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Atomization and Sprays
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ISSN Imprimer: 1044-5110
ISSN En ligne: 1936-2684

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Atomization and Sprays

DOI: 10.1615/AtomizSpr.v14.i6.50
26 pages

POLAR INSTABILITY OF SUPERIMPOSED DISTURBANCES IN SPRAY FORMATION FROM LIQUID JETS

S. Sadik
Department of Civil Engineering, Technion—Israel Institute of Technology, Haifa, Israel
Yoram Zimmels
Faculty of Civil and Environmental Engineering, Technion - Israel Institute of Technology
Rabin building,room 624

RÉSUMÉ

The concept of superimposed sequence of nonaxial and polar disturbances that propagate one on top of the other, in the process of spray formation for jets, is introduced. The axisymetric ligaments and drops that are formed in this process, including toroidal forms of drops, can sustain a wide range of polar disturbances on their surface. A new dispersion equation that generalizes the one of the Rayleigh model is developed. This dispersion equation provides solutions for axipolar instability parameters of hollow jets, and radially disconnected parts of axisymmetric ligaments and drops.
The axipolar instability parameter is shown to depend on axial and polar wave numbers and on the solution parameter, kf, obtained, in conjunction with Kn(kr) which satisfies the modified Bessel equation of the pressure perturbation. Domains where a positive axipolar instability parameter exists are defined and related to the axial and polar wave numbers. Larger domains are associated with larger polar wave numbers. These domains include axial and polar wavelength that are shorter than the jet circumference 2πα and 2π, being in contrast to the Rayleigh model, which allows only values that exceed 2πα and 2π, respectively.
The concept of a limiting polar wave number is introduced and used to characterize the system with respect to instability at lower polar wave numbers. It is shown that for systems that can sustain high levels of the limiting polar wave number, the attendant instability parameter turns virtually independent of all lower polar wave numbers. This implies existence of jets that can develop multimodal instability, involving many wave numbers that coexist under the same instability parameter. In this context, the existence of multimodal instability opens new avenues for understanding the process whereby jets evolve into sprays.


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