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Absolute and convective instability of a viscous liquid curtain in a viscous gas

Published online by Cambridge University Press:  10 February 1997

C. H. Teng ,
S. P. Lin  and
J. N. Chen
C. H. Teng
Affiliation:
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699, USA
S. P. Lin
Affiliation:
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699, USA
J. N. Chen
Affiliation:
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699, USA
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Extract

The linear instability of a viscous liquid flowing in a vertical sheet sandwiched between two viscous gases bounded externally by two vertical walls is investigated. The critical Weber number below which the flow is absolutely unstable and above which the flow is convectively unstable is found to be approximately equal to one and is weakly dependent on the rest of the parameters. The Weber number is defined as We ≡ ρ1 U20d/S where S is the surface tension, ρ1is the liquid density, U0 is the centreline velocity of the liquid sheet, and d is the half-thickness of the uniform liquid sheet. The sinuous mode is found to have a greater amplification rate than the varicose mode in the convective instability regime. While absolute instability is caused by the surface tension, convective instability is caused by the amplification of disturbances near the liquid-gas interface. The surface tension, and viscosities of liquids and gases all suppress the amplification of the convectively unstable disturbances. An increase in the gravitational force or the gas density results in an enhancement of the amplification rate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 332 , February 1997 , pp. 105 - 120
Copyright
Copyright © Cambridge University Press 1997

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