Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-18T16:15:49.213Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stability of laminar flow of a dusty gas

Published online by Cambridge University Press:  28 March 2006

P. G. Saffman
P. G. Saffman
Affiliation:
Department of Mathematics, King's College, London
Get access Rights & Permissions [Opens in a new window]

Abstract

The equations describing the motion of a gas carrying small dust particles are given and the equations satisfied by small disturbances of a steady laminar flow are derived. The effect of the dust is described by two parameters; the concentration of dust and a relaxation time τ which measures the rate at which the velocity of a dust particle adjusts to changes in the gas velocity and depends upon the size of the individual particles. It is shown that if the dust is fine enough for τ to be small compared with a characteristic time scale associated with the flow, then the addition of dust destabilizes a gas flow; whereas if the dust is coarse so that τ is relatively large, then the dust has a stabilizing action.

For plane parallel flow, it is shown that the stability characteristics for a dusty gas are still determined by solutions of the Orr-Sommerfeld equation, but with the basic velocity profile replaced by a modified profile which is in general complex. A simple, although unrealistic, example is used to illustrate some features of the action of dust. It is intended to describe the solution of the modified Orr-Sommerfeld equation for plane Poiseuille flow in a later paper.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 13 , Issue 1 , May 1962 , pp. 120 - 128
Copyright
© 1962 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.)

References

Brooke Benjamin, T. 1960 J. Fluid Mech. 9, 513.
Kazakevich, F. P. & Krapivin, A. M. 1958 Izv. Vyssh. Uchebn. Zavedenii. Energetica, no. 1, 101.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. London: Pergamon.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Sproull, W. T. 1961 Nature, 190, 976.
Squire, H. B. 1933 Proc. Roy. Soc. A, 142, 621.