Capillary instability of elliptic liquid jets

• Published in: Physics of fluids (1994) Vol. 23; no. 8; pp. 084109 - 084109-9
• Main Authors: Amini, Ghobad, Dolatabadi, Ali
• Format: Journal Article
• Language: English
• Published: Melville, NY American Institute of Physics 01.08.2011
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Jets; Physics; Surface-tension-driven instability; Turbulent flows, convection, and heat transfer; Ellipticity; Elliptical section; Modelling; Capillary waves; Liquid jet; Hydrodynamic instability
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.3626550

Instability of a liquid jet issuing from an elliptic nozzle in Rayleigh mode is investigated and its behavior is compared with a circular jet. Mathematical solution of viscous free-surface flow for asymmetric geometry is complicated if 3-D analytical solutions are to be obtained. Hence, one-dimensional Cosserat (directed curve) equations are used which can be assumed as a low order form of Navier-Stokes equations for slender jets. Linear solution is performed using perturbation method. Temporal dispersion equation is derived to find the most unstable wavelength responsible for the jet breakup. The obtained results for a circular jet (i.e., an ellipse with an aspect ratio of one) are compared with the classical results of Rayleigh and Weber for inviscid and viscous cases, respectively. It is shown that in the Rayleigh regime, which is the subject of this research, symmetric perturbations are unstable while asymmetric perturbations are stable. Consequently, spatial analysis is performed and the variation of growth rate under the effect of perturbation frequencies for various jet velocities is demonstrated. Results reveal that in comparison with a circular jet, the elliptic jet is more unstable. Furthermore, among liquid jets with elliptical cross sections, those with larger ellipticities have a larger instability growth rate.