Instability evolution of the viscous elliptic liquid jet in the Rayleigh regime

Shibo Gu, Lipo Wang, and David L. S. Hung
Phys. Rev. E 95, 063112 – Published 21 June 2017

Abstract

For jet flow emanating from noncircular orifices, an unbalanced surface tension force leads to capillary instability, which is independent of influence from the ambient air in the Rayleigh regime. In the present article, the dynamic behavior of incompressible elliptical jets in the Rayleigh regime is investigated. Theoretically, with the consideration of the fluid viscosity, the solution of the Cosserat equation consists of a particular solution and a complementary solution. For the complementary solution the wave number of disturbance modes has two complex conjugate roots, which are responsible for the jet breakup. To match the nonzero particular solution, a spatial wave needs to be introduced, which is independent of external perturbations. Physically, such a spatial wave is interpreted as the axis-switching phenomenon. The predicted features of the axis-switching wavelength and the damping effect from the fluid viscosity have been successfully verified by experimental results. Moreover, the dispersion relations from the present theory suggest that the growth rate of spatial instability is influenced by orifice eccentricity, the Weber number, and the Ohnesorge number.

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  • Received 10 March 2017

DOI:https://doi.org/10.1103/PhysRevE.95.063112

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Shibo Gu, Lipo Wang*, and David L. S. Hung

  • UM-SJTU Joint Institute, Shanghai Jiao Tong University, Shanghai, China

  • *lipo.wang@sjtu.edu.cn

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Issue

Vol. 95, Iss. 6 — June 2017

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