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

Published online by Cambridge University Press:  08 March 2016

Wilco Bouwhuis ,
Xin Huang ,
Chon U Chan ,
Philipp E. Frommhold ,
Claus-Dieter Ohl ,
Detlef Lohse ,
Jacco H. Snoeijer  and
Devaraj van der Meer
Wilco Bouwhuis*
Affiliation:
Physics of Fluids Group, Mesa$+$ Institute and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500AE Enschede, The Netherlands
Xin Huang
Affiliation:
Cavitation Lab, Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371, Singapore Fluid Mechanics Labs, Department of Mechanical Engineering, National University of Singapore, Singapore 117575, Singapore
Chon U Chan
Affiliation:
Cavitation Lab, Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371, Singapore
Philipp E. Frommhold
Affiliation:
Christian Doppler Laboratory for Cavitation and Micro-Erosion, Third Institute of Physics, Georg-August-University Göttingen, 37077 Göttingen, Germany
Claus-Dieter Ohl
Affiliation:
Cavitation Lab, Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371, Singapore
Detlef Lohse
Affiliation:
Physics of Fluids Group, Mesa$+$ Institute and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500AE Enschede, The Netherlands Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
Jacco H. Snoeijer
Affiliation:
Physics of Fluids Group, Mesa$+$ Institute and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500AE Enschede, The Netherlands Mesoscopic Transport Phenomena, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands
Devaraj van der Meer
Affiliation:
Physics of Fluids Group, Mesa$+$ Institute and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500AE Enschede, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Drops and Bubbles: Drops Drops and Bubbles: Drops and Bubbles Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 792 , 10 April 2016 , pp. 850 - 868
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Copyright
© 2016 Cambridge University Press 

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References

Aristoff, J. M. & Bush, J. W. M. 2009 Water entry of small hydrophobic spheres. J. Fluid Mech. 93, 45–78.Google Scholar
Basaran, O. A., Gao, H. & Bhat, P. P. 2013 Nonstandard inkjets. Annu. Rev. Fluid Mech. 45, 85–113.Google Scholar
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, 381–409.Google Scholar
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.CrossRefGoogle ScholarPubMed
Bick, A. G., Ristenpart, W. D., van Nierop, E. A. & Stone, H. A. 2010 Bubble formation via multidrop impacts. Phys. Fluids 22, 042105.CrossRefGoogle Scholar
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, 193–221.CrossRefGoogle Scholar
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, 503–519.Google Scholar
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.Google Scholar
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.Google ScholarPubMed
Brenn, G. 2000 On the controlled production of sprays with discrete polydisperse drop size spectra. Chem. Engng Sci. 55 (22), 5437–5444.Google Scholar
Chen, S. & Guo, L. 2014 Viscosity effect on regular air bubble entrapment during drop impact into a deep pool. Chem. Engng Sci. 109, 1–16.CrossRefGoogle Scholar
Clanet, C. & Lasheras, J. C. 1997 Depth of penetration of bubbles entrained by a plunging water jet. Phys. Fluids 9 (7), 1864–1866.CrossRefGoogle Scholar
Davidson, M. R. 2002 Spreading of an inviscid drop impacting on a liquid film. Chem. Engng Sci. 57, 3639–3647.Google Scholar
Driessen, T. W., Jeurissen, R. J. M., Wijshoff, H., Toschi, F. & Lohse, D. 2013 Stability of viscous long filaments. Phys. Fluids 25, 062109.CrossRefGoogle Scholar
Duchemin, L., Eggers, J. & Josserand, C. 2003 Inviscid coalescence of drops. J. Fluid Mech. 487, 167–178.Google Scholar
Eggers, J., Fontelos, M. A., Leppinen, D. & Snoeijer, J. H. 2007 Theory of the collapsing axisymmetric cavity. Phys. Rev. Lett. 98, 094502.CrossRefGoogle ScholarPubMed
Eggers, J., Lister, J. R. & Stone, H. A. 1999 Coalescence of liquid drops. J. Fluid Mech. 401, 293–310.CrossRefGoogle Scholar
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, 1–12.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Gibson, I., Rosen, D. W. & Stucker, B. 2010 Additive Manufacturing Technologies, 12th edn. Springer.Google Scholar
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, 708–725.Google Scholar
Kedrinskii, V. K. 2005 Hydrodynamics of Explosion: Experiments and Models, 1st edn. Springer.Google Scholar
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.Google Scholar
Kersten, B., Ohl, C. D. & Prosperetti, A. 2003 Transient impact of a liquid column on a miscible liquid surface. Phys. Fluids 15, 821–824.Google Scholar
Kim, H. Y., Park, S. Y. & Min, K. 2003 Imaging the high-speed impact of microdrop on solid surface. Rev. Sci. Instrum. 74 (11), 4930–4937.CrossRefGoogle Scholar
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.Google Scholar
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, 2809–2820.Google Scholar
Lamb, H. 1957 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
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.CrossRefGoogle ScholarPubMed
Lindblad, N. R. & Schneider, J. R. 1965 Production of uniform-sized liquid droplets. J. Sci. Instrum. 42, 635–638.Google Scholar
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.Google Scholar
Oguz, H. N. & Prosperetti, A. 1993 Dynamics of bubble growth and detachment from a needle. J. Fluid Mech. 257, 111–145.CrossRefGoogle Scholar
Oguz, H. N., Prosperetti, A. & Kolaini, A. R. 1995 Air entrapment by a falling water mass. J. Fluid Mech. 294, 181–207.Google Scholar
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.Google Scholar
Pozrikidis, C. 1997 Introduction to Theoretical and Computational Fluid Dynamics, 1st edn. Oxford University Press.Google Scholar
Prosperetti, A. 1977 On the stability of spherically symmetric flows. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 62, 196–203.Google Scholar
Prosperetti, A. & Oguz, H. N. 1993 The impact of drops on liquid surfaces and the underwater noise of rain. Annu. Rev. Fluid Mech. 25, 577–602.Google Scholar
Pumphrey, H. C. & Elmore, P. A. 1990 The entrainment of bubbles by drop impacts. J. Fluid Mech. 220, 539–567.Google Scholar
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, 722–731.Google Scholar
Storr, G. J. & Behnia, M. 1999 Experiments with large diameter gravity driven impacting liquid jets. Exp. Fluids 27, 60–69.Google Scholar
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, 375–389.Google Scholar
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, 469–479.Google Scholar
Tran, T., de Maldeprade, H., Sun, C. & Lohse, D. 2013 Air entrainment during impact of droplets on liquid surfaces. J. Fluid Mech. 726, R3.Google Scholar
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), 1708–1722.Google Scholar
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.Google Scholar