On the stability of laminar flow of a dusty gas
- Creators
- Saffman, P. G.
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.
Additional Information
© 1962 Cambridge University Press. (Received 19 December 1961) I wish to thank Dr J. T. Stuart for the benefit of several most helpful discussions and his wide experience of hydrodynamic stability.Attached Files
Published - on_the_stability_of_laminar_flow_of_a_dusty_gas.pdf
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Additional details
- Eprint ID
- 91053
- Resolver ID
- CaltechAUTHORS:20181119-161053230
- Created
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2018-11-20Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field