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

Abstract

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 R³₀S²₀/σ, which expresses the ratio of the capillary time to the inverse of the local strain rate, S₀. Here, ρ and σ indicate the liquid density and the interfacial tension coefficient, respectively, and R₀ is the initial radius of the jet. Our physical arguments predict the dimensionless size of the drops to scale as D_drop/R₀ ~ We^−1/7_S and the dimensionless time to break up as TS₀ ~ We^2/7_S. These theoretical predictions are in good agreement with the numerical results.