Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-29T05:27:28.208Z Has data issue: false hasContentIssue false

Air entrainment during impact of droplets on liquid surfaces

Published online by Cambridge University Press:  06 June 2013

Tuan Tran*
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, University of Twente, 7500 AE Enschede, The Netherlands
Hélène de Maleprade
Affiliation:
Département de Mécanique, École Polytechnique, 91128 Palaiseau Cedex, France
Chao Sun*
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, University of Twente, 7500 AE Enschede, The Netherlands
Detlef Lohse*
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, University of Twente, 7500 AE Enschede, The Netherlands
*
Email addresses for correspondence: [email protected], [email protected], [email protected]
Email addresses for correspondence: [email protected], [email protected], [email protected]
Email addresses for correspondence: [email protected], [email protected], [email protected]

Abstract

We study drop impact on a deep pool of the same fluid, with an emphasis on the air layer trapped under the droplets from its formation to its rupture. The penetration velocity of the air layer at a very short time scale prior to its rupture is shown, using an energy argument and experimental verification, to be one-half of the impact velocity. We then deduce the dependence of the rupture position on the liquid viscosity and the impact velocity. We show that the volume of the resulting air bubbles can be related to both those resulting from droplets impacting on solid surfaces and those resulting from rigid spheres impacting on liquid surfaces.

Type
Rapids
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Birkhoff, G., MacDougall, D. P., Pugh, E. M. & Taylor, G. 1948 Explosives with lined cavities. J. Appl. Phys. 19 (6), 563582.Google Scholar
Bisighini, A., Cossali, G. E., Tropea, C. & Roisman, I. V. 2010 Crater evolution after the impact of a drop onto a semi-infinite liquid target. Phys. Rev. E 82, 036319.CrossRefGoogle ScholarPubMed
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
Chandra, S. & Avedisian, C. T. 1991 On the collision of a droplet with a solid surface. Proc. R. Soc. Lond. A 432, 1341.Google Scholar
Couder, Y., Fort, E., Gautier, C. H. & Boudaoud, A. 2005 From bouncing to floating: noncoalescence of drops on a fluid bath. Phys. Rev. Lett. 94, 177801.Google Scholar
van Dam, D. B. & Le Clerc, C. 2004 Experimental study of the impact of an ink-jet printed droplet on a solid substrate. Phys. Fluids 16, 34033414.Google Scholar
Deng, Q., Anilkumar, A. V. & Wang, T. G. 2010 The role of viscosity and surface tension in bubble entrapment during drop impact onto a deep liquid pool. J. Fluid Mech. 578, 119138.CrossRefGoogle Scholar
Dorbolo, S., Reyssat, E., Vandewalle, N. & Quéré, D. 2005 Aging of an antibubble. Eur. Phys. Lett. 69, 966970.Google Scholar
Duchemin, L. & Josserand, C. 2011 Curvature singularity and film-skating during drop impact. Phys. Fluids 23, 091701.Google Scholar
Duez, C., Christophe, Y., Clanet, C. & Bocquet, L. 2007 Making a splash with water repellency. Nat. Phys. 3 (3), 180183.CrossRefGoogle Scholar
Engel, O. G. 1967 Initial pressure, initial flow velocity, and the time dependence of crater depth in fluid impacts. J. Appl. Phys. 38 (10), 39353940.Google Scholar
Esmailizadeh, L. & Mesler, R. 1986 Bubble entrainment with drops. J. Colloid Interface Sci. 110 (2), 561574.Google Scholar
Hicks, P. D., Ermanyuk, E. V., Gavrilov, N. V. & Purvis, R. 2012 Air trapping at impact of a rigid sphere onto a liquid. J. Fluid Mech. 695, 310320.Google Scholar
Hicks, P. D. & Purvis, R. 2010 Air cushioning and bubble entrapment in three-dimensional droplet impacts. J. Fluid Mech. 649, 135163.CrossRefGoogle Scholar
Hicks, P. D. & Purvis, R. 2011 Air cushioning in droplet impacts with liquid layers and other droplets. Phys. Fluids 23, 062104.Google Scholar
Kolinski, J. M., Rubinstein, S. M., Mandre, S., Brenner, M. P., Weitz, D. A. & Mahadevan, L. 2012 Skating on a film of air: drops impacting on a surface. Phys. Rev. Lett. 108 (7), 074503.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 (20), 204501.CrossRefGoogle ScholarPubMed
Liu, Y., Tan, P. & Xu, L. 2013 Compressible air entrapment in high-speed drop impacts on solid surfaces. J. Fluid Mech. 716, doi:10.1017/jfm.2012.583.Google Scholar
Mandre, S. & Brenner, M. P. 2012 The mechanism of a splash on a dry solid surface. J. Fluid Mech. 690, 148172.CrossRefGoogle Scholar
Mandre, S., Mani, M. & Brenner, M. P. 2009 Precursors to splashing of liquid droplets on a solid surface. Phys. Rev. Lett. 102 (13), 134502.Google Scholar
Mani, M., Mandre, S. & Brenner, M. P. 2010 Events before droplet splashing on a solid surface. J. Fluid Mech. 647, 163185.Google Scholar
Marston, J. O., Vakarelski, I. U. & Thoroddsen, S. T. 2011 Bubble entrapment during sphere impact onto quiescent liquid surfaces. J. Fluid Mech. 680 (1), 660670.CrossRefGoogle 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 (1), 577602.CrossRefGoogle Scholar
Pumphrey, H. C., Crum, L. A. & Bjørnø, L. 1989 Underwater sound produced by individual drop impacts and rainfall. J. Acoust. Soc. Am. 85, 15181526.Google Scholar
Pumphrey, H. C. & Elmore, P. A. 1990 Entrainment of bubbles by drop impacts. J. Fluid Mech. 220, 539567.CrossRefGoogle Scholar
Rein, M. 1993 Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12 (2), 6193.Google Scholar
Saylor, J. & Bounds, G. D. 2012 Experimental study of the role of the Weber and capillary numbers on Mesler entrainment. AIChE J. 58 (12), 38413851.CrossRefGoogle Scholar
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2003 Air entrapment under an impacting drop. J. Fluid Mech. 478, 125134.Google Scholar
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.Google Scholar
Thoroddsen, S. T. & Sakakibara, J. 1998 Evolution of the fingering pattern of an impacting drop. Phys. Fluids 10, 13591374.CrossRefGoogle Scholar
Thoroddsen, S. T., Thoraval, M. J., Takehara, K. & Etoh, T. G. 2012 Micro-bubble morphologies following drop impacts onto a pool surface. J. Fluid Mech. 708, 469479.Google Scholar
Tran, T., Staat, H. J. J., Prosperetti, A., Sun, C. & Lohse, D. 2012 Drop impact on superheated surfaces. Phys. Rev. Lett. 108 (3), 036101.CrossRefGoogle ScholarPubMed
van der Veen, R. C. A., Tran, T., Lohse, D. & Sun, C. 2012 Direct measurements of air layer profiles under impacting droplets using high-speed color interferometry. Phys. Rev. E 85 (2), 026315.Google Scholar
Weiss, D. A. & Yarin, A. L. 1999 Single drop impact onto liquid films: neck distortion, jetting, tiny bubble entrainment, and crown formation. J. Fluid Mech. 385, 229254.CrossRefGoogle Scholar
Worthington, A. M. 1908 A Study of Splashes. Longmans, Green.Google Scholar
Xu, L., Zhang, W. W. & Nagel, S. R. 2005 Drop splashing on a dry smooth surface. Phys. Rev. Lett. 94 (18), 184505.Google Scholar
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159192.CrossRefGoogle Scholar
Yarin, A. L., Rubin, M. B. & Roisman, I. V. 1995 Penetration of a rigid projectile into an elastic–plastic target of finite thickness. Intl J. Impact Engng 16 (5), 801831.Google Scholar