Hostname: page-component-6bf8c574d5-7jkgd Total loading time: 0 Render date: 2025-02-17T15:46:30.194Z Has data issue: false hasContentIssue false
  • English
  • Français

Coalescence of immiscible sessile droplets on a partial wetting surface

Published online by Cambridge University Press:  21 September 2023

Huadan Xu ,
Xinjin Ge ,
Tianyou Wang  and
Zhizhao Che Open the ORCID record for Zhizhao Che [Opens in a new window]
Huadan Xu
Affiliation:
State Key Laboratory of Engines, Tianjin University, Tianjin 300350, PR China
Xinjin Ge
Affiliation:
State Key Laboratory of Engines, Tianjin University, Tianjin 300350, PR China
Tianyou Wang
Affiliation:
State Key Laboratory of Engines, Tianjin University, Tianjin 300350, PR China
Zhizhao Che*
Affiliation:
State Key Laboratory of Engines, Tianjin University, Tianjin 300350, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Droplet coalescence is a common phenomenon and plays an important role in multidisciplinary applications. Previous studies mainly consider the coalescence of miscible liquids, even though the coalescence of immiscible droplets on a solid surface is a common process. In this study, we explore the coalescence of two immiscible droplets on a partial wetting surface experimentally and theoretically. We find that the coalescence process can be divided into three stages based on the time scales and force interactions involved, namely (I) the growth of a liquid bridge, (II) the oscillation of the coalescing sessile droplet and (III) the formation of a partially engulfed compound sessile droplet and the subsequent retraction. In stage I, the immiscible interface is found not to affect the scaling of the temporal evolution of the liquid bridge, which follows the same 2/3 power law as that of miscible droplets. In stage II, by developing a new capillary time scale considering both surface and interfacial tensions, we show that the interfacial tension between the two immiscible liquids functions as a non-negligible resistance to the oscillation which decreases the oscillation periods. In stage III, a modified Ohnesorge number is developed to characterize the visco-capillary and inertia-capillary time scales involved during the displacement of water by oil; a new model based on energy balance is proposed to analyse the maximum retraction velocity, highlighting that the viscous resistance is concentrated in a region close to the contact line.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 971 , 25 September 2023 , A34
Check for updates
Copyright
© The Author(s), 2023. 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.)

References

Aarts, D.G.A.L., Lekkerkerker, H.N.W., Guo, H., Wegdam, G.H. & Bonn, D. 2005 Hydrodynamics of droplet coalescence. Phys. Rev. Lett. 95 (16), 164503.CrossRefGoogle ScholarPubMed
Adamson, A.W. & Gast, A.P. 1967 Physical Chemistry of Surfaces, vol. 150. Interscience.Google Scholar
Ahmadlouydarab, M. & Feng, J.J. 2014 Motion and coalescence of sessile drops driven by substrate wetting gradient and external flow. J. Fluid Mech. 746, 214–235.CrossRefGoogle Scholar
Anand, V., Roy, S., Naik, V.M., Juvekar, V.A. & Thaokar, R.M. 2019 Electrocoalescence of a pair of conducting drops in an insulating oil. J. Fluid Mech. 859, 839–850.CrossRefGoogle Scholar
Andrieu, C., Beysens, D.A., Nikolayev, V.S. & Pomeau, Y. 2002 Coalescence of sessile drops. J. Fluid Mech. 453, 427–438.CrossRefGoogle Scholar
Bernard, R., Baumgartner, D., Brenn, G., Planchette, C., Weigand, B. & Lamanna, G. 2020 Miscibility and wettability: how interfacial tension influences droplet impact onto thin wall films. J. Fluid Mech. 908, A36.CrossRefGoogle Scholar
Beysens, D.A. & Narhe, R.D. 2006 Contact line dynamics in the late-stage coalescence of diethylene glycol drops. J. Phys. Chem. B 110 (44), 22133–22135.CrossRefGoogle ScholarPubMed
Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81 (2), 739–805.CrossRefGoogle Scholar
Borcia, R. & Bestehorn, M. 2013 Partial coalescence of sessile drops with different miscible liquids. Langmuir 29 (14), 4426–4429.CrossRefGoogle ScholarPubMed
Cha, H., Xu, C., Sotelo, J., Chun, J.M., Yokoyama, Y., Enright, R. & Miljkovic, N. 2016 Coalescence-induced nanodroplet jumping. Phys. Rev. Fluids 1, 064102.CrossRefGoogle Scholar
Chashechkin, Y.D. 2019 Oscillations and short waves on a free falling drop surface (experiment and theory). In Conference Topical Problems of Fluid Mechanics 2019: Proceedings (ed. D. Šimurda & T. Bodnár), pp. 45–52.Google Scholar
Chireux, V., Fabre, D., Risso, F. & Tordjeman, P. 2015 Oscillations of a liquid bridge resulting from the coalescence of two droplets. Phys. Fluids 27 (6), 062103.CrossRefGoogle Scholar
Choi, K., Ng, A.H.C., Fobel, R. & Wheeler, A.R. 2012 Digital microfluidics. Annu. Rev. Anal. Chem. 5 (1), 413–440.CrossRefGoogle ScholarPubMed
Cuttle, C., Thompson, A.B., Pihler-Puzović, D. & Juel, A. 2021 The engulfment of aqueous droplets on perfectly wetting oil layers. J. Fluid Mech. 915, A66.CrossRefGoogle Scholar
Deepu, P., Chowdhuri, S. & Basu, S. 2014 Oscillation dynamics of sessile droplets subjected to substrate vibration. Chem. Engng Sci. 118, 9–19.CrossRefGoogle Scholar
Dekker, P.J., Hack, M.A., Tewes, W., Datt, C., Bouillant, A. & Snoeijer, J.H. 2022 When elasticity affects drop coalescence. Phys. Rev. Lett. 128 (2), 028004.CrossRefGoogle ScholarPubMed
Duchemin, L., Eggers, J. & Josserand, C. 2003 Inviscid coalescence of drops. J. Fluid Mech. 487, 167–178.CrossRefGoogle Scholar
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
Edwards, A.M.J., Ledesma-Aguilar, R., Newton, M.I., Brown, C.V. & McHale, G. 2016 Not spreading in reverse: the dewetting of a liquid film into a single drop. Sci. Adv. 2 (9), e1600183.CrossRefGoogle ScholarPubMed
de Gennes, P.G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.CrossRefGoogle Scholar
de Gennes, P.-G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves, vol. 315. Springer.CrossRefGoogle Scholar
Gokhale, S.J., DasGupta, S., Plawsky, J.L. & Wayner, P.C. 2004 Reflectivity-based evaluation of the coalescence of two condensing drops and shape evolution of the coalesced drop. Phys. Rev. E 70 (5), 051610.CrossRefGoogle ScholarPubMed
Gong, X.J., Gao, X.F. & Jiang, L. 2017 Recent progress in bionic condensate microdrop self-propelling surfaces. Adv. Mater. 29 (45), 14.CrossRefGoogle ScholarPubMed
Goossens, S., Seveno, D., Rioboo, R., Vaillant, A., Conti, J. & De Coninck, J. 2011 Can we predict the spreading of a two-liquid system from the spreading of the corresponding liquid-air systems? Langmuir 27 (16), 9866–9872.CrossRefGoogle ScholarPubMed
Hernandez-Sanchez, 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
Huang, K.-L. & Pan, K.-L. 2021 Transitions of bouncing and coalescence in binary droplet collisions. J. Fluid Mech. 928, A7.CrossRefGoogle Scholar
Iqbal, R., Dhiman, S., Sen, A.K. & Shen, A.Q. 2017 Dynamics of a water droplet over a sessile oil droplet: compound droplets satisfying a Neumann condition. Langmuir 33 (23), 5713–5723.CrossRefGoogle Scholar
Ji, B., Yang, Z. & Feng, J. 2021 Compound jetting from bubble bursting at an air-oil-water interface. Nat. Commun. 12 (1), 6305.CrossRefGoogle ScholarPubMed
Jiang, X., Zhao, B. & Chen, L. 2019 Sessile microdrop coalescence on partial wetting surfaces: effects of surface wettability and stiffness. Langmuir 35 (40), 12955–12961.CrossRefGoogle ScholarPubMed
Kamp, J., Villwock, J. & Kraume, M. 2017 Drop coalescence in technical liquid/liquid applications: a review on experimental techniques and modeling approaches. Rev. Chem. Engng 33 (1), 1–47.CrossRefGoogle Scholar
Karpitschka, S. & Riegler, H. 2010 Quantitative experimental study on the transition between fast and delayed coalescence of sessile droplets with different but completely miscible liquids. Langmuir 26 (14), 11823–11829.CrossRefGoogle Scholar
Keiser, A., Keiser, L., Clanet, C. & Quéré, D. 2017 Drop friction on liquid-infused materials. Soft Matt. 13 (39), 6981–6987.CrossRefGoogle ScholarPubMed
Khattab, I., Bandarkar, F., Abolghassemi Fakhree, M.A. & Jouyban, A. 2012 Density, viscosity, and surface tension of ${\rm water}+{\rm ethanol}$ mixtures from 293 to 323 K. Korean J. Chem. Engng 29, 812–817.CrossRefGoogle Scholar
Khismatullin, D.B. & Nadim, A. 2001 Shape oscillations of a viscoelastic drop. Phys. Rev. E 63 (6), 061508.CrossRefGoogle ScholarPubMed
Koldeweij, R.B.J., van Capelleveen, B.F., Lohse, D. & Visser, C.W. 2019 Marangoni-driven spreading of miscible liquids in the binary pendant drop geometry. Soft Matt. 15, 8525–8531.CrossRefGoogle ScholarPubMed
Kusumaatmaja, H., May, A.I. & Knorr, R.L. 2021 Intracellular wetting mediates contacts between liquid compartments and membrane-bound organelles. J. Cell Biol. 220 (10), e202103175.CrossRefGoogle ScholarPubMed
Lamb, H. 1924 Hydrodynamics. Cambridge University Press.Google Scholar
Lee, M.W., Kim, N.Y., Chandra, S. & Yoon, S.S. 2013 Coalescence of sessile droplets of varying viscosities for line printing. Intl J. Multiphase Flow 56, 138–148.CrossRefGoogle Scholar
Li, X., Li, S., Lu, Y., Liu, M., Li, F., Yang, H., Tang, S.-Y., Zhang, S., Li, W. & Sun, L. 2020 Programmable digital liquid metal droplets in reconfigurable magnetic fields. ACS Appl. Mater. Interfaces 12 (33), 37670–37679.CrossRefGoogle ScholarPubMed
Lu, L.L., Pei, Y.Q., Qin, J., Peng, Z.J., Wang, Y.Q. & Zhu, Q.Y. 2020 Impingement behaviour of single ethanol droplet on a liquid film of glycerol solution. Fuel 276, 117820.CrossRefGoogle Scholar
Mahadevan, L., Adda-Bedia, M. & Pomeau, Y. 2002 Four-phase merging in sessile compound drops. J. Fluid Mech. 451, 411–420.CrossRefGoogle Scholar
Menchaca-Rocha, A., Martínez-Dávalos, A., Núñez, R., Popinet, S. & Zaleski, S. 2001 Coalescence of liquid drops by surface tension. Phys. Rev. E 63 (4), 046309.CrossRefGoogle ScholarPubMed
Narhe, R., Beysens, D. & Nikolayev, V.S. 2004 Contact line dynamics in drop coalescence and spreading. Langmuir 20 (4), 1213–1221.CrossRefGoogle ScholarPubMed
Narhe, R.D., Beysens, D.A. & Pomeau, Y. 2008 Dynamic drying in the early-stage coalescence of droplets sitting on a plate. Europhys. Lett. 81 (4), 46002.CrossRefGoogle Scholar
Neogi, P. & Miller, C.A. 1982 Spreading kinetics of a drop on a smooth solid surface. J. Colloid Interface Sci. 86 (2), 525–538.CrossRefGoogle Scholar
Paulsen, J.D. 2013 Approach and coalescence of liquid drops in air. Phys. Rev. E 88 (6), 063010.CrossRefGoogle ScholarPubMed
Pawar, N., Bahga, S., Kale, S. & Kondaraju, S. 2019 a Symmetric and asymmetric coalescence of droplets on a solid surface in the inertia-dominated regime. Phys. Fluids 31, 092106.CrossRefGoogle Scholar
Pawar, N.D., Bahga, S.S., Kale, S.R. & Kondaraju, S. 2019 b Symmetric and asymmetric coalescence of droplets on a solid surface in the inertia-dominated regime. Phys. Fluids 31 (9), 092106.CrossRefGoogle Scholar
Ristenpart, W.D., McCalla, P.M., Roy, R.V. & Stone, H.A. 2006 Coalescence of spreading droplets on a wettable substrate. Phys. Rev. Lett. 97 (6), 064501.CrossRefGoogle ScholarPubMed
Rostami, P. & Auernhammer, G.K. 2022 Capillary filling in drop merging: dynamics of the four-phase contact point. Phys. Fluids 34 (1), 012107.CrossRefGoogle Scholar
Sanjay, V., Sen, U., Kant, P. & Lohse, D. 2022 Taylor–Culick retractions and the influence of the surroundings. J. Fluid Mech. 948, A14.CrossRefGoogle Scholar
Shyam, S., Dhapola, B. & Mondal, P.K. 2022 Magnetofluidic-based controlled droplet breakup: effect of non-uniform force field. J. Fluid Mech. 944, A51.CrossRefGoogle Scholar
Siahcheshm, P., Goharpey, F. & Foudazi, R. 2018 Droplet retraction in the presence of nanoparticles with different surface modifications. Rheol. Acta 57 (11), 729–743.CrossRefGoogle Scholar
Sohrabi, S., Kassir, N. & Keshavarz Moraveji, M. 2020 Droplet microfluidics: fundamentals and its advanced applications. RSC Adv. 10 (46), 27560–27574.CrossRefGoogle ScholarPubMed
Somwanshi, P.M., Muralidhar, K. & Khandekar, S. 2017 Wall shear rates generated during coalescence of pendant and sessile drops. In Fluid Mechanics and Fluid Power – Contemporary Research (ed. A.K. Saha, D. Das, R. Srivastava, P.K. Panigrahi & K. Muralidhar), pp. 33–42. Springer.CrossRefGoogle Scholar
Somwanshi, P.M., Muralidhar, K. & Khandekar, S. 2018 Coalescence dynamics of sessile and pendant liquid drops placed on a hydrophobic surface. Phys. Fluids 30 (9), 092103.CrossRefGoogle Scholar
Song, H., Chen, D.L. & Ismagilov, R.F. 2006 Reactions in droplets in microfluidic channels. Angew. Chem. Intl Ed. Engl. 45 (44), 7336–7356.CrossRefGoogle ScholarPubMed
Sprittles, J.E. & Shikhmurzaev, Y.D. 2014 Dynamics of liquid drops coalescing in the inertial regime. Phys. Rev. E 89, 063008.CrossRefGoogle ScholarPubMed
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), 101701.CrossRefGoogle Scholar
Sykes, T.C., Castrejón-Pita, A.A., Castrejón-Pita, J.R., Harbottle, D., Khatir, Z., Thompson, H.M. & Wilson, M.C.T. 2020 a Surface jets and internal mixing during the coalescence of impacting and sessile droplets. Phys. Rev. Fluids 5 (2), 023602.CrossRefGoogle Scholar
Sykes, T.C., Harbottle, D., Khatir, Z., Thompson, H.M. & Wilson, M.C.T. 2020 b Substrate wettability influences internal jet formation and mixing during droplet coalescence. Langmuir 36 (32), 9596–9607.CrossRefGoogle ScholarPubMed
Thoroddsen, S.T., Qian, B., Etoh, T.G. & Takehara, K. 2007 The initial coalescence of miscible drops. Phys. Fluids 19 (7), 072110.CrossRefGoogle Scholar
Wang, X., Xu, B., Chen, Z., Del Col, D., Li, D., Zhang, L., Mou, X., Liu, Q., Yang, Y. & Cao, Q. 2022 Review of droplet dynamics and dropwise condensation enhancement: theory, experiments and applications. Adv. Colloid Interface Sci. 305, 102684.CrossRefGoogle ScholarPubMed
Winkelmann, M., Grimm, E.-M., Comunian, T., Freudig, B., Zhou, Y., Gerlinger, W., Sachweh, B. & Petra Schuchmann, H. 2013 Controlled droplet coalescence in miniemulsions to synthesize zinc oxide nanoparticles by precipitation. Chem. Engng Sci. 92, 126–133.CrossRefGoogle Scholar
Xie, H., Zhao, W., Zhang, X. & Wang, Z. 2022 Demulsification of bacteria-stabilized pickering emulsions using modified silica nanoparticles. ACS Appl. Mater. Interfaces 14 (21), 24102–24112.CrossRefGoogle ScholarPubMed
Xu, H., Wang, T. & Che, Z. 2022 Bridge evolution during the coalescence of immiscible droplets. J. Colloid Interface Sci. 628, 869–877.CrossRefGoogle ScholarPubMed
Yokota, M. & Okumura, K. 2011 Dimensional crossover in the coalescence dynamics of viscous drops confined in between two plates. Proc. Natl Acad. Sci. USA 108 (16), 6395–6398.CrossRefGoogle Scholar
Yu, H., Kant, P., Dyett, B., Lohse, D. & Zhang, X. 2019 Splitting droplets through coalescence of two different three-phase contact lines. Soft Matt. 15 (30), 6055–6061.CrossRefGoogle ScholarPubMed
Yuan, B., He, Z., Fang, W., Bao, X. & Liu, J. 2015 Liquid metal spring: oscillating coalescence and ejection of contacting liquid metal droplets. Sci. Bull. 60 (6), 648–653.CrossRefGoogle Scholar
Zhang, Y., Oberdick, S.D., Swanson, E.R., Anna, S.L. & Garoff, S. 2015 Gravity driven current during the coalescence of two sessile drops. Phys. Fluids 27 (2), 022101.CrossRefGoogle Scholar
Zhao, H., Orejon, D., Sefiane, K. & Shanahan, M.E.R. 2021 Droplet motion and oscillation on contrasting micro-striated surfaces. J. Fluid Mech. 916, A54.CrossRefGoogle Scholar

Xu et al. Supplementary Movie 1

Calescence process of two immiscible droplets, corresponding to figure 2. The two immiscible liquids are water (right) and n-dodecane (left).

Download Xu et al. Supplementary Movie 1(Video)
Video 6 MB

Xu et al. Supplementary Movie 2

Close-up view of the liquid bridge for the coalescence of a water droplet (right) and a low-viscosity oil droplet (bromocyclopentane, left), corresponding to figure 3c.

Download Xu et al. Supplementary Movie 2(Video)
Video 2.7 MB

Xu et al. Supplementary Movie 3

Close-up view of the liquid bridge for the coalescence of a water droplet (right) and a high-viscosity oil droplet (silicone oil 100 cSt, left) , corresponding to figure 3d.

Download Xu et al. Supplementary Movie 3(Video)
Video 8.1 MB

Xu et al. Supplementary Movie 4

Close-up view of the liquid bridge for the coalescence of a water droplet (right) and an ethanol droplet (left), corresponding to figure 3e.

Download Xu et al. Supplementary Movie 4(Video)
Video 371.6 KB