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Role of melting and solidification in the spreading of an impacting water drop

Published online by Cambridge University Press:  03 October 2024

Wladimir Sarlin Open the ORCID record for Wladimir Sarlin [Opens in a new window] ,
Rodolphe Grivet Open the ORCID record for Rodolphe Grivet [Opens in a new window] ,
Julien Xu ,
Axel Huerre Open the ORCID record for Axel Huerre [Opens in a new window] ,
Thomas Séon Open the ORCID record for Thomas Séon [Opens in a new window]  and
Christophe Josserand Open the ORCID record for Christophe Josserand [Opens in a new window]
Wladimir Sarlin*
Affiliation:
Laboratoire d'Hydrodynamique, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
Rodolphe Grivet
Affiliation:
Laboratoire d'Hydrodynamique, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
Julien Xu
Affiliation:
Laboratoire d'Hydrodynamique, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
Axel Huerre
Affiliation:
Laboratoire Matière et Systèmes Complexes (MSC), UMR CNRS 7057, Université Paris Cité, 75013 Paris, France
Thomas Séon
Affiliation:
Institut Franco-Argentin de Dynamique des Fluides pour l'Environnement (IFADyFE), IRL 2027, CNRS, UBA, CONICET, Buenos Aires, Argentine
Christophe Josserand*
Affiliation:
Laboratoire d'Hydrodynamique, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
*
†Email addresses for correspondence: wladimirsarlin@outlook.com, christophe.josserand@ladhyx.polytechnique.fr
†Email addresses for correspondence: wladimirsarlin@outlook.com, christophe.josserand@ladhyx.polytechnique.fr
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Abstract

The present study reports experiments of water droplets impacting on ice or on a cold metal substrate, with the aim of understanding the effects of liquid solidification or substrate melting on the impingement process. Both liquid and substrate temperatures are varied, as well as the height of fall of the droplet. The dimensionless maximum spreading diameter, $\beta _m$, is found to increase with both temperatures as well as with the impact velocity. Here $\beta _m$ is reduced when liquid solidification, which enhances dissipation, is present, whereas fusion, i.e. substrate melting, favours the spreading of the impacting droplet. These observations are rationalized by extending an existing model of effective viscosity, in which phase change alters the size and shape of the developing viscous boundary layer, thereby modifying the value of $\beta _m$. The use of this correction allows us to adapt a scaling recently developed in the context of isothermal drop impacts to propose a law giving the maximum diameter of an impacting water droplet in the presence of melting or solidification. Finally, additional experiments of dimethyl sulfoxide drop impacts onto a cold brass substrate have been performed and are also captured by the proposed modelling, generalizing our results to other fluids.

JFM classification

Drops and Bubbles: Drops Phase change: Solidification/melting
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 996 , 10 October 2024 , A14
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Antonini, C., Bernagozzi, I., Jung, S., Poulikakos, D. & Marengo, M. 2013 Water drops dancing on ice: how sublimation leads to drop rebound. Phys. Rev. Lett. 111, 014501.10.1103/PhysRevLett.111.014501CrossRefGoogle ScholarPubMed
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.2018.02.008CrossRefGoogle Scholar
Blanken, N., Saleem, M.S., Thoraval, M.-J. & Antonini, C. 2021 Impact of compound drops: a perspective. Curr. Opin. Colloid Interface Sci. 51, 101389.10.1016/j.cocis.2020.09.002CrossRefGoogle Scholar
Breitenbach, J., Roisman, I.V. & Tropea, C. 2018 From drop impact physics to spray cooling models: a critical review. Exp. Fluids 59 (3), 55.10.1007/s00348-018-2514-3CrossRefGoogle Scholar
Chandra, S. & Avedisian, C.T. 1991 On the collision of a droplet with a solid surface. Proc. R. Soc. Lond. A 432 (1884), 13–41.Google Scholar
Cheng, X., Sun, T.-P. & Gordillo, L. 2022 Drop impact dynamics: impact force and stress distributions. Annu. Rev. Fluid Mech. 54 (1), 57–81.10.1146/annurev-fluid-030321-103941CrossRefGoogle Scholar
Dehaoui, A., Issenmann, B. & Caupin, F. 2015 Viscosity of deeply supercooled water and its coupling to molecular diffusion. Proc. Natl Acad. Sci. USA 112 (39), 12020–12025.10.1073/pnas.1508996112CrossRefGoogle ScholarPubMed
Eggers, J., Fontelos, M.A., Josserand, C. & Zaleski, S. 2010 Drop dynamics after impact on a solid wall: theory and simulations. Phys. Fluids 22 (6), 062101.10.1063/1.3432498CrossRefGoogle Scholar
Ghabache, E., Josserand, C. & Séon, T. 2016 Frozen impacted drop: from fragmentation to hierarchical crack patterns. Phys. Rev. Lett. 117, 074501.10.1103/PhysRevLett.117.074501CrossRefGoogle ScholarPubMed
Gielen, M.V., de Ruiter, R., Koldeweij, R.B.J., Lohse, D., Snoeijer, J.H. & Gelderblom, H. 2020 Solidification of liquid metal drops during impact. J. Fluid Mech. 883, A32.10.1017/jfm.2019.886CrossRefGoogle Scholar
Huerre, A., Monier, A., Séon, T. & Josserand, C. 2021 Solidification of a rivulet: shape and temperature fields. J. Fluid Mech. 914, A32.10.1017/jfm.2021.41CrossRefGoogle Scholar
Jin, Z., Zhang, H. & Yang, Z. 2017 Experimental investigation of the impact and freezing processes of a water droplet on an ice surface. Intl J. Heat Mass Transfer 109, 716–724.10.1016/j.ijheatmasstransfer.2017.02.055CrossRefGoogle Scholar
Josserand, C. & Thoroddsen, S.T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48, 365–391.10.1146/annurev-fluid-122414-034401CrossRefGoogle Scholar
Joung, Y.S. & Buie, C.R. 2015 Aerosol generation by raindrop impact on soil. Nat. Commun. 6 (1), 6083.10.1038/ncomms7083CrossRefGoogle ScholarPubMed
Ju, J., Yang, Z., Yi, X. & Jin, Z. 2019 Experimental investigation of the impact and freezing processes of a hot water droplet on an ice surface. Phys. Fluids 31 (5), 057107.10.1063/1.5094691CrossRefGoogle Scholar
Laan, N., de Bruin, K.G., Bartolo, D., Josserand, C. & Bonn, D. 2014 Maximum diameter of impacting liquid droplets. Phys. Rev. Appl. 2, 044018.10.1103/PhysRevApplied.2.044018CrossRefGoogle Scholar
Lagubeau, G., Fontelos, M.A., Josserand, C., Maurel, A., Pagneux, V. & Petitjeans, P. 2012 Spreading dynamics of drop impacts. J. Fluid Mech. 713, 50–60.10.1017/jfm.2012.431CrossRefGoogle Scholar
Lee, J.B., Laan, N., de Bruin, K.G., Skantzaris, G., Shahidzadeh, N., Derome, D., Carmeliet, J. & Bonn, D. 2016 Universal rescaling of drop impact on smooth and rough surfaces. J. Fluid Mech. 786, R4.10.1017/jfm.2015.620CrossRefGoogle Scholar
Liang, G. & Mudawar, I. 2017 Review of drop impact on heated walls. Intl J. Heat Mass Transfer 106, 103–126.10.1016/j.ijheatmasstransfer.2016.10.031CrossRefGoogle Scholar
Liu, L., Cai, G. & Tsai, P.A. 2020 Drop impact on heated nanostructures. Langmuir 36 (34), 10051–10060.10.1021/acs.langmuir.0c01151CrossRefGoogle ScholarPubMed
Lohse, D. 2022 Fundamental fluid dynamics challenges in inkjet printing. Annu. Rev. Fluid Mech. 54, 349–382.CrossRefGoogle Scholar
Lolla, V.Y., Ahmadi, S.F., Park, H., Fugaro, A.P. & Boreyko, J.B. 2022 Arrested dynamics of droplet spreading on ice. Phys. Rev. Lett. 129, 074502.10.1103/PhysRevLett.129.074502CrossRefGoogle ScholarPubMed
Madejski, J. 1976 Solidification of droplets on a cold surface. Intl J. Heat Mass Transfer 19 (9), 1009–1013.CrossRefGoogle Scholar
Moita, A.S., Moreira, A.L.N. & Roisman, I.V. 2010 Heat transfer during drop impact onto a heated solid substrate. In 14th International Heat Transfer Conference, vol. 6, pp. 803–810. ASME.CrossRefGoogle Scholar
Pasandideh-Fard, M., Bhola, R., Chandra, S. & Mostaghimi, J. 1998 Deposition of tin droplets on a steel plate: simulations and experiments. Intl J. Heat Mass Transfer 41 (19), 2929–2945.CrossRefGoogle Scholar
Pasandideh-Fard, M., Pershin, V., Chandra, S. & Mostaghimi, J. 2002 Splat shapes in a thermal spray coating process: simulations and experiments. J. Therm. Spray Technol. 11, 206–217.CrossRefGoogle Scholar
Pátek, J., Součková, M. & Klomfar, J. 2016 Generation of recommendable values for the surface tension of water using a nonparametric regression. J. Chem. Engng Data 61 (2), 928–935.10.1021/acs.jced.5b00776CrossRefGoogle Scholar
Pátek, J., Hrubý, J., Klomfar, J., Součková, M. & Harvey, A.H. 2009 Reference correlations for thermophysical properties of liquid water at 0.1 MPa. J. Phys. Chem. Ref. Data 38 (1), 21–29.10.1063/1.3043575CrossRefGoogle Scholar
Quéré, D. 2013 Leidenfrost dynamics. Annu. Rev. Fluid Mech. 45, 197–215.CrossRefGoogle Scholar
Roisman, I.V. 2010 Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition. J. Fluid Mech. 656, 189–204.10.1017/S0022112010001126CrossRefGoogle Scholar
Rubinshteĭn, L.I. 1971 The Stefan Problem, 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), 35–39.CrossRefGoogle 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.CrossRefGoogle Scholar
Shirota, M., van Limbeek, M.A.J., Sun, C., Prosperetti, A. & Lohse, D. 2016 Dynamic Leidenfrost effect: relevant time and length scales. Phys. Rev. Lett. 116, 064501.CrossRefGoogle ScholarPubMed
Shukla, R.K. & Kumar, A. 2015 Substrate melting and re-solidification during impact of high-melting point droplet material. J. Therm. Spray Technol. 24 (8), 1368–1376.10.1007/s11666-015-0326-zCrossRefGoogle Scholar
Staat, H.J.J., Tran, T., Geerdink, B., Riboux, G., Sun, C., Gordillo, J.M. & Lohse, D. 2015 Phase diagram for droplet impact on superheated surfaces. J. Fluid Mech. 779, R3.10.1017/jfm.2015.465CrossRefGoogle Scholar
Thiévenaz, V. 2019 Impact et solidification de gouttes d'eau. PhD thesis, Sorbonne Université.Google Scholar
Thiévenaz, V., Séon, T. & Josserand, C. 2019 Solidification dynamics of an impacted drop. J. Fluid Mech. 874, 756–773.10.1017/jfm.2019.459CrossRefGoogle Scholar
Thiévenaz, V., Séon, T. & Josserand, C. 2020 Freezing-damped impact of a water drop. Europhysics. Lett. 132 (2), 24002.CrossRefGoogle Scholar
Tran, T., Staat, H.J.J., Prosperetti, A., Sun, C. & Lohse, D. 2012 Drop impact on superheated surfaces. Phys. Rev. Lett. 108, 036101.CrossRefGoogle ScholarPubMed
Wang, C.-H., Tsai, H.-L., Wu, Y.-C. & Hwang, W.-S. 2016 Investigation of molten metal droplet deposition and solidification for 3D printing techniques. J. Micromech. Microengng 26 (9), 095012.10.1088/0960-1317/26/9/095012CrossRefGoogle Scholar
Yuge, T. 1960 Experiments on heat transfer from spheres including combined natural and forced convection. Trans. ASME J. Heat Transfer 82 (3), 214–220.CrossRefGoogle Scholar
Zhao, R., Zhang, Q., Tjugito, H. & Cheng, X. 2015 Granular impact cratering by liquid drops: understanding raindrop imprints through an analogy to asteroid strikes. Proc. Natl Acad. Sci. USA 112 (2), 342–347.10.1073/pnas.1419271112CrossRefGoogle ScholarPubMed