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On the stability of laminar flow of a dusty gas

Saffman, P. G. (1962) On the stability of laminar flow of a dusty gas. Journal of Fluid Mechanics, 13 (1). pp. 120-128. ISSN 0022-1120. doi:10.1017/s0022112062000555.

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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.

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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.
Issue or Number:1
Record Number:CaltechAUTHORS:20181119-161053230
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Official Citation:Saffman, P. (1962). On the stability of laminar flow of a dusty gas. Journal of Fluid Mechanics, 13(1), 120-128. doi:10.1017/S0022112062000555
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91053
Deposited By: George Porter
Deposited On:20 Nov 2018 19:14
Last Modified:16 Nov 2021 03:38

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