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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: [email protected]
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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
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Copyright
© 2016 Cambridge University Press 

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