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Impact of a high-speed train of microdrops on a liquid pool

  • Wilco Bouwhuis (a1), Xin Huang (a2) (a3), Chon U Chan (a2), Philipp E. Frommhold (a4), Claus-Dieter Ohl (a2), Detlef Lohse (a1) (a5), Jacco H. Snoeijer (a1) (a6) and Devaraj van der Meer (a1)...


A train of high-speed microdrops impacting on a liquid pool can create a very deep and narrow cavity, reaching depths more than 1000 times the size of the individual drops. The impact of such a droplet train is studied numerically using boundary integral simulations. In these simulations, we solve the potential flow in the pool and in the impacting drops, taking into account the influence of liquid inertia, gravity and surface tension. We show that for microdrops the cavity shape and maximum depth primarily depend on the balance of inertia and surface tension and discuss how these are influenced by the spacing between the drops in the train. Finally, we derive simple scaling laws for the cavity depth and width.


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Aristoff, J. M. & Bush, J. W. M. 2009 Water entry of small hydrophobic spheres. J. Fluid Mech. 93, 4578.
Basaran, O. A., Gao, H. & Bhat, P. P. 2013 Nonstandard inkjets. Annu. Rev. Fluid Mech. 45, 85113.
Bergmann, R. P. H. M., van der Meer, D., Gekle, S., van der Bos, J. & Lohse, D. 2009 Controlled impact of a disk on a water surface: cavity dynamics. J. Fluid Mech. 633, 381409.
Bergmann, R. P. H. M., van der Meer, D., Stijnman, M. A., Sandtke, M., Prosperetti, A. & Lohse, D. 2006 Giant bubble pinch-off. Phys. Rev. Lett. 96, 154505.
Bick, A. G., Ristenpart, W. D., van Nierop, E. A. & Stone, H. A. 2010 Bubble formation via multidrop impacts. Phys. Fluids 22, 042105.
Billingham, J. & King, A. C. 2005 Surface-tension-driven flow outside a slender wedge with an application to the inviscid coalescence of drops. J. Fluid Mech. 533, 193221.
Bouwhuis, W., Hendrix, M. H. W., van der Meer, D. & Snoeijer, J. H. 2015 Initial surface deformations during impact on a liquid pool. J. Fluid Mech. 771, 503519.
Bouwhuis, W., van der Veen, R. C. A., Tran, T., Keij, D. L., Winkels, K. G., Peters, I. R., van der Meer, D., Sun, C., Snoeijer, J. H. & Lohse, D. 2012 Maximal air bubble entrainment at liquid-drop impact. Phys. Rev. Lett 109, 264501.
Bouwhuis, W., Winkels, K. G., Peters, I. R., Brunet, P., van der Meer, D. & Snoeijer, J. H. 2013 Oscillating and star-shaped drops levitated by an airflow. Phys. Rev. E 88, 023017.
Brenn, G. 2000 On the controlled production of sprays with discrete polydisperse drop size spectra. Chem. Engng Sci. 55 (22), 54375444.
Chen, S. & Guo, L. 2014 Viscosity effect on regular air bubble entrapment during drop impact into a deep pool. Chem. Engng Sci. 109, 116.
Clanet, C. & Lasheras, J. C. 1997 Depth of penetration of bubbles entrained by a plunging water jet. Phys. Fluids 9 (7), 18641866.
Davidson, M. R. 2002 Spreading of an inviscid drop impacting on a liquid film. Chem. Engng Sci. 57, 36393647.
Driessen, T. W., Jeurissen, R. J. M., Wijshoff, H., Toschi, F. & Lohse, D. 2013 Stability of viscous long filaments. Phys. Fluids 25, 062109.
Duchemin, L., Eggers, J. & Josserand, C. 2003 Inviscid coalescence of drops. J. Fluid Mech. 487, 167178.
Eggers, J., Fontelos, M. A., Leppinen, D. & Snoeijer, J. H. 2007 Theory of the collapsing axisymmetric cavity. Phys. Rev. Lett. 98, 094502.
Eggers, J., Lister, J. R. & Stone, H. A. 1999 Coalescence of liquid drops. J. Fluid Mech. 401, 293310.
Frommhold, P. E., Lippert, A., Holsteyns, F. L. & Mettin, R. 2014 High-speed monodisperse droplet generation by ultrasonically controlled micro-jet breakup. Exp. Fluids 55, 112.
Gekle, S., van der Bos, A., Bergmann, R. P. H. M., van der Meer, D. & Lohse, D. 2008 Noncontinuous Froude number scaling for the closure depth of a cylindrical cavity. Phys. Rev. Lett. 100, 084502.
Gekle, S., Peters, I. R., Gordillo, J. M., van der Meer, D. & Lohse, D. 2010 Supersonic airflow due to solid–liquid impact. Phys. Rev. Lett. 104, 024501.
Gekle, S., Snoeijer, J. H., Lohse, D. & van der Meer, D. 2009 Approach to universality in axisymmetric bubble pinch-off. Phys. Rev. E 80, 036305.
Gibson, I., Rosen, D. W. & Stucker, B. 2010 Additive Manufacturing Technologies, 12th edn. Springer.
Hendrix, M. H. W., Bouwhuis, W., van der Meer, D., Lohse, D. & Snoeijer, J. H. 2016 Universal mechanism for air entrainment during liquid impact. J. Fluid Mech. 789, 708725.
Kedrinskii, V. K. 2005 Hydrodynamics of Explosion: Experiments and Models, 1st edn. Springer.
Keij, D. L., Winkels, K. G., Castelijns, H., Riepen, M. & Snoeijer, J. H. 2013 Bubble formation during the collision of a sessile drop with a meniscus. Phys. Fluids 25, 082005.
Kersten, B., Ohl, C. D. & Prosperetti, A. 2003 Transient impact of a liquid column on a miscible liquid surface. Phys. Fluids 15, 821824.
Kim, H. Y., Park, S. Y. & Min, K. 2003 Imaging the high-speed impact of microdrop on solid surface. Rev. Sci. Instrum. 74 (11), 49304937.
Klein, A. L., Bouwhuis, W., Visser, C. W., Lhuissier, H., Sun, C., Snoeijer, J. H., Villermaux, E., Lohse, D. & Gelderblom, H. 2015 Drop shaping by laser-pulse impact. Phys. Rev. Appl. 3, 044018.
Kolaini, A. R., Roy, R. A., Crum, L. A. & Mao, Y. 1993 Low-frequency underwater sound generation by impacting transient water jets. J. Acoust. Soc. Am. 94, 28092820.
Lamb, H. 1957 Hydrodynamics, 6th edn. Cambridge University Press.
Lee, J. S., Weon, B. M., Je, J. H. & Fezzaa, K. 2012 How does an air film evolve into a bubble during drop impact? Phys. Rev. Lett. 109, 204501.
Lindblad, N. R. & Schneider, J. R. 1965 Production of uniform-sized liquid droplets. J. Sci. Instrum. 42, 635638.
Lohse, D., Bergmann, R. P. H. M., Mikkelsen, R., Zeilstra, C., van der Meer, D., Versluis, M., van der Weele, K., van der Hoef, M. A. & Kuipers, J. A. M. 2004 Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93, 198003.
Oguz, H. N. & Prosperetti, A. 1993 Dynamics of bubble growth and detachment from a needle. J. Fluid Mech. 257, 111145.
Oguz, H. N., Prosperetti, A. & Kolaini, A. R. 1995 Air entrapment by a falling water mass. J. Fluid Mech. 294, 181207.
Pohl, R., Visser, C. W., Römer, G. R. B. E., Lohse, D., Sun, C. & Huis in ’t Veld, A. J. 2015 Ejection regimes in picosecond laser-induced forward transfer of metals. Phys. Rev. Appl. 3, 024001.
Pozrikidis, C. 1997 Introduction to Theoretical and Computational Fluid Dynamics, 1st edn. Oxford University Press.
Prosperetti, A. 1977 On the stability of spherically symmetric flows. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 62, 196203.
Prosperetti, A. & Oguz, H. N. 1993 The impact of drops on liquid surfaces and the underwater noise of rain. Annu. Rev. Fluid Mech. 25, 577602.
Pumphrey, H. C. & Elmore, P. A. 1990 The entrainment of bubbles by drop impacts. J. Fluid Mech. 220, 539567.
Qu, X. L., Khezzar, L., Danciu, D., Labois, M. & Lakehal, D. 2011 Characterization of plunging liquid jets: a combined experimental and numerical investigation. Intl J. Multiphase Flow 37, 722731.
Storr, G. J. & Behnia, M. 1999 Experiments with large diameter gravity driven impacting liquid jets. Exp. Fluids 27, 6069.
Szymczak, W. G., Means, S. L. & Rogers, J. C. W. 2004 Computations of bubble formation and pulsations generated by impacting cylindrical water jets. J. Engng Maths 48, 375389.
Thoroddsen, S., Thoraval, M.-J., Takehara, K. & Etoh, T. G. 2012 Micro-bubble morphologies following drop impacts onto a pool surface. J. Fluid Mech. 708, 469479.
Tran, T., de Maldeprade, H., Sun, C. & Lohse, D. 2013 Air entrainment during impact of droplets on liquid surfaces. J. Fluid Mech. 726, R3.
Visser, C. W., Frommhold, P. E., Wildeman, S., Mettin, R., Lohse, D. & Sun, C. 2015 Dynamics of high-speed micro-drop impact: numerical simulations and experiments at frame-to-frame times below 100 ns. Soft Matt. 11 (9), 17081722.
Wang, A., Kuan, C.-C. & Tsai, P.-H. 2013 Do we understand the bubble formation by a single drop impacting upon liquid surface? Phys. Fluids 25 (10), 101702.
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Impact of a high-speed train of microdrops on a liquid pool

  • Wilco Bouwhuis (a1), Xin Huang (a2) (a3), Chon U Chan (a2), Philipp E. Frommhold (a4), Claus-Dieter Ohl (a2), Detlef Lohse (a1) (a5), Jacco H. Snoeijer (a1) (a6) and Devaraj van der Meer (a1)...


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