Generation and breakup of Worthington jets after cavity collapse. Part 2. Tip breakup of stretched jets

The capillary breakup of the high-speed Worthington jets ejected after a cavity collapse in water occurs due to the high-Reynolds-number version of the capillary end-pinching mechanism first described, in the creeping flow limit, by Stone & Leal ( J. Fluid Mech. , vol. 198, 1989, p. 399). Using potential flow numerical simulations and theory, we find that the resulting drop ejection process does not depend on external noise and can be described as a function of a single dimensionless parameter, We S = ρ R 3 0 S 2 0 /σ, which expresses the ratio of the capillary time to the inverse of the local strain rate, S 0 . Here, ρ and σ indicate the liquid density and the interfacial tension coefficient, respectively, and R 0 is the initial radius of the jet. Our physical arguments predict the dimensionless size of the drops to scale as D drop / R 0 ~ We −1/7 S and the dimensionless time to break up as TS 0 ~ We 2/7 S . These theoretical predictions are in good agreement with the numerical results.