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Transition from dripping to jetting

Published online by Cambridge University Press:  25 March 1999

CHRISTOPHE CLANET  and
JUAN C. LASHERAS
CHRISTOPHE CLANET
Affiliation:
Department of Applied Mechanics and Engineering Sciences, University of California San Diego, La Jolla, CA 92093-0411, USA Present address: Institut de Recherches sur les Phénoménes Hors Equilibre, Université de Provence, Centre de St Jérôme, Service 252, Marseille Cedex 20, France.
JUAN C. LASHERAS
Affiliation:
Department of Applied Mechanics and Engineering Sciences, University of California San Diego, La Jolla, CA 92093-0411, USA
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Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 383 , 25 March 1999 , pp. 307 - 326
Copyright
© 1999 Cambridge University Press

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