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Bubble entrapment during sphere impact onto quiescent liquid surfaces

  • J. O. MARSTON (a1), I. U. VAKARELSKI (a1) and S. T. THORODDSEN (a1) (a2)


We report observations of air bubble entrapment when a solid sphere impacts a quiescent liquid surface. Using high-speed imaging, we show that a small amount of air is entrapped at the bottom tip of the impacting sphere. This phenomenon is examined across a broad range of impact Reynolds numbers, 0.2 ≤ Re = (DU0l) ≤ 1.2 × 105. Initially, a thin air pocket is formed due to the lubrication pressure in the air layer between the sphere and the liquid surface. As the liquid surface deforms, the liquid contacts the sphere at a finite radius, producing a thin sheet of air which usually contracts to a nearly hemispherical bubble at the bottom tip of the sphere depending on the impact parameters and liquid properties. When a bubble is formed, the final bubble size increases slightly with the sphere diameter, decreases with impact speed but appears independent of liquid viscosity. In contrast, for the largest viscosities tested herein, the entrapped air remains in the form of a sheet, which subsequently deforms upon close approach to the base of the tank. The initial contact diameter is found to conform to scalings based on the gas Reynolds number whilst the initial thickness of the air pocket or ‘dimple’ scales with a Stokes' number incorporating the influence of the air viscosity, sphere diameter and impact speed and liquid density.


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Akers, B. & Belmonte, A. 2006 Impact dynamics of a solid sphere falling into a viscoelastic micellar fluid. J. Non-Newtonian Fluid Mech. 135, 97108.
Aristoff, J. M. & Bush, J. W. M. 2009 Water entry of small hydrophobic spheres. J. Fluid Mech. 619, 4578.
Aristoff, J. M., Truscott, T., Techet, A. H. & Bush, J. W. M. 2010 The water entry of decelerating spheres. Phys. Fluids 22, 032102.
Benkreira, H. & Cohu, O. 1998 Angling the wetting line retards air entrainment in premetered coating flows. AIChE J. 44 (5), 12071209.
Bergmann, R., van der Meer, D., Gekle, S., van der Bos, A. & Lohse, D. 2009 Controlled impact of a disk on a water surface: cavity dynamics. J. Fluid Mech. 633, 381409.
Chan, D. Y. C., Klaseboer, E. & Manica, R. 2011 Film drainage and coalescence between deformable drops and bubbles. Soft Matter 7, 22352264.
Chandra, S. & Avedisian, C. T. 1991 On the collision of a droplet with a solid surface. Proc. R. Soc. Lond. A 432, 1341.
van Dam, D. B. & Le Clerc, C. 2004 Experimental study on the impact of an ink-jet printed droplet on a solid surface. Phys. Fluids 16 (9), 34033414.
Deng, Q., Anilkumar, A. V. & Wang, T. G. 2009 The phenomenon of bubble entrapment during capsule formation. J. Colloid Interface Sci. 333, 523532.
Do-Quang, M. & Amberg, G. 2009 The splash of a solid sphere impacting on a liquid surface: numerical simulation of the influence of wetting. Phys. Fluids 21, 022102.
Driscoll, M. M., Stevens, C. S. & Nagel, S. R. 2010 Thin film formation during splashing of viscous liquids. Phys. Rev. E 83, 036302.
Duclaux, V., Caille, F., Duez, C., Bocquet, L. & Clanet, C. 2007 Dynamics of transient cavities. J. Fluid Mech. 591, 119.
Duez, C., Ybert, C., Clanet, C. & Bocquet, L. 2007 Making a splash with water repellency. Nat. Phys. 3, 180183.
Mani, M., Mandre, S. & Brenner, M. P. 2010 Events before droplet splashing on a solid surface. J. Fluid Mech. 647, 163185.
Marston, J. O., Yong, W. & Thoroddsen, S. T. 2010 Direct verification of the lubrication force on a sphere travelling through a viscous film upon approach to a solid wall. J. Fluid Mech. 655, 515526.
May, A. 1951 Effect of surface condition of a sphere on its water-entry cavity. J. Appl. Phys. 22, 12191222.
McMillen, J. H. 1945 Shock wave pressures in water produced by impact of small spheres. Phys. Rev. 68, 198209.
Mehdi-Nejad, V., Mostaghimi, J. & Chandra, S. 2003 Air bubble entrapment under an impacting drop. Phys. Fluids 15, 173183.
Moghishi, M. & Squire, P. T. 1981 An experimental investigation of the initial force of impact on a sphere striking a liquid surface. J. Fluid Mech. 108, 133146.
Peck, B. & Sigurdson, L. 1994 Three-dimensional vortex structure of an impacting water drop. Phys. Fluids 6, 564576.
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2003 Air entrapment under an impacting drop. J. Fluid Mech. 478, 125134.
Thoroddsen, S. T., Etoh, T. G., Takehara, K., Ootsuka, N. & Hatsuki, Y. 2005 The air bubble entrapped under a drop impacting on a solid surface. J. Fluid Mech. 545, 203212.
Thoroddsen, S. T., Etoh, T. G., Takehara, K. & Takano, Y. 2004 Impact jetting by a solid sphere. J. Fluid Mech. 499, 139148.
Thoroddsen, S. T., Takehara, K. & Etoh, T. G. 2010 Bubble entrapment through topological change. Phys. Fluids 22, 051701.
Worthington, A. M. & Cole, R. S. 1900 Impact with a liquid surface studied by the aid of instantaneous photography. Phil. Trans. R. Soc. Lond. A 194, 175199.
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Bubble entrapment during sphere impact onto quiescent liquid surfaces

  • J. O. MARSTON (a1), I. U. VAKARELSKI (a1) and S. T. THORODDSEN (a1) (a2)


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