Hostname: page-component-f554764f5-sl7kg Total loading time: 0 Render date: 2025-04-20T16:55:37.068Z Has data issue: false hasContentIssue false
  • English
  • Français

Evaporation-driven coalescence of two droplets undergoing freezing

Published online by Cambridge University Press:  14 March 2025

Sivanandan Kavuri ,
George Karapetsas Open the ORCID record for George Karapetsas [Opens in a new window] ,
Chander Shekhar Sharma  and
Kirti Chandra Sahu Open the ORCID record for Kirti Chandra Sahu [Opens in a new window]
Sivanandan Kavuri
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Sangareddy 502284, Telangana, India
George Karapetsas*
Affiliation:
Department of Chemical Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
Chander Shekhar Sharma
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Ropar, Rupnagar 140001, India
Kirti Chandra Sahu*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Sangareddy 502284, Telangana, India
*
Corresponding authors: Kirti Chandra Sahu, [email protected]; George Karapetsas, [email protected]
Corresponding authors: Kirti Chandra Sahu, [email protected]; George Karapetsas, [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We examine the evaporation-induced coalescence of two droplets undergoing freezing by conducting numerical simulations employing the lubrication approximation. When two sessile drops undergo freezing in close vicinity over a substrate, they interact with each other through the gaseous phase and the simultaneous presence of evaporation/condensation. In an unsaturated environment, the evaporation flux over the two volatile sessile drops is asymmetric, with lower evaporation in the region between the two drops. This asymmetry in the evaporation flux generates an asymmetric curvature in each drop, which results in a capillary flow that drives the drops closer to each other, eventually leading to their coalescence. This capillary flow, driven by evaporation, competes with the upward movement of the freezing front, depending on the relative humidity in the surrounding environment. We found that higher relative humidity reduces the evaporative flux, delaying capillary flow and impeding coalescence by restricting contact line motion. For a constant relative humidity, the substrate temperature governs the coalescence phenomenon and the resulting condensation can accelerate this process. Interestingly, lower substrate temperatures are observed to facilitate faster propagation of the freezing front, which, in turn, restricts coalescence.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops Interfacial Flows (free surface): Liquid bridges
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1006 , 10 March 2025 , A21
Check for updates
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Ajaev, V.S. & Davis, S.H. 2004 The effect of tri-junction conditions in droplet solidification. J. Cryst. Growth 264 (1-3), 452–462.CrossRefGoogle Scholar
Ajaev, V.S. & Homsy, G.M. 2001 Steady vapor bubbles in rectangular microchannels. J. Colloid Interface Sci. 240 (1), 259–271.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Angell, C.A. 1983 Supercooled water. Annu. Rev. Phys. Chem. 34 (1), 593–630.CrossRefGoogle Scholar
Assegehegn, G., Brito-de la Fuente, E., Franco, J. & Gallegos, C. 2019 The importance of understanding the freezing step and its impact on freeze-drying process performance. J. Pharm. Sci 108 (4), 1378–1395.CrossRefGoogle ScholarPubMed
Blake, J., Thompson, D., Raps, D. & Strobl, T. 2015 Simulating the freezing of supercooled water droplets impacting a cooled substrate. AIAA J. 53 (7), 1725–1739.CrossRefGoogle Scholar
Boinovich, L., Emelyanenko, A.M., Korolev, V.V. & Pashinin, A.S. 2014 Effect of wettability on sessile drop freezing: when superhydrophobicity stimulates an extreme freezing delay. Langmuir 30 (6), 1659–1668.CrossRefGoogle ScholarPubMed
Cao, Y., Tan, W. & Wu, Z. 2018 Aircraft icing: an ongoing threat to aviation safety. Aerosp. Sci. Technol. 75, 353–385.CrossRefGoogle Scholar
Cao, Y., Wu, Z., Su, Y. & Xu, Z. 2015 Aircraft flight characteristics in icing conditions. Prog. Aerosp. Sci. 74, 62–80.CrossRefGoogle Scholar
Castillo, J.E., Huang, Y., Pan, Z. & Weibel, J.A. 2021 Quantifying the pathways of latent heat dissipation during droplet freezing on cooled substrates. Intl J. Heat Mass Transfer 164, 120608.CrossRefGoogle Scholar
Charitatos, V. & Kumar, S. 2020 A thin-film model for droplet spreading on soft solid substrates. Soft Matt. 16 (35), 8284–8298.CrossRefGoogle ScholarPubMed
Cira, N.J., Benusiglio, A. & Prakash, M. 2015 Vapour-mediated sensing and motility in two-component droplets. Nature 519 (7544), 446–450.CrossRefGoogle ScholarPubMed
Craster, R.V., Matar, O.K. & Sefiane, K. 2009 Pinning, retraction, and terracing of evaporating droplets containing nanoparticles. Langmuir 25 (6), 3601–3609.CrossRefGoogle ScholarPubMed
Eddi, A., Winkels, K.G. & Snoeijer, J.H. 2013 Influence of droplet geometry on the coalescence of low viscosity drops. Phys. Rev. Lett. 111 (14), 144502.CrossRefGoogle ScholarPubMed
Espín, L. & Kumar, S. 2015 Droplet spreading and absorption on rough, permeable substrates. J. Fluid Mech. 784, 465–486.CrossRefGoogle Scholar
Fakorede, O., Feger, Z., Ibrahim, H., Ilinca, A., Perron, J. & Masson, C. 2016 Ice protection systems for wind turbines in cold climate: characteristics, comparisons and analysis. Renew. Sustain. Energy Rev. 65, 662–675.CrossRefGoogle Scholar
Franks, F. 1998 Freeze-drying of bioproducts: putting principles into practice. Eur. J. Pharm. Biopharm. 45 (3), 221–229.CrossRefGoogle ScholarPubMed
Fuller, A., Kant, K. & Pitchumani, R. 2024 Analysis of freezing of a sessile water droplet on surfaces over a range of wettability. J. Colloid Interface Sci. 653, 960–970.CrossRefGoogle Scholar
Gent, R.W., Dart, N.P. & Cansdale, J.T. 2000 Aircraft icing. Phil. Trans. R. Soc. Lond. A 358 (1776), 2873–2911.CrossRefGoogle Scholar
George, R.M. 1993 Freezing proceseses used in the food industry. Trends Food Sci. Technol. 4 (5), 134–138.CrossRefGoogle Scholar
Graeber, G., Dolder, V., Schutzius, T.M. & Poulikakos, D. 2018 Cascade freezing of supercooled water droplet collectives. ACS Nano 12 (11), 11274–11281.CrossRefGoogle ScholarPubMed
Guo, C., Zhang, M. & Hu, J. 2021 Icing delay of sessile water droplets on superhydrophobic titanium alloy surfaces. Colloids Surf. A 621, 126587.CrossRefGoogle Scholar
Hao, P., Lv, C. & Zhang, X. 2014 Freezing of sessile water droplets on surfaces with various roughness and wettability. Appl. Phys. Lett. 104 (16), 161609.CrossRefGoogle Scholar
Hari Govindha, A., Balusamy, S., Banerjee, S. & Sahu, K.C. 2024 Intricate evaporation dynamics in different multi-droplet configurations. Langmuir 40 (35), 18555–18567.Google Scholar
Hari Govindha, A., Katre, P., Balusamy, S., Banerjee, S. & Sahu, K.C. 2022 Counter-intuitive evaporation in nanofluids droplets due to stick-slip nature. Langmuir 38 (49), 15361–15371.CrossRefGoogle ScholarPubMed
Hernández-Sánchez, J.F., Lubbers, L.A., Eddi, A. & Snoeijer, J.H. 2012 Symmetric and asymmetric coalescence of drops on a substrate. Phys. Rev. Lett. 109 (18), 184502.CrossRefGoogle ScholarPubMed
Hu, H. & Jin, Z. 2010 An icing physics study by using lifetime-based molecular tagging thermometry technique. Intl J. Multiphase Flow 36 (8), 672–681.CrossRefGoogle Scholar
James, C., Purnell, G. & James, S.J. 2015 A review of novel and innovative food freezing technologies. Food Bioprocess Technol. 8 (8), 1616–1634.CrossRefGoogle Scholar
Jin, Z., Zhang, H. & Yang, Z. 2017 The impact and freezing processes of a water droplet on different cold cylindrical surfaces. Intl J. Heat Mass Transfer 113, 318–323.CrossRefGoogle Scholar
Ju, J., Jin, Z., Zhang, H., Yang, Z. & Zhang, J. 2018 The impact and freezing processes of a water droplet on different cold spherical surfaces. Exp. Therm. Fluid Sci. 96, 430–440.CrossRefGoogle Scholar
Jung, S., Dorrestijn, M., Raps, D., Das, A., Megaridis, C.M. & Poulikakos, D. 2011 Are superhydrophobic surfaces best for icephobicity? Langmuir 27 (6), 3059–3066.CrossRefGoogle ScholarPubMed
Jung, S., Tiwari, M.K. & Poulikakos, D. 2012 Frost halos from supercooled water droplets. Proc. Natl Acad. Sci. USA 109 (40), 16073–16078.CrossRefGoogle ScholarPubMed
Kapur, N. & Gaskell, P.H. 2007 Morphology and dynamics of droplet coalescence on a surface. Phys. Rev. E 75 (5), 056315.CrossRefGoogle ScholarPubMed
Karapetsas, G., Matar, O.K., Valluri, P. & Sefiane, K. 2012 Convective rolls and hydrothermal waves in evaporating sessile drops. Langmuir 28 (31), 11433–11439.CrossRefGoogle ScholarPubMed
Karapetsas, G., Sahu, K.C. & Matar, O.K. 2013 Effect of contact line dynamics on the thermocapillary motion of a droplet on an inclined plate. Langmuir 29 (28), 8892–8906.CrossRefGoogle Scholar
Karapetsas, G., Sahu, K.C. & Matar, O.K. 2016 Evaporation of sessile droplets laden with particles and insoluble surfactants. Langmuir 32 (27), 6871–6881.CrossRefGoogle ScholarPubMed
Karapetsas, G., Sahu, K.C., Sefiane, K. & Matar, O.K. 2014 Thermocapillary-driven motion of a sessile drop: effect of non-monotonic dependence of surface tension on temperature. Langmuir 30 (15), 4310–4321.CrossRefGoogle ScholarPubMed
Katre, P., Gurrala, P., Balusamy, S., Banerjee, S. & Sahu, K.C. 2020 Evaporation of sessile ethanol-water droplets on a critically inclined heated surface. Intl J. Multiphase Flow 131, 103368.CrossRefGoogle Scholar
Kavuri, S., Karapetsas, G., Sharma, C.S. & Sahu, K.C. 2023 Freezing of sessile droplet and frost halo formation. Phys. Rev. Fluid 8 (12), 124003.CrossRefGoogle Scholar
Kraj, A.G. & Bibeau, E.L. 2010 Phases of icing on wind turbine blades characterized by ice accumulation. Renewable Energy 35 (5), 966–972.CrossRefGoogle Scholar
Lee, H.J., Choi, C.K. & Lee, S.H. 2023 Vapor-shielding effect and evaporation characteristics of multiple droplets. Intl Commun. Heat Mass Transfer 144, 106789.CrossRefGoogle Scholar
Liu, X., Min, J., Zhang, X., Hu, Z. & Wu, X. 2021 Supercooled water droplet impacting-freezing behaviors on cold superhydrophobic spheres. Intl J. Multiphase Flow 141, 103675.CrossRefGoogle Scholar
Malachtari, A. & Karapetsas, G. 2024 Dynamics of the interaction of multiple evaporating droplets on compliant substrates. J. Fluid Mech. 978, A8.CrossRefGoogle Scholar
Man, X. & Doi, M. 2017 Vapor-induced motion of liquid droplets on an inert substrate. Phys. Rev. Lett. 119 (4), 044502.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Meng, Z. & Zhang, P. 2020 Dynamic propagation of ice-water phase front in a supercooled water droplet. Intl J. Heat Mass Transfer 152, 119468.CrossRefGoogle Scholar
Moosman, S. & Homsy, G.M. 1980 Evaporating menisci of wetting fluids. J. Colloid Interface Sci. 73 (1), 212–223.CrossRefGoogle Scholar
Nath, S., Ahmadi, S.F. & Boreyko, J.B. 2017 A review of condensation frosting. Nanoscale Microscale Thermophys. Engng 21 (2), 81–101.CrossRefGoogle 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.CrossRefGoogle Scholar
Pan, Y., Shi, K., Duan, X. & Naterer, G.F. 2019 Experimental investigation of water droplet impact and freezing on micropatterned stainless steel surfaces with varying wettabilities. Intl J. Heat Mass Transfer 129, 953–964.CrossRefGoogle Scholar
Paulsen, J.D., Burton, J.C. & Nagel, S.R. 2011 Viscous to inertial crossover in liquid drop coalescence. Phys. Rev. Lett. 106 (11), 114501.CrossRefGoogle ScholarPubMed
Peng, H., Wang, Q., Wang, T., Li, L., Xia, Z., Du, J., Zheng, B., Zhou, H. & Ye, L. 2020 Study on dynamics and freezing behaviors of water droplet on superhydrophobic aluminum surface. Appl. Phys. A 126 (10), 1–11.CrossRefGoogle Scholar
Pérez, J.G., Leclaire, S., Ammar, S., Trépanier, J., Reggio, M. & Benmeddour, A. 2021 Investigations of water droplet impact and freezing on a cold substrate with the lattice boltzmann method. Int. J. Thermofluids 12, 100109.Google Scholar
Pham, T. & Kumar, S. 2019 Imbibition and evaporation of droplets of colloidal suspensions on permeable substrates. Phys. Rev. Fluid 4 (3), 034004.CrossRefGoogle Scholar
Prosperetti, A. & Plesset, M.S. 1984 The stability of an evaporating liquid surface. Phys. Fluids 27 (7), 1590–1602.CrossRefGoogle Scholar
Sadafi, H., Dehaeck, S., Rednikov, A. & Colinet, P. 2019 Vapor-mediated versus substrate-mediated interactions between volatile droplets. Langmuir 35 (21), 7060–7065.CrossRefGoogle ScholarPubMed
Schwartz, L.W. & Eley, R.R. 1998 Simulation of droplet motion on low-energy and heterogeneous surfaces. J. Colloid Interface Sci. 202 (1), 173–188.CrossRefGoogle Scholar
Sebilleau, J., Ablonet, E., Tordjeman, P. & Legendre, D. 2021 Air humidity effects on water-drop icing. Phys. Rev. E 104 (3), L032802.CrossRefGoogle ScholarPubMed
Sharma, A., Parth, P., Shobhana, S., Bobin, M. & Hardik, B.K. 2022 Numerical study of ice freezing process on fin aided thermal energy storage system. Intl Commun. Heat Mass Transfer 130, 105792.CrossRefGoogle Scholar
Shi, K. & Duan, X. 2022 Freezing delay of water droplets on metallic hydrophobic surfaces in a cold environment. Appl. Therm. Engng 216, 119131.CrossRefGoogle Scholar
Starostin, A., Strelnikov, V., Dombrovsky, L.A., Shoval, S., Gendelman, O. & Bormashenko, E. 2022 On the universality of shapes of the freezing water droplets. Colloid Interface Sci. Commun. 47, 100590.CrossRefGoogle Scholar
Starostin, A., Strelnikov, V., Dombrovsky, L.A., Shoval, S., Gendelman, O. & Bormashenko, E. 2023 Effects of asymmetric cooling and surface wettability on the orientation of the freezing tip. Surf. Innovations 12 (1-2), 54–61.CrossRefGoogle Scholar
Sui, Y., Maglio, M., Spelt, P.D.M., Legendre, D. & Ding, H. 2013 Inertial coalescence of droplets on a partially wetting substrate. Phys. Fluids 25 (10)CrossRefGoogle Scholar
Sultan, E., Boudaoud, A. & Amar, M.B. 2005 Evaporation of a thin film: diffusion of the vapour and Marangoni instabilities. J. Fluid Mech. 543, 183.CrossRefGoogle Scholar
Tembely, M., Attarzadeh, R. & Dolatabadi, A. 2018 On the numerical modeling of supercooled micro-droplet impact and freezing on superhydrophobic surfaces. Intl J. Heat Mass Transfer 127, 193–202.CrossRefGoogle Scholar
Tembely, M. & Dolatabadi, A. 2019 A comprehensive model for predicting droplet freezing features on a cold substrate. J. Fluid Mech. 859, 566–585.CrossRefGoogle Scholar
Varma, S.C., Saha, A. & Kumar, A. 2021 Coalescence of polymeric sessile drops on a partially wettable substrate. Phys. Fluids 33 (12), 123101.CrossRefGoogle Scholar
Vu, T.V., Dao, K.V. & Pham, B.D. 2018 Numerical simulation of the freezing process of a water drop attached to a cold plate. J. Mech. Sci. Technol. 32 (5), 2119–2126.CrossRefGoogle Scholar
Vu, T.V., Tryggvason, G., Homma, S. & Wells, J.C. 2015 Numerical investigations of drop solidification on a cold plate in the presence of volume change. Intl J. Multiphase Flow 76, 73–85.CrossRefGoogle Scholar
Wang, C., Xu, Z., Zhang, H., Zheng, J., Hao, P., He, F. & Zhang, X. 2022 A new freezing model of sessile droplets considering ice fraction and ice distribution after recalescence. Phys. Fluids 34 (9), 092115.CrossRefGoogle Scholar
Wang, Z., Karapetsas, G., Valluri, P. & Inoue, C. 2024 Role of volatility and thermal properties in droplet spreading: a generalisation to Tanner’s law. J. Fluid Mech. 987, A15.CrossRefGoogle Scholar
Wen, Y., Kim, P.Y., Shi, S., Wang, D., Man, X., Doi, M. & Russell, T.P. 2019 Vapor-induced motion of two pure liquid droplets. Soft Matt. 15 (10), 2135–2139.CrossRefGoogle ScholarPubMed
Williams, A., Karapetsas, G., Mamalis, D., Sefiane, K., Matar, O. & Valluri, P. 2021 Spreading and retraction dynamics of sessile evaporating droplets comprising volatile binary mixtures. J. Fluid Mech. 907, A22.CrossRefGoogle Scholar
Xia, X., He, C. & Zhang, P. 2019 Universality in the viscous-to-inertial coalescence of liquid droplets. Proc. Natl Acad. Sci. USA 116 (47), 23467–23472.CrossRefGoogle ScholarPubMed
Yancheshme, A.A., Momen, G. & Aminabadi, R.J. 2020 Mechanisms of ice formation and propagation on superhydrophobic surfaces: a review. Adv. Colloid Interface Sci. 279, 102155.CrossRefGoogle Scholar
Zadražil, A., Stepanek, F. & Matar, O.K. 2006 Droplet spreading, imbibition and solidification on porous media. J. Fluid Mech. 562, 1–33.CrossRefGoogle Scholar
Zhang, H., Jin, Z., Jiao, M. & Yang, Z. 2018a Experiment investigation of the impact and freezing processes of a water droplet on different cold concave surfaces. Intl J. Therm. Sci. 132, 498–508.CrossRefGoogle Scholar
Zhang, H., Zhao, Y., Lv, R. & Yang, C. 2016 Freezing of sessile water droplet for various contact angles. Intl J. Therm. Sci. 101, 59–67.CrossRefGoogle Scholar
Zhang, X., Liu, X., Min, J. & Wu, X. 2019 Shape variation and unique tip formation of a sessile water droplet during freezing. Appl. Therm. Engng 147, 927–934.CrossRefGoogle Scholar
Zhang, X., Liu, X., Wu, X. & Min, J. 2018b Simulation and experiment on supercooled sessile water droplet freezing with special attention to supercooling and volume expansion effects. Intl J. Heat Mass Transfer 127, 975–985.CrossRefGoogle Scholar
Zhou, L., Liu, R. & Yi, X. 2022 Research and development of anti-icing/deicing techniques for vessels. Ocean Engng 260, 112008.CrossRefGoogle Scholar
Zhu, Z., Zhang, Y. & Sun, D. 2021 Biomimetic modification of freezing facility surfaces to prevent icing and frosting during freezing for the food industry. Trends Food Sci. Technol 111, 581–594.CrossRefGoogle Scholar