Transition from dripping to jetting
We consider the critical Weber number (Wec[identical with] 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
where Bo and Boo are the Bond numbers (Bo[identical with][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.(Received March 18 1997)
(Revised October 9 1998)
p1 Present address: Institut de Recherches sur les Phénoménes Hors Equilibre, Université de Provence, Centre de St Jérôme, Service 252, Marseille Cedex 20, France.