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International Journal of Fluid Mechanics Research

ISSN Print: 1064-2277
ISSN Online: 2152-5102

International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.2017016533
pages 93-113

THREE-DIMENSIONAL INSTABILITY OF NON-NEWTONIAN VISCOELASTIC LIQUID JETS ISSUED INTO A STREAMING VISCOUS (OR INVISCID) GAS

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

ABSTRACT

A linear stability analysis is presented for a Rivlin-Ericksen viscoelastic liquid jet moving in a streaming viscous (or inviscid) gas medium with three-dimensional disturbances. The dispersion relation between the nondimensional growth rate and nondimensional wave number is derived using appropriate boundary conditions, and it is solved numerically via a new technique using Mathematica software. The effects of different parameters on the stability behavior of the system are discussed in detail. It is shown that a viscoelastic liquid jet streaming in a viscous gas is more unstable than that in an inviscid one, and less unstable than the corresponding case of a viscous liquid jet. It is shown also that the Weber number, Raynolds number, liquid velocity, gas density, gas-to-liquid density ratio, and the gas-to-liquid viscosity ratio have destabilizing effects on the system, while the viscoelasticity parameter and surface tension have usually stabilizing influences. The Ohnesorge number and gas-to-liquid velocity ratio are found to have dual roles on the stability of the system. Finally, comparisons between the cases of ambient viscous and inviscid gases as well as the cases of symmetric and antisymmetric disturbances are examined in detail.