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Atomization and Sprays
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ISSN Imprimer: 1044-5110
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Atomization and Sprays

DOI: 10.1615/AtomizSpr.2014011471
pages 123-151

HYDRODYNAMIC INSTABILITIES OF TWO VISCOELASTIC LIQUID SHEET MODELS IN AN INVISCID GAS MEDIUM

Mohamed F. El-Sayed
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis (Roxy), Cairo, Egypt; Department of Mathematics, College of Science, Qassim University, P. O. Box 6644, Buraidah 51452, Saudi Arabia
G. M. Moatimid
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
F. M. F. Elsabaa
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy 11757, Cairo, Egypt
M. F. E. Amer
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy 11757, Cairo, Egypt

RÉSUMÉ

The instabilities of two viscoelastic liquid sheet models (of Walters B' and Rivlin-Ericksen types) issued in an inviscid gas medium have been separetely invistigated. The dispersion relations between the growth rate and wave number of both symmetric and antisymmetric disturbances are derived for both models, and solved numerically using a new technique. The effects of the Weber number, Ohnesorge number, gas-to-liquid density ratio, and viscoelasticity parameter on the growth rates of two-and three-dimensional disturbances in both models are studied. We conclude, at low values of the Weber number, that two-dimensional disturbances dominate the instability process for both symmetric and antisymmetric disturbances, whereas if the Weber number is high, symmetric three-dimensional disturbances become more unstable than two-dimensional ones only when the x-direction wave number is small. In the antisymmetric disturbances case for all various parameters, the two-dimensional instability disturbances are found to be more unstable than the three-dimensional ones. It is found, in both models, that the gas-to-liquid density ratio, Ohnesorge number and the viscoelasticity parameter have stabilizing effects on the considered system, while the Weber number has a destabilizing effect. It found also that the instabilities in the Walters B' liquid sheet occur faster than those in the Rivlin-Ericksen liquid sheet.