education, Taiwan, R.O.C. The Aim for the Top University Project to the National Cheng Kung University.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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.

AB - 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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U2 - 10.1007/s10955-017-1717-y

DO - 10.1007/s10955-017-1717-y

M3 - Article

AN - SCOPUS:85009766184

VL - 166

SP - 1247

EP - 1275

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5

ER -