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Instability of a high-speed submerged elastic jet

Published online by Cambridge University Press:  26 April 2006

J. M. Rallison  and
E. J. Hinch
J. M. Rallison
Affiliation:
Department of Applied Mathematics and Theoretical Physics, The University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
E. J. Hinch
Affiliation:
Department of Applied Mathematics and Theoretical Physics, The University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

The linearized inertial instability of the parallel shear flow of a viscoelastic liquid is considered. An elastic Rayleigh equation is derived, for high Reynolds numbers and high Weissenberg numbers, and for a viscoelastic liquid whose first normal stress dominates other stresses. The equation is used to investigate the stability of a submerged jet, that may be planar or axisymmetric, having a parabolic velocity profile. The sinuous mode is found to be fully stabilized by sufficiently large elasticity. The varicose mode in the planar case is partially stabilized, being unstable only at longer wavelengths and with a reduced growth rate. An axisymmetric jet, which is stable to varicose perturbations at zero elasticity, is found to be unstable to short-wave disturbances for small non-zero elasticity. This novel instability involves elastic waves in the shear. It is also present in other modes but does not have the fastest growth rate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 288 , 10 April 1995 , pp. 311 - 324
Copyright
© 1995 Cambridge University Press

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References

Azaiez, J. & Homsy, G. M. 1994 Linear stability of free shear flow of viscoelastic liquids. J. Fluid Mech. 268, 37–69.Google Scholar
Batchelor, G. K. & Gill, A. E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14, 529–551.Google Scholar
Bickley, W.G. 1937 The plane jet. Phil. Mag. 26, 268–324.Google Scholar
Boger, D.V. & Walters, K. 1993 Rheological Phenomena in Focus Elsevier.
Drazin, P. G. & Howard, L. N. 1966 Hydrodynamic instability of parallel flow of inviscid fluids. In Advances in Applied Mechanics, vol 7 (ed. G. Kuerti), pp 1–89. Academic Press.
Goldin, M., Yerushalmi, J., Pfeffer, R. & Shinnar, R. 1969 Breakup of a laminar capillary jet of a viscoelastic fluid. J. Fluid Mech. 38, 689–711.Google Scholar
Hinch, E. J., Harris, O. J. & Rallison, J. M. 1992 The instability mechanism for two elastic liquids being co-extruded. J. Non-Newtonian Fluid Mech. 43, 311–324.Google Scholar
Howard, L.N. 1961 Note on a paper by J.W. Miles. J. Fluid Mech. 10, 509–512.Google Scholar