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Instability of a viscous coflowing jet in a radial electric field

Published online by Cambridge University Press:  17 January 2008

FANG LI ,
XIE-YUAN YIN  and
XIE-ZHEN YIN
FANG LI
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, [email protected]
XIE-YUAN YIN
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, [email protected]
XIE-ZHEN YIN
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, [email protected]
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Abstract

A temporal linear instability analysis of a charged coflowing jet with two immiscible viscous liquids in a radial electric field is carried out for axisymmetric disturbances. According to the magnitude of the liquid viscosity relative to the ambient air viscosity, two generic cases are considered. The analytical dimensionless dispersion relations are derived and solved numerically. Two unstable modes, namely the para-sinuous mode and the para-varicose mode, are identified in the Rayleigh regime. The para-sinuous mode is found to always be dominant in the jet instability. Liquid viscosity clearly stabilizes the growth rates of the unstable modes, but its effect on the cut-off wavenumber is negligible. The radial electric field has a dual effect on the modes, stabilizing them when the electrical Euler number is smaller than a critical value and destabilizing them when it exceeds that value. Moreover, the electrical Euler number and Weber number increase the dominant and cut-off wavenumbers significantly. Based on the Taylor–Melcher leaky dielectric theory, two limit cases, i.e. the small electrical relaxation time limit (SERT) and the large electrical relaxation time limit (LERT), are discussed. For coflowing jets having a highly conducting outer liquid, SERT may serve as a good approximation. In addition, the dispersion relations under the thin layer approximation are derived, and it is concluded that the accuracy of the thin layer approximation is closely related to the values of the dimensionless parameters.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 596 , 25 January 2008 , pp. 285 - 311
Copyright
Copyright © Cambridge University Press 2008

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