Transition from dripping to jetting

• Published in: Journal of fluid mechanics 1999-03, Vol.383, p.307-326
• Main Authors: CLANET, CHRISTOPHE, LASHERAS, JUAN C.
• Format: Article
• Language: English
• Subjects: Engineering Sciences; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Jets; Physics; Reactive fluid environment; Surface-tension-driven instability; Turbulent flows, convection, and heat transfer
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112098004066

We consider the critical Weber number (Wec≡ ρV20D/σ) at which the transition from dripping to jetting occurs when a Newtonian liquid of density ρ and surface tension σ is injected with a velocity V0 through a tube of diameter D downward into stagnant air, under gravity g. We extend Taylor's (1959) model for the recession speed of a free edge, and obtain in the inviscid limit an exact solution which includes gravity and inertia effects. This solution provides a criterion for the transition which is shown to occur at a critical Weber number formula here where Bo and Boo are the Bond numbers (Bo≡[ρgD2/(2σ)]1/2), respectively based on the inside and outside diameter of the tube, and K is a constant equal to 0.37 for the case of water injected in air. This critical Weber number is shown to be in good agreement with existing experimental values as well as with new measurements performed over a wide range of Bond numbers.