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Droplet impacts on cold surfaces

Published online by Cambridge University Press:  28 June 2022

B. Gorin Open the ORCID record for B. Gorin [Opens in a new window] ,
D. Bonn Open the ORCID record for D. Bonn [Opens in a new window]  and
H. Kellay Open the ORCID record for H. Kellay [Opens in a new window]
B. Gorin*
Affiliation:
Van der Waals Zeeman Institute, University of Amsterdam, 1018 XE Amsterdam, The Netherlands Laboratoire Ondes et Matière d'Aquitaine, Université de Bordeaux, 33400 Talence, France
D. Bonn*
Affiliation:
Van der Waals Zeeman Institute, University of Amsterdam, 1018 XE Amsterdam, The Netherlands
H. Kellay*
Affiliation:
Laboratoire Ondes et Matière d'Aquitaine, Université de Bordeaux, 33400 Talence, France
*
†Email addresses for correspondence: benjamin.gorin@u-bordeaux.fr, d.bonn@uva.nl, hamid.kellay@u-bordeaux.fr
†Email addresses for correspondence: benjamin.gorin@u-bordeaux.fr, d.bonn@uva.nl, hamid.kellay@u-bordeaux.fr
†Email addresses for correspondence: benjamin.gorin@u-bordeaux.fr, d.bonn@uva.nl, hamid.kellay@u-bordeaux.fr
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Abstract

We study drop impact for the case where the impacted surface is cooled below the freezing temperature of the liquid droplet. The freezing is found to affect the spreading dynamics of the impacting drops and, thus, the degree of surface coverage. The cooling of the surface leads to the arrest of the three-phase contact line, impeding droplet spreading and, thus, drastically reducing the maximum spreading diameter. Besides the surface temperature, the impact speed is also an important parameter: the higher the impact speed, the more the droplet spreads before arrest. Based on experimental observations of droplet impacts using two different liquids and two different substrates, we show using a combination of experiments and a one-dimensional freezing model, that droplet arrest occurs when a solid layer of the liquid forms on the substrate: droplet arrest occurs when this solid layer reaches a well-defined critical thickness. We then devise a simple model that efficiently predicts the maximum spreading diameter of droplets impinging, at different velocities, and freezing onto surfaces maintained at different temperatures below the liquid freezing point.

JFM classification

Drops and Bubbles: Drops Interfacial Flows (free surface): Contact lines
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 944 , 10 August 2022 , A23
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Bartolo, D., Josserand, C. & Bonn, D. 2005 Retraction dynamics of aquous drops upon impact on non-wetting surfaces. J. Fluid Mech. 545 (1), 329–338.10.1017/S0022112005007184CrossRefGoogle Scholar
Biance, A.-L., Clanet, C. & Quéré, D. 2003 Leidenfrost drops. Phys. Fluids 15 (6), 1632–1637.10.1063/1.1572161CrossRefGoogle Scholar
Biance, A.-L., Clanet, C. & Quéré, D. 2004 First steps in the spreading of a liquid droplet. Phys. Rev. E 69 (1), 016301.10.1103/PhysRevE.69.016301CrossRefGoogle ScholarPubMed
Cebeci, T. & Kafyeke, F. 2003 Aircraft icing. Annu. Rev. Fluid Mech. 35 (1), 11–21.10.1146/annurev.fluid.35.101101.161217CrossRefGoogle 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
Clanet, C., Béguin, C., Richard, D. & Quéré, D. 2004 Maximal deformation of an impacting drop. J. Fluid Mech. 517, 199–208.10.1017/S0022112004000904CrossRefGoogle Scholar
Eddi, A., Winkels, K.G. & Snoeijer, J.H. 2013 Short time dynamics of viscous drop spreading. Phys. Fluids 25 (1), 013102.10.1063/1.4788693CrossRefGoogle Scholar
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
Enríquez, O.R., Brunet, P., Colinet, P., Snoeijer, J.H. & Marín, A.G. 2014 Universality of tip singularity formation in freezing water drops. Phys. Rev. Lett. 113 (5), 054301.Google Scholar
Fukai, J., Zhao, Z., Poulikakos, D., Megaridis, C.M. & Miyatake, O. 1993 Modeling of the deformation of a liquid droplet impinging upon a flat surface. Phys. Fluids A: Fluid Dyn. 5 (11), 2588–2599.10.1063/1.858724CrossRefGoogle Scholar
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
Gordillo, J.M., Riboux, G. & Quintero, E.S. 2019 A theory on the spreading of impacting droplets. J. Fluid Mech. 866, 298–315.10.1017/jfm.2019.117CrossRefGoogle Scholar
Gorin, B., Di Mauro, G., Bonn, D. & Kellay, H. 2022 Universal aspects of droplet spreading dynamics in Newtonian and non-Newtonian fluids. Langmuir 38 (8), 2608–2613.10.1021/acs.langmuir.1c03288CrossRefGoogle ScholarPubMed
Herbaut, R., Brunet, P., Limat, L. & Royon, L. 2019 Liquid spreading on cold surfaces: solidification-induced stick-slip dynamics. Phys. Rev. Fluids 4 (3), 033603.10.1103/PhysRevFluids.4.033603CrossRefGoogle Scholar
Herbaut, R., Dervaux, J., Brunet, P., Royon, L. & Limat, L. 2020 A criterion for the pinning and depinning of an advancing contact line on a cold substrate. Eur. Phys. J. Special Topics 229 (10), 1867–1880.10.1140/epjst/e2020-900261-5CrossRefGoogle Scholar
Jalaal, M., Seyfert, C., Stoeber, B. & Balmforth, N.J. 2018 Gel-controlled droplet spreading. J. Fluid Mech. 837, 115–128.10.1017/jfm.2017.844CrossRefGoogle Scholar
Jambon-Puillet, E., Shahidzadeh, N. & Bonn, D. 2018 Singular sublimation of ice and snow crystals. Nat. Commun. 9 (1), 4191.10.1038/s41467-018-06689-xCrossRefGoogle ScholarPubMed
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
Kant, P., Koldeweij, R.B.J., Harth, K., van Limbeek, M.A.J. & Lohse, D. 2020 Fast-freezing kinetics inside a droplet impacting on a cold surface. Proc. Natl Acad. Sci. 117 (6), 2788–2794.10.1073/pnas.1912406117CrossRefGoogle ScholarPubMed
Koldeweij, R.B.J., Kant, P., Harth, K., de Ruiter, R., Gelderblom, H., Snoeijer, J.H., Lohse, D. & van Limbeek, M.A.J. 2021 Initial solidification dynamics of spreading droplets. Phys. Rev. Fluids 6 (12), L121601.10.1103/PhysRevFluids.6.L121601CrossRefGoogle 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.2.044018CrossRefGoogle Scholar
Lee, J.B., Derome, D., Guyer, R. & Carmeliet, J. 2016 Modeling the maximum spreading of liquid droplets impacting wetting and non-wetting surfaces. Langmuir 32 (5), 1299–1308.10.1021/acs.langmuir.5b04557CrossRefGoogle Scholar
Madejski, J. 1976 Solidification of droplets on a cold surface. Intl J. Heat Mass Transfer 19 (9), 1009–1013.10.1016/0017-9310(76)90183-6CrossRefGoogle Scholar
Mostaghimi, J., Pasandideh-Fard, M. & Chandra, S. 2002 Dynamics of splat formation in plasma spray coating process. Plasma Chem. Plasma Process. 22 (1), 59–84.10.1023/A:1012940515065CrossRefGoogle Scholar
Nauenberg, M. 2016 Theory and experiments on the ice-water front propagation in droplets freezing on a subzero surface. Eur. J. Phys. 37 (4), 045102.10.1088/0143-0807/37/4/045102CrossRefGoogle Scholar
Pasandideh-Fard, M., Chandra, S. & Mostaghimi, J. 2002 A three-dimensional model of droplet impact and solidification. Intl J. Heat Mass Transfer 45 (11), 2229–2242.10.1016/S0017-9310(01)00336-2CrossRefGoogle Scholar
Pasandideh-Fard, M., Qiao, Y.M., Chandra, S. & Mostaghimi, J. 1996 Capillary effects during droplet impact on a solid surface. Phys. Fluids 8 (3), 650–659.10.1063/1.868850CrossRefGoogle Scholar
Roisman, I.V. 2009 Inertia dominated drop collisions. II. An analytical solution of the Navier–Stokes equations for a spreading viscous film. Phys. Fluids 21 (5), 052104.10.1063/1.3129283CrossRefGoogle Scholar
Roisman, I.V., Rioboo, R. & Tropea, C. 2002 Normal impact of a liquid drop on a dry surface: model for spreading and receding. Proc. R. Soc. Lond. A 458 (2022), 1411–1430.10.1098/rspa.2001.0923CrossRefGoogle 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.2.043602CrossRefGoogle Scholar
Schiaffino, S. & Sonin, A.A. 1997 Molten droplet deposition and solidification at low Weber numbers. Phys. Fluids 9 (11), 3172–3187.10.1063/1.869434CrossRefGoogle Scholar
Schremb, M., Roisman, I.V. & Tropea, C. 2017 Transient effects in ice nucleation of a water drop impacting onto a cold substrate. Phys. Rev. E 95 (2), 022805.10.1103/PhysRevE.95.022805CrossRefGoogle ScholarPubMed
Stiti, M., Castanet, G., Labergue, A. & Lemoine, F. 2020 Icing of a droplet deposited onto a subcooled surface. Intl J. Heat Mass Transfer 159, 120116.10.1016/j.ijheatmasstransfer.2020.120116CrossRefGoogle Scholar
Symons, L. & Perry, A. 1997 Predicting road hazards caused by rain, freezing rain and wet surfaces and the role of weather radar. Meteorol. Appl. 4 (1), 17–21. doi:10.1017/S1350482797000339CrossRefGoogle Scholar
Tanner, L.H. 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D: Appl. Phys. 12 (9), 1473.10.1088/0022-3727/12/9/009CrossRefGoogle 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/la5017998CrossRefGoogle ScholarPubMed
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
Tran, T., Staat, H.J.J., Susarrey-Arce, A., Foertsch, T.C., van Houselt, A., Gardeniers, H.J.G.E., Prosperetti, A., Lohse, D. & Sun, C. 2013 Droplet impact on superheated micro-structured surfaces. Soft Matter 9 (12), 3272–3282.10.1039/c3sm27643kCrossRefGoogle Scholar
Ukiwe, C. & Kwok, D.Y. 2005 On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces. Langmuir 21 (2), 666–673.10.1021/la0481288CrossRefGoogle ScholarPubMed
Vélez, C., Khayet, M. & Ortiz de Zárate, J.M. 2015 Temperature-dependent thermal properties of solid/liquid phase change even-numbered n-alkanes: n-Hexadecane, n-octadecane and n-eicosane. Appl. Energy 143, 383–394.10.1016/j.apenergy.2015.01.054CrossRefGoogle Scholar
Worthington, A.M. & Clifton, R.B. 1877 XXVIII. On the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc. R. Soc. Lond. 25 (171–178), 261–272.Google Scholar