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

  • J. M. GORDILLO (a1) and STEPHAN GEKLE (a2) (a3)

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, WeS = 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 Ddrop/R0 ~ We−1/7S and the dimensionless time to break up as TS0 ~ We2/7S. These theoretical predictions are in good agreement with the numerical results.

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Antkowiak A., Bremond N., Dizès S. L. & Villermaux E. 2007 a Inertial jets. Bull. Am. Phys. Soc. 52, 104.
Antkowiak A., Bremond N., Dizès S. L. & Villermaux E. 2007 b Short-term dynamics of a density interface following an impact. J. Fluid Mech. 577, 241250.
Antkowiak A., Bremond N., Duplat J., Dizès S. L. & Villermaux E. 2007 c Cavity jets. Phys. Fluids 19, 091112.
Bolanos-Jiménez R., Sevilla A., Martínez-Bazán C. & Gordillo J. M. 2008 Axisymmetric bubble collapse in a quiescent liquid pool. Part II. Experimental study. Phys. Fluids 20, 112104.
Boulton-Stone J. M. & Blake J. R. 1993 Gas bubbles bursting at a free surface. J. Fluid Mech. 254, 437466.
Eggers J. & Villermaux E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.
Frankel I. & Weihs D. 1985 Stability of a capillary jet with linearly increasing axial velocity (with application to shaped charges). J. Fluid Mech. 155, 289307.
Gekle S. & Gordillo J. M. 2010 Generation and breakup of Worthington jets after cavity collapse. Part 1. Jet formation. J. Fluid Mech. doi:10.1017/S0022112010003526.
Gekle S., Gordillo J. M., van der Meer D. & Lohse D. 2009 High-speed jet formation after solid object impact. Phys. Rev. Lett. 102, 034502.
Gordillo J. M. & Pérez-Saborid M. 2005 Aerodynamic effects in the break-up of liquid jets: on the first wind-induced breakup regime. J. Fluid Mech. 541, 120.
Gordillo J. M., Sevilla A. & Martínez-Bazán C. 2007 Bubbling in a co-flow at high Reynolds numbers. Phys. Fluids 19, 077102.
Keller J. B., Rubinow S. I. & Tu Y. O. 1973 Spatial instability of a jet. Phys. Fluids 16, 20522055.
Mikami T., Cox R. G. & Manson S. G. 1975 Breakup of extending liquid threads. Intl J. Multiph. Flow 2, 113138.
Notz P. K. & Basaran O. A. 2004 Dynamics and breakup of a contracting liquid filament. J. Fluid Mech. 512, 223256.
Plateau J. 1873 Statique Expérimentale et Théorique des Liquides. Gauthier-Villars.
Rayleigh W. S. 1878 On the instability of jets. Proc. Lond. Math. Soc. 10, 413.
Rein M. 1996 The transitional regime between coalescing and splashing drops. J. Fluid Mech. 306, 145165.
Savart F. 1833 Mémoire sur la constitution des veines liquides lancées par des orifices circulaires en mince paroi. Ann. Chim. 53, 337386.
Schulkes R. M. S. M. 1996 The contraction of liquid filaments. J. Fluid Mech. 309, 277300.
Shield T. W., Bogy D. B. & Talke F. 1986 A numerical comparison of one-dimensional fluid jet models applied to drop-on-demand printing. J. Comput. Phys. 67, 327347.
Shield T. W., Bogy D. B. & Talke F. 1987 Drop formation by DOD ink-jet nozzles: a comparison of experiment and numerical simulation. IBM J. Res. Dev. 31, 96110.
Sterling A. & Sleicher C. 1975 The instability of capillary jets. J. Fluid Mech. 68, 477495.
Stone H. A., Bentley B. J. & Leal L. G. 1986 An experimental study of transient effects in the breakup of viscous drops. J. Fluid Mech. 173, 131158.
Stone H. & Leal L. 1989 Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399427.
Taylor G. I. 1959 The dynamics of thin sheets of fluid. Part III. Disintegration of fluid sheets. Proc. R. Soc. Lond. A 253, 313321.
Thoroddsen S. T., Takehara K., Etoh T. G. & Ohl C. D. 2009 Spray and microjets produced by focusing a laser pulse into a hemispherical drop. Phys. Fluids 21, 112101.
Tomotika S. 1936 Breaking up of a drop of viscous liquid immersed in another viscous fluid which is extending at a uniform rate. Proc. R. Soc. 153, 302318.
Yarin A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159192.
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Journal of Fluid Mechanics
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