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Air entrapment at impact of a conus onto a liquid
Published online by Cambridge University Press: 03 July 2023
Abstract
In this experimental work, a conus impacts a deep liquid pool at a speed varying from 1.3 to 
$19.0\ {\rm cm}\ {\rm s}^{-1}$. Two liquids (2.5 % butanol–water solution or distilled water) and four coni made from duralumin with a diameter of 180 mm and different deadrise angles 
$\beta$ (
$2^{\circ }$, 
$3^{\circ }$, 
$4^{\circ }$ and 5
$^{\circ }$) are tested. An air cushion is trapped between the conus solid surface and the liquid. Several types of bubble patterns after the collapse of the air cushion are observed: one or multiple bubbles near the conus centre (vertex), irregular trails of bubbles on the conus surface and a ring of bubbles in a ‘necklace’-shaped arrangement. With a total internal reflection set-up and appropriate image post-processing, the external and internal radii of the ring-shaped wetted area are estimated for each frame. The external (internal) radius increases (decreases) in time following a linear (exponential) law. The speed of the outer border of the wetted area is in agreement with the Wagner theory for a body impacting onto a liquid. The initial radius of the annular touchdown region is estimated as the intersection of the relevant fitting curves. In the studied range of parameters, the initial radius obeys a universal scaling law, which follows from the air–water lubrication–inertia balance.
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- JFM Rapids
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- © The Author(s), 2023. Published by Cambridge University Press
References
Bagg, J., Pitto, M. & Allen, T. 2022 Quantification of spatial free-surface air entrapment during rigid body impacts into a quiescent fluid. Ocean Engng 259, 112060.CrossRefGoogle Scholar
Carrat, J.-B., Shmakova, N.D., Cherdantsev, A.V., Gavrilov, N.V. & Ermanyuk, E.V. 2021 Initial stage of an oblique impact of a large solid sphere on a water layer. J. Appl. Mech. Tech. Phys. 62 (4), 616–623.CrossRefGoogle Scholar
Cherdantsev, A.V., Gavrilov, N.V. & Ermanyuk, E.V. 2021 Study of initial stage of entry of a solid sphere into shallow liquid with synthetic Schlieren technique. Exp. Therm. Fluid Sci. 125, 110375.CrossRefGoogle Scholar
Chuang, S.-L. 1970 Investigation of impact of rigid and elastic bodies with water. Tech. Rep. 3248. Department of the Naval Ship Research and Development Center, Washington, D.C.Google Scholar
Chuang, S.-L. & Milne, D.T. 1971 Drop tests of cones to investigate the three-dimensional effects of slamming. Tech. Rep. 3543. Defense Technical Information Center, Fort Belvoir, VA.CrossRefGoogle Scholar
Ermanyuk, E.V. & Gavrilov, N.V. 2011 Experimental study of disk impact onto shallow water. J. Appl. Mech. Tech. Phys. 52 (6), 889–895.CrossRefGoogle Scholar
Ermanyuk, E.V. & Ohkusu, M. 2005 Impact of a disk on shallow water. J. Fluids Struct. 20 (3), 345–357.CrossRefGoogle Scholar
Gao, Y., Jung, S. & Pan, L. 2019 Interaction forces between water droplets and solid surfaces across air films. ACS Omega 4 (15), 16674–16682.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.CrossRefGoogle 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
Jain, U. 2020 Slamming liquid impact and the mediating role of air. PhD, University of Twente, Enschede, The Netherlands.Google Scholar
Jain, U., Gauthier, A. & van der Meer, D. 2021 a Total-internal-reflection deflectometry for measuring small deflections of a fluid surface. Exp. Fluids 62 (11), 235.CrossRefGoogle Scholar
Jain, U., Vega-Martínez, P. & van der Meer, D. 2021 b Air entrapment and its effect on pressure impulses in the slamming of a flat disc on water. J. Fluid Mech. 928, A31.CrossRefGoogle Scholar
Josserand, C. & Thoroddsen, S.T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48 (1), 365–391.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Korobkin, A.A. & Pukhnachov, V.V. 1988 Initial stage of water impact. Annu. Rev. Fluid Mech. 20 (1), 159–185.CrossRefGoogle Scholar
Korobkin, A.A. & Scolan, Y.-M. 2006 Three-dimensional theory of water impact. Part 2. Linearized Wagner problem. J. Fluid Mech. 549 (-1), 343.CrossRefGoogle 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
Lee, J.S., Weon, B.M., Park, S.J., Kim, J.T., Pyo, J., Fezzaa, K. & Je, J.H. 2020 Air evolution during drop impact on liquid pool. Sci. Rep. 10 (1), 5790.CrossRefGoogle ScholarPubMed
Li, E.Q., Langley, K.R., Tian, Y.S., Hicks, P.D. & Thoroddsen, S.T. 2017 Double contact during drop impact on a solid under reduced air pressure. Phys. Rev. Lett. 119 (21), 214502.CrossRefGoogle ScholarPubMed
Li, E.Q. & Thoroddsen, S.T. 2015 Time-resolved imaging of a compressible air disc under a drop impacting on a solid surface. J. Fluid Mech. 780, 636–648.CrossRefGoogle Scholar
Liang, G. & Mudawar, I. 2016 Review of mass and momentum interactions during drop impact on a liquid film. Intl J. Heat Mass Transfer 101, 577–599.CrossRefGoogle Scholar
Liu, Y., Tan, P. & Xu, L. 2013 Compressible air entrapment in high-speed drop impacts on solid surfaces. J. Fluid Mech. 716, R9.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.CrossRefGoogle ScholarPubMed
Marston, J.O. & Thoroddsen, S.T. 2014 Ejecta evolution during cone impact. J. Fluid Mech. 752, 410–438.CrossRefGoogle 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.CrossRefGoogle Scholar
Mayer, H.C. & Krechetnikov, R. 2018 Flat plate impact on water. J. Fluid Mech. 850, 1066–1116.CrossRefGoogle Scholar
Moore, M.R. 2021 Introducing pre-impact air-cushioning effects into the Wagner model of impact theory. J. Engng Maths 129 (1), 6.CrossRefGoogle Scholar
Moore, M.R., Howison, S.D., Ockendon, J.R. & Oliver, J.M. 2012 Three-dimensional oblique water-entry problems at small deadrise angles. J. Fluid Mech. 711, 259–280.CrossRefGoogle Scholar
Okada, S. & Sumi, Y. 2000 On the water impact and elastic response of a flat plate at small impact angles. J. Mar. Sci. Technol. 5 (1), 31–39.CrossRefGoogle Scholar
Ross, S. & Hicks, P.D. 2019 A comparison of pre-impact gas cushioning and Wagner theory for liquid-solid impacts. Phys. Fluids 31 (4), 042101.CrossRefGoogle Scholar
Schmieden, C. 1953 Der Aufschlag von Rotationskörpern auf eine Wasseroberfläche. Richard v. Mises zum 70. Geburtstag gewidmet. Z. Angew. Math. Mech. 33 (4), 147–151.CrossRefGoogle Scholar
Thoroddsen, S.T., Etoh, T.G. & Takehara, K. 2003 Air entrapment under an impacting drop. J. Fluid Mech. 478, 125–134.CrossRefGoogle 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 (-1), 203.CrossRefGoogle Scholar
Wagner, H. 1932 Über Stoß- und Gleitvorgänge an der Oberfläche von Flüssigkeiten. Z. Angew. Math. Mech. 12 (4), 193–215.CrossRefGoogle Scholar
Carrat et al. Supplementary Movie 1
Typical impact event. Experimental conditions : liquid BWS, V = 4.2 cm/s and β = 2°.
Video
8.3 MB
Carrat et al. Supplementary Movie 2
One bubble. Experimental conditions : liquid BWS, V = 7.7 cm/s and β = 2°.
Video
6.9 MB
Carrat et al. Supplementary Movie 3
Multiple bubbles. Experimental conditions : liquid BWS, V = 4.9 cm/s and β = 2°.
Video
6.7 MB
Carrat et al. Supplementary Movie 4
Trail of bubbles. Experimental conditions : liquid BWS, V = 2.0 cm/s and β = 3°.
Video
7.4 MB
Carrat et al. Supplementary Movie 5
Ring of bubbles in regular “necklace” arrangement. Experimental conditions : liquid BWS, V = 1.4 cm/s and β = 3
Video
8.3 MB