两相同液滴在部分互溶液池表面的行为

doi:10.7523/j.ucas.2026.031

摘要/Abstract

摘要： 液滴在液面上的相互作用对很多自然过程和工业应用都非常重要。在很多情况下,其系统是多组分的,这导致液面产生马兰戈尼流动,有可能使液滴之间出现斥力。本研究通过观察两个漂浮在乙醇-水混合液表面且完全相同的油滴的运动,研究“麦圈效应”产生的吸引力与溶质马兰戈尼流产生的斥力的综合影响。实验中发现了三种典型行为：排斥、吸引-合并和吸引-反弹;即液滴相互排斥,相互吸引后合并,相互吸引后接触并反弹。通过对引力与斥力的分析得到了用于区分液滴排斥和吸引行为的标度律。对于相互吸引的液滴,液滴由合并到反弹的转变则是由于润滑效应：当液滴浸没在液池中的部分大于半个球体时,两液滴之间会在接触时形成一个润滑液层,这阻止了液滴的合并。该研究有助于加深对液面上液滴操控的理解。

关键词: 漂浮液滴, 麦圈效应, 马兰戈尼流

Abstract: The interaction of drops floating on liquid surfaces is important for many natural processes and industrial applications. In many cases, the system is multicomponent, leading to Marangoni flows on the surface, which might lead to repulsive forces between the drops. Here we investigate the combined effect of the attractive ``Cheerios effect'' and the repulsive solutal Marangoni flow by observing the behaviors of two identical oil drops floating on a partially miscible pool made of ethanol-water mixtures. Three typical behaviors are found: Repel, Attract-Coalesce and Attract-Rebound, in which the drops repel each other, attract each other and then coalesce, and attract and rebound upon contact. A scaling theory based on the two competing forces is developed to distinguish the repulsive and attractive behaviors of the drops. For the transition from Attract-Coalesce to Attract-Rebound, a lubrication layer is found to form when the immersed lower halves of the drops are more than half a sphere, which prevents the drops from coalescing. Our work may improve the knowledge on drop manipulations on liquid surfaces.

Key words: floating drops, Cheerios effect, Marangoni flows

中图分类号:

O351.2

高远, 李延深. 两相同液滴在部分互溶液池表面的行为[J]. 中国科学院大学学报, DOI: 10.7523/j.ucas.2026.031.

GAO Yuan, LI Yanshen. The behaviors of two identical drops floating on a partially miscible liquid pool^*[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2026.031.

参考文献

[1] Chen L J, Jeng J F, Robert M, et al.Experimental study of interfacial phase transitions in three-component surfactant systems[J]. Physical Review A, 1990, 42(8): 4716-4723. DOI:10.1103/PhysRevA.42.4716.
[2] Prasad D R G, Anuprakash M M V V S. Pollution due to oil spills in marine environment and control measures[J]. IOSR Journal of Environmental Science, Toxicology and Food Technology, 2016, 10(9): 1-8. DOI:10.9790/2402-1009010108.
[3] Kornilios S, Drakopoulos P G, Dounas C.Pelagic tar, dissolved/dispersed petroleum hydrocarbons and plastic distribution in the Cretan Sea, Greece[J]. Marine Pollution Bulletin, 1998, 36(12): 989-993. DOI:10.1016/S0025-326X(98)00102-7.
[4] Li Q X, Kang C B, Zhang C K.Waste water produced from an oilfield and continuous treatment with an oil-degrading bacterium[J]. Process Biochemistry, 2005, 40(2): 873-877. DOI:10.1016/j.procbio.2004.02.011.
[5] Zhang D H, Liu W K, Feng L, et al.Innovative advances in droplet microfluidics[J]. Research, 2025, 8: 856. DOI:10.34133/research.0856.
[6] Liu H F, Qiao X M, Zhang Q L, et al.Recent advances of sustained drug delivery system using droplet microfluidic platforms[J]. Journal of Drug Delivery Science and Technology, 2025, 107: 106806. DOI:10.1016/j.jddst.2025.106806.
[7] Čejková J, Schwarzenberger K, Eckert K, et al.Dancing performance of organic droplets in aqueous surfactant solutions[J]. Colloids and Surfaces, A: Physicochemical and Engineering Aspects, 2019, 566: 141-147. DOI:10.1016/j.colsurfa.2019.01.027.
[8] Kumar P, Horváth D, Tóth Á.Self-assembly to synchrony of active gels[J]. Soft Matter, 2023, 19(22): 4137-4143. DOI:10.1039/d3sm00461a.
[9] Chen Y J, Sadakane K, Sakuta H, et al.Spontaneous Oscillations and Synchronization of Active Droplets on a Water Surface via Marangoni Convection[J]. Langmuir, 2017, 33(43): 12362-12368. DOI:10.1021/acs.langmuir.7b03061.
[10] Li Y T, Pahlavan A A, Chen Y G, et al.Oil-on-water droplets faceted and stabilized by vortex halos in the subphase[J]. Proceedings of the National Academy of Sciences of the United States of America, 2023, 120(4): e2214657120. DOI:10.1073/pnas.2214657120.
[11] Marangoni C. Sul principio della viscosita’ superficiale dei liquidi stabilito dalsig. J. Plateau[J]. Il Nuovo Cimento (1869-1876), 1871, 5(1): 239-273. DOI:10.1007/BF02718643.
[12] Shiri S, Sinha S, Baumgartner D A, et al.Thermal Marangoni Flow Impacts the Shape of Single Component Volatile Droplets on Thin, Completely Wetting Substrates[J]. Physical Review Letters, 2021, 127(2): 024502. DOI:10.1103/PhysRevLett.127.024502.
[13] Gao A T, Butt H J, Steffen W, et al.Optical Manipulation of Liquids by Thermal Marangoni Flow along the Air-Water Interfaces of a Superhydrophobic Surface[J]. Langmuir, 2021, 37(29): 8677-8686. DOI:10.1021/acs.langmuir.1c00539.
[14] Nicolson M M.The interaction between floating particles[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1949, 45(2): 288-295. DOI:10.1017/S0305004100024841.
[15] Gifford W A, Scriven L E.On the attraction of floating particles[J]. Chemical Engineering Science, 1971, 26(3): 287-297. DOI:10.1016/0009-2509(71)83003-8.
[16] Chan D Y C, Henry J D, White L R. The interaction of colloidal particles collected at fluid interfaces[J]. Journal of Colloid and Interface Science, 1981, 79(2): 410-418. DOI:10.1016/0021-9797(81)90092-8.
[17] Allain C, Cloitre M.Interaction between Particles Trapped at Fluid Interfaces Ⅰ[J]. Journal of Colloid and Interface Science, 1993, 157(2): 261-268. DOI:10.1006/jcis.1993.1184.
[18] Allain C, Cloitre M.Interaction between Particles Trapped at Fluid Interfaces Ⅱ[J]. Journal of Colloid and Interface Science, 1993, 157(2): 269-277. DOI:10.1006/jcis.1993.1185.
[19] Vella D, Mahadevan L.The “Cheerios effect”[J]. American Journal of Physics, 2005, 73(9): 817-825. DOI:10.1119/1.1898523.
[20] Cooray H, Cicuta P, Vella D.Floating and sinking of a pair of spheres at a liquid-fluid interface[J]. Langmuir, 2017, 33(6): 1427-1436. DOI:10.1021/acs.langmuir.6b03373.
[21] Ho I, Pucci G, Harris D M.Direct Measurement of Capillary Attraction between Floating Disks[J]. Physical Review Letters, 2019, 123(25): 254502. DOI:10.1103/PhysRevLett.123.254502.
[22] Botto L, Lewandowski E P, Cavallaro M, et al.Capillary interactions between anisotropic particles[J]. Soft Matter, 2012, 8(39): 9957-9971. DOI:10.1039/c2sm25929j.
[23] Mansfield E H, Sepangi H R, Eastwood E A.Equilibrium and mutual attraction or repulsion of objects supported by surface tension[J]. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1997, 355(1726): 869-919. DOI:10.1098/rsta.1997.0049.
[24] Karpitschka S, Pandey A, Lubbers L A, et al.Liquid drops attract or repel by the inverted Cheerios effect[J]. Proceedings of the National Academy of Sciences of the United States of America, 2016, 113(27): 7403-7407. DOI:10.1073/pnas.1601411113.
[25] Pandey A, Karpitschka S, Lubbers L A, et al.Dynamical theory of the inverted cheerios effect[J]. Soft Matter, 2017, 13(35): 6000-6010. DOI:10.1039/c7sm00690j.
[26] Clift R, Grace J R, Weber M E.Bubbles, drops, and particles[J]. 2005.
[27] Lohse D, Zhang X H.Physicochemical hydrodynamics of droplets out of equilibrium[J]. Nature Reviews Physics, 2020, 2(8): 426-443. DOI:10.1038/s42254-020-0199-z.
[28] Burton J C, Huisman F M, Alison P, et al.Experimental and numerical investigation of the equilibrium geometry of liquid lenses[J]. Langmuir, 2010, 26(19): 15316-15324. DOI:10.1021/la102268n.
[29] Lide D R.CRC handbook of chemistry and physics: Vol. 84[M]. CRC press, 2004.
[30] Li Y S, Chong K L, Bazyar H, et al.Universality in microdroplet nucleation during solvent exchange in Hele-Shaw-like channels[J]. Journal of Fluid Mechanics, 2021, 912: A35. DOI:10.1017/jfm.2020.1137.
[31] Ruschak K J, Miller C A.Spontaneous emulsification in ternary systems with mass transfer[J]. Industrial & Engineering Chemistry Fundamentals, 1972, 11(4): 534-540. DOI:10.1021/i160044a017.
[32] Gennes P G, Brochard-Wyart F, Quéré D.Capillarity and wetting phenomena: drops, bubbles, pearls, waves[M]. Springer New York, 2004. DOI:10.1007/978-0-387-21656-0.
[33] Mogilevskiy E.Levitation of a nonboiling droplet over hot liquid bath[J]. Physics of Fluids, 2020, 32: 012114. DOI:10.1063/1.5131818.