Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-17T03:45:49.823Z Has data issue: false hasContentIssue false

A linearized kinetic formulation including a second-order slip model for an impulsive start problem at arbitrary Knudsen numbers

Published online by Cambridge University Press:  15 June 2005

N. G. HADJICONSTANTINOU
Affiliation:
Mechanical Engineering Department, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 3-364, Cambridge, MA 02139, USA
H. A. AL-MOHSSEN
Affiliation:
Mechanical Engineering Department, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 3-364, Cambridge, MA 02139, USA

Abstract

We investigate the time evolution of an impulsive start problem for arbitrary Knudsen numbers ($\hbox{\it Kn}$) using a linearized kinetic formulation. The early-time behaviour is described by a solution of the collisionless Boltzmann equation. The same solution can be used to describe the late-time behaviour for $\hbox{\it Kn}\,{\gg}\,1$. The late-time behaviour for $\hbox{\it Kn}\,{<}\,0.5$ is captured by a newly proposed second-order slip model with no adjustable parameters. All theoretical results are verified by direct Monte Carlo solutions of the nonlinear Boltzmann equation. A measure of the timescale to steady state, normalized by the momentum diffusion timescale, shows that the timescale to steady state is significantly extended by ballistic transport, even at low Knudsen numbers where the latter is only important close to the system walls. This effect is captured for $\hbox{\it Kn}\,{<}\,0.5$ by the slip model which predicts the equivalent effective domain size increase (slip length).

Type
Papers
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)