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.
[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.
