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Solidification dynamics of an impacted drop

Published online by Cambridge University Press:  12 July 2019

V. Thiévenaz ,
T. Séon Open the ORCID record for T. Séon [Opens in a new window]  and
C. Josserand Open the ORCID record for C. Josserand [Opens in a new window]
V. Thiévenaz
Affiliation:
Sorbonne Université, CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, F-75005 Paris, France
T. Séon*
Affiliation:
Sorbonne Université, CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, F-75005 Paris, France
C. Josserand
Affiliation:
Laboratoire d’Hydrodynamique (LadHyX), UMR7646 CNRS-Ecole Polytechnique, 91128 Palaiseau CEDEX, France
*
†Email address for correspondence: [email protected]
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Abstract

This paper is dedicated to the solidification of a water drop impacting a cold solid surface. In the first part, we establish a one-dimensional (1-D) solidification model, derived from the Stefan problem, that aims at predicting the freezing dynamics of a liquid on a cold substrate, taking into account the thermal properties of this substrate. This model is then experimentally validated through a 1-D solidification set-up, using different liquids and substrates. In the second part, we show that during the actual drop spreading, a thin layer of ice develops between the water and the substrate and pins the contact line at its edge when the drop reaches its maximal diameter. The liquid film then remains still on the ice and keeps freezing. This configuration lasts until the contact line eventually unpins and the liquid film retracts on the ice. We measure and interpret this crucial time of freezing during which the main ice layer is built. Finally, we compare our 1-D model prediction to the thickness of this ice pancake and we find a very good agreement. This allows us to provide a general expression for the frozen drop’s main thickness, using the drop’s impact and liquid parameters.

JFM classification

Drops and Bubbles: Drops Phase change: Solidification/melting
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 756 - 773
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Copyright
© 2019 Cambridge University Press 

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References

von Allmen, M. & Blatter, A. 2013 Laser–Beam Interactions with Materials: Physical Principles and Applications, vol. 2. Springer Science & Business Media.Google Scholar
Anderson, D. M., Worster, M. G. & Davis, S. H. 1996 The case for a dynamic contact angle in containerless solidification. J. Cryst. Growth 163 (3), 329–338.10.1016/0022-0248(95)00970-1Google Scholar
Bartolo, D., Josserand, C. & Bonn, D. 2005 Retraction dynamics of aqueous drops upon impact on non-wetting surfaces. J. Fluid Mech. 545, 329–338.10.1017/S0022112005007184Google Scholar
Baumert, A., Bansmer, S., Trontin, P. & Villedieu, P. 2018 Experimental and numerical investigations on aircraft icing at mixed phase conditions. Intl J. Heat Mass Transfer 123, 957–978.10.1016/j.ijheatmasstransfer.2018.02.008Google Scholar
Brillouin, M. 1930 Sur quelques problèmes non résolus de la physique mathématique classique propagation de la fusion. Ann. Inst. Henri Poincaré 1, 285–308.Google Scholar
Cao, L., Jones, A. K., Sikka, V. K., Wu, J. & Gao, D. 2009 Anti-icing superhydrophobic coatings. Langmuir 25 (21), 12444–12448.10.1021/la902882bGoogle Scholar
Chandra, S. & Fauchais, P. 2009 Formation of solid splats during thermal spray deposition. J. Thermal Spray Technol. 18, 148–180.10.1007/s11666-009-9294-5Google Scholar
Cline, H. E. & Anthony, T. R. 1977 Heat treating and melting material with a scanning laser or electron beam. J. Appl. Phys. 48 (9), 3895–3900.10.1063/1.324261Google Scholar
De Ruiter, R., Colinet, P., Brunet, P., Snoeijer, J. H. & Gelderblom, H. 2017 Contact line arrest in solidifying spreading drops. Phys. Rev. Fluids 2 (4), 043602.10.1103/PhysRevFluids.2.043602Google Scholar
Dhiman, R. & Chandra, S. 2005 Freezing-induced splashing during impact of molten metal droplets with high Weber numbers. Intl J. Heat Mass Transfer 48, 5625–5638.10.1016/j.ijheatmasstransfer.2005.05.044Google Scholar
Dhiman, R., McDonald, A. G. & Chandra, S. 2007 Predicting splat morphology in a thermal spray process. Surf. Coatings Technol. 201 (18), 7789–7801.10.1016/j.surfcoat.2007.03.010Google Scholar
Fauchais, P., Vardelle, A., Vardelle, M. & Fukumoto, M. 2004 Knowledge concerning splat formation: an invited review. J. Thermal Spray Technol. 13 (3), 337–360.10.1361/10599630419670Google Scholar
Font, F., Afkhami, S. & Kondic, L. 2017 Substrate melting during laser heating of nanoscale metal films. Intl J. Heat Mass Transfer 113, 237–245.10.1016/j.ijheatmasstransfer.2017.05.072Google Scholar
Gao, F. & Sonin, A. A. 1994 Precise deposition of molten microdrops: the physics of digital microfabrication. Proc. R. Soc. Lond. A 444 (1922), 533–554.Google Scholar
Ghabache, E., Josserand, C. & Séon, T. 2016 Frozen impacted drop: from fragmentation to hierarchical crack patterns. Phys. Rev. Lett. 117 (7), 074501.10.1103/PhysRevLett.117.074501Google Scholar
Griffiths, R. W. 2000 The dynamics of lava flows. Annu. Rev. Fluid Mech. 32 (1), 477–518.10.1146/annurev.fluid.32.1.477Google Scholar
Gupta, S. C. 2003 The Classical Stefan Problem – Basic Concepts, Modelling and Analysis. Elsevier.Google Scholar
Hauk, T., Bonaccurso, E., Roisman, I. V. & Tropea, C. 2015 Ice crystal impact onto a dry solid wall. Particle fragmentation. Proc. R. Soc. Lond. A 471, 20150399.Google Scholar
Huppert, H. E. 1986 The intrusion of fluid mechanics into geology. J. Fluid Mech. 173, 557–594.10.1017/S0022112086001271Google Scholar
Huppert, H. E. 1989 Phase changes following the initiation of a hot turbulent flow over a cold solid surface. J. Fluid Mech. 198, 293–319.10.1017/S0022112089000145Google Scholar
Jones, K. F.1996 Ice accretion in freezing rain. Tech. Rep. Cold Regions Research and Engineering Lab Hanover NH.10.21236/ADA310659Google Scholar
Jones, K. F. 1998 A simple model for freezing rain ice loads. Atmos. Res. 46 (1–2), 87–97.10.1016/S0169-8095(97)00053-7Google Scholar
Josserand, C. & Thoroddsen, S. T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48, 365–391.10.1146/annurev-fluid-122414-034401Google Scholar
Knight, C. A. 1971 Experiments on the contact angle of water on ice. Phil. Mag. 23 (181), 153–165.10.1080/14786437108216369Google Scholar
Kreder, M. J., Alvarenga, J., Kim, P. & Aizenberg, J. 2016 Design of anti-icing surfaces: smooth, textured or slippery? Nat. Rev. Mater. 1 (1), 15003.10.1038/natrevmats.2015.3Google Scholar
Laan, N., de Bruin, K. G., Bartolo, D., Josserand, C. & Bonn, D. 2014 Maximum diameter of impacting liquid droplets. Phys. Rev. Appl. 2 (4), 044018.10.1103/PhysRevApplied.2.044018Google Scholar
Lamé, G. & Clapeyron, B. P. 1831 Mémoire sur la solidification par refroidissement d’un globe liquide. Ann. Chim. Phys. 47, 250–256.Google Scholar
Langer, J. S. 1980 Instabilities and pattern formation in crystal growth. Rev. Mod. Phys. 52 (1), 1.10.1103/RevModPhys.52.1Google Scholar
Lipson, H. & Kurman, M. 2013 Fabricated: The New World of 3D Printing. Wiley.Google Scholar
Marin, A. G., Enriquez, O. R., Brunet, P., Colinet, P. & Snoeijer, J. H. 2014 Universality of tip singularity formation in freezing water drops. Phys. Rev. Lett. 113 (5), 054301.10.1103/PhysRevLett.113.054301Google Scholar
Neufeld, J. A., Goldstein, R. E. & Worster, M. G. 2010 On the mechanisms of icicle evolution. J. Fluid Mech. 647, 287–308.10.1017/S0022112009993910Google Scholar
Nishinaga, T. 2014 Handbook of Crystal Growth: Fundamentals. Elsevier.Google Scholar
Pasandideh-Fard, M., Pershin, V., Chandra, S. & Mostaghimi, J. 2002 Splat shapes in a thermal spray coating process: simulations and experiments. J. Thermal Spray Technol. 11 (2), 206–217.10.1361/105996302770348862Google Scholar
Rivetti, M., Salez, T., Benzaquen, M., Raphaël, E. & Bäumchen, O. 2015 Universal contact-line dynamics at the nanoscale. Soft Matt. 11 (48), 9247–9253.10.1039/C5SM01907AGoogle Scholar
Rubinstein, L. I. 1971 The Stefan Problem, Translations of Mathematical Monographs, vol. 27. American Mathematical Society.Google Scholar
de Ruiter, J., Soto, D. & Varanasi, K. K. 2018 Self-peeling of impacting droplets. Nat. Phys. 14 (1), 35.10.1038/nphys4252Google Scholar
Schiaffino, S. & Sonin, A. A. 1997 Motion and arrest of a molten contact line on a cold surface: an experimental study. Phys. Fluids 9 (8), 2217–2226.10.1063/1.869344Google Scholar
Schremb, M., Roisman, I. V. & Tropea, C. 2018 Normal impact of supercooled water drops onto a smooth ice surface: experiments and modelling. J. Fluid Mech. 835, 1087–1107.10.1017/jfm.2017.797Google Scholar
Snoeijer, J. H. & Brunet, P. 2012 Pointy ice-drops: how water freezes into a singular shape. Am. J. Phys. 80 (9), 764–771.10.1119/1.4726201Google Scholar
Stefan, J. 1891 Über die theorie der eisbildung, insbesondere über die eisbildung im polarmeere. Ann. Phys. Chem. 42, 269–286.10.1002/andp.18912780206Google Scholar
Tavakoli, F., Davis, S. H. & Kavehpour, H. P. 2014 Spreading and arrest of a molten liquid on cold substrates. Langmuir 30 (34), 10151–10155.10.1021/la5017998Google Scholar
Vidaurre, G. & Hallett, J. 2009 Particle impact and breakup in aircraft measurement. J. Atmos. Ocean. Technol. 26, 972–983.10.1175/2008JTECHA1147.1Google Scholar
Viskanta, R. 1988 Heat transfer during melting and solidification of metals. Trans. ASME J. Heat Transfer 110 (4b), 1205–1219.10.1115/1.3250621Google Scholar
Worster, M. G. 2000 Solidification of fluids. In Perspectives in Fluid Dynamics: A Collective Introduction to Current Research. Cambridge University Press.Google Scholar