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Controlled impact of a disk on a water surface: cavity dynamics


In this paper we study the transient surface cavity which is created by the controlled impact of a disk of radius h0 on a water surface at Froude numbers below 200. The dynamics of the transient free surface is recorded by high-speed imaging and compared to boundary integral simulations giving excellent agreement. The flow surrounding the cavity is measured with high-speed particle image velocimetry and is found to also agree perfectly with the flow field obtained from the simulations.

We present a simple model for the radial dynamics of the cavity based on the collapse of an infinite cylinder. This model accounts for the observed asymmetry of the radial dynamics between the expansion and the contraction phases of the cavity. It reproduces the scaling of the closure depth and total depth of the cavity which are both found to scale roughly as ∝ Fr1/2 with a weakly Froude-number-dependent prefactor. In addition, the model accurately captures the dynamics of the minimal radius of the cavity and the scaling of the volume Vbubble of air entrained by the process, namely, Vbubble/h03∝(1 + 0.26Fr1/2)Fr1/2.

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R. Bergmann , M. Stijnman , M. Sandtke , D. van der Meer , A. Prosperetti & D. Lohse 2006 Giant bubble collapse. Phys. Rev. Lett. 96, 154505/1–4.

G. Caballero , R. Bergmann , D. van der Meer , A. Prosperetti & D. Lohse 2007 Role of air in granular jet formation. Phys. Rev. Lett. 99, 018001/1–4.

A. Chen & O. Basaran 2002 A new method for significantly reducing drop radius without reducing nozzle radius in drop-on-demand drop production. Phys. Fluids 14, L1.

A. Fedorchenko & A.-B. Wang 2004 On some common features of drop impact on liquid surfaces. Phys. Fluids 16, 13491365.

S. Gaudet 1998 Numerical simulation of circular disks entering the free surface of a fluid. Phys. Fluids 10, 24892499.

S. Gekle , A. van der Bos , R. Bergmann , D. van der Meer & D. Lohse 2008 Noncontinuous froude number scaling for the closure depth of a cylindrical cavity. Phys. Rev. Lett. 100, 084502/1–4.

S. Gekle , J. M. Gordillo , D. van der Meer & D. Lohse 2009 High-speed jet formation after solid object impact. Phys. Rev. Lett. 102, 034502/1–4.

D. Gilbarg & R. A. Anderson 1948 Influence of atmospheric pressure on the phenomena accompanying the entry of spheres into water. J. Appl. Phys. 19, 127139.

J. W. Glasheen & T. A. McMahon 1996 A hydrodynamic model of locomotion in the basilisk lizard. Nature 380, 340342.

J. de Jong , G. de Bruin , H. Reinten , M. van den Berg , H. Wijshoff , M. Versluis & D. Lohse 2006 aAir entrapment in piezo-driven inkjet printheads. J. Acoust. Soc. Am. 120, 12571265.

J. de Jong , R. Jeurissen , H. Borel , M. van den Berg , H. Wijshoff , H. Reinten , M. Versluis , A. Prosperetti & D. Lohse 2006 bEntrapped air bubbles in piezo-driven inkjet printing: their effect on the droplet velocity. Phys. Fluids 18, 121511121517.

M. Lee , R. Longoria & D. Wilson 1997 Cavity dynamics in high-speed water entry. Phys. Fluids 9, 540550.

D. Lohse , R. Bergmann , R. Mikkelsen , C. Zeilstra , D. van der Meer , M. Versluis , K. van der Weele , M. van der Hoef & H. Kuipers 2004 Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93, 198003/1–4.

D. Morton , J.-L. Liow & M. Rudman 2000 An investigation of the flow regimes resulting from splashing drops. Phys. Fluids 12, 747763.

A. Prosperetti 2002 Drop Surface Interactions. CISM Courses and Lectures No. 456. Springer.

A. Prosperetti , L. Crum & H. Pumphrey 1989 Underwater noise of rain. J. Geophys. Res. 94, 32553259.

A. Prosperetti & H. Oguz 1997 Air entrainment upon liquid impact. Phil. Trans. R. Soc. Lond. A 355, 491506.

M. Rein 1993 Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12, 6193.

J. Royer , E. Corwin , A. Flior , M.-L. Cordero , M. Rivers , P. Eng & H. Jaeger 2005 Formation of granular jets observed by high-speed X-ray radiography. Nat. Phys. 1, 164167.

S. T. Thoroddsen , T. G. Etoh & K. Takehara 2007 Experiments on bubble pinch-off. Phys. Fluids 19, 042101042129.

S. Thoroddsen & A. Shen 2001 Granular jets. Phys. Fluids 13, 46.

A. M. Worthington & R. S. Cole 1897 Impact with a liquid surface, studied by the aid of instantaneous photography. Phil. Trans. R. Soc. Lond. A 189, 137.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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