Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-25T11:09:09.970Z Has data issue: false hasContentIssue false
  • English
  • Français

Universal mechanism for air entrainment during liquid impact

Published online by Cambridge University Press:  26 January 2016

Maurice H. W. Hendrix ,
Wilco Bouwhuis ,
Devaraj van der Meer ,
Detlef Lohse  and
Jacco H. Snoeijer
Maurice H. W. Hendrix*
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands Laboratory for Aero and Hydrodynamics, Delft University of Technology, Leeghwaterstraat 21, NL-2628 CA Delft, The Netherlands
Wilco Bouwhuis
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands
Devaraj van der Meer
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands
Detlef Lohse
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands
Jacco H. Snoeijer
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands Mesoscopic Transport Phenomena, Eindhoven University of Technology, Den Dolech 2, 5612 AZ Eindhoven, The Netherlands
*
†Email address for correspondence: m.h.hendrix@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

When a millimetre-sized liquid drop approaches a deep liquid pool, both the interface of the drop and the pool deform before the drop touches the pool. The build-up of air pressure prior to coalescence is responsible for this deformation. Due to this deformation, air can be entrained at the bottom of the drop during the impact. We quantify the amount of entrained air numerically, using the boundary integral method for potential flow for the drop and the pool, coupled to viscous lubrication theory for the air film that has to be squeezed out during impact. We compare our results with various experimental data and find excellent agreement for the amount of air that is entrapped during impact onto a pool. Next, the impact of a rigid sphere onto a pool is numerically investigated and the air that is entrapped in this case also matches with available experimental data. In both cases of drop and sphere impact onto a pool the numerical air bubble volume $V_{b}$ is found to be in agreement with the theoretical scaling $V_{b}/V_{drop/sphere}\sim \mathit{St}^{-4/3}$, where $\mathit{St}$ is the Stokes number. This is the same scaling as has been found for drop impact onto a solid surface in previous research. This implies a universal mechanism for air entrainment for these different impact scenarios, which has been suggested in recent experimental work, but is now further elucidated with numerical results.

JFM classification

Drops and Bubbles: Drops and Bubbles Low-Reynolds-number flows: Lubrication theory Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 789 , 25 February 2016 , pp. 708 - 725
Check for updates
Copyright
© 2016 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

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 (26), 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 (2), 023017.Google Scholar
Chen, S. & Guo, L. 2014 Viscosity effect on regular bubble entrapment during drop impact into a deep pool. Chem. Engng Sci. 109, 1–16.CrossRefGoogle 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 (9), 3403–3414.Google Scholar
Esmailizadeh, L. & Mesler, R. 1986 Bubble entrainment with drops. J. Colloid Interface Sci. 110 (2), 561–574.CrossRefGoogle Scholar
Gekle, S. & Gordillo, J. M. 2011 Compressible air flow through a collapsing liquid cavity. Intl J. Numer. Meth. Fluids 67 (11), 1456–1469.CrossRefGoogle Scholar
Guo, Y., Wei, L., Liang, G. & Shen, S. 2014 Simulation of droplet impact on liquid film with CLSVOF. Intl Commun. Heat Mass Transfer 53, 26–33.CrossRefGoogle Scholar
Hendrix, M. H. W., Manica, R., Klaseboer, E., Chan, D. Y. C. & Ohl, C. D. 2012 Spatiotemporal evolution of thin liquid films during impact of water bubbles on glass on a micrometer to nanometer scale. Phys. Rev. Lett. 108 (24), 247803.CrossRefGoogle ScholarPubMed
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, 310–320.Google Scholar
Hicks, P. D. & Purvis, R. 2010 Air cushioning and bubble entrapment in three-dimensional droplet impacts. J. Fluid Mech. 649, 135–163.CrossRefGoogle Scholar
Hicks, P. D. & Purvis, R. 2011 Air cushioning in droplet impacts with liquid layers and other droplets. Phys. Fluids 23 (6), 062104.Google Scholar
Klaseboer, E., Chevaillier, J. P., Gourdon, C. & Masbernat, O. 2000 Film drainage between colliding drops at constant approach velocity: experiments and modeling. J. Colloid Interface Sci. 229 (1), 274–285.Google Scholar
Klaseboer, E., Manica, R. & Chan, D. Y. C. 2014 Universal behavior of the initial stage of drop impact. Phys. Rev. Lett. 113 (19), 194501.CrossRefGoogle ScholarPubMed
Korobkin, A. A., Ellis, A. S. & Smith, F. T. 2008 Trapping of air in impact between a body and shallow water. J. Fluid Mech. 611, 365–394.Google Scholar
Leal, L. Gary 1992 Laminar Flow and Convective Transport Processes, pp. 345–448. Butterworth-Heinemann.Google 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.CrossRefGoogle ScholarPubMed
Mani, M., Mandre, S. & Brenner, M. P. 2010 Events before droplet splashing on a solid surface. J. Fluid Mech. 647, 163–185.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, 660–670.Google Scholar
Oguz, H. N. & Prosperetti, A. 1990 Bubble entrainment by the impact of drops on liquid surfaces. J. Fluid Mech. 219, 143–179.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
Pumphrey, H. C. & Elmore, P. A. 1990 Entrainment of bubbles by drop impacts. J. Fluid Mech. 220, 539–567.CrossRefGoogle Scholar
Saylor, J. R. & Bounds, G. D. 2012 Experimental study of the role of the Weber and capillary numbers on Mesler entrainment. AIChE J. 58 (12), 3841–3851.Google Scholar
Sun, Q., Klaseboer, E., Khoo, B. C. & Chan, D. Y. C. 2014 A robust and non-singular formulation of the boundary integral method for the potential problem. Engng Anal. Bound. Elem. 43, 117–123.CrossRefGoogle Scholar
Thoraval, M., Takehara, K., Etoh, T. G., Popinet, S., Ray, P., Josserand, C., Zaleski, S. & Thoroddsen, S. T. 2012 von Kármán vortex street within an impacting drop. Phys. Rev. Lett. 108 (26), 264506.Google Scholar
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2003 Air entrapment under an impacting drop. J. Fluid Mech. 478, 125–134.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, 203–212.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, 469–479.CrossRefGoogle Scholar
Tran, T., De Maleprade, H., Sun, C. & Lohse, D. 2013 Air entrainment during impact of droplets on liquid surfaces. J. Fluid Mech. 726, R3.CrossRefGoogle Scholar
van der Veen, R. C. A., Hendrix, M. H. W., Tran, T., Sun, C., Tsai, P. A. & Lohse, D. 2014 How microstructures affect air film dynamics prior to drop impact. Soft Matt. 10 (21), 3703–3707.Google Scholar
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
Wang, A., Kuan, C. & Tsai, P. 2013 Do we understand the bubble formation by a single drop impacting upon liquid surface? Phys. Fluids 25 (10), 101702.Google Scholar