Skip to main content
Log in

Surfing of particles and droplets on the free surface of a liquid: a review

  • Review
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Active systems have been a matter of great interest across various scientific disciplines owing to the host of potential applications. While bulk active matter systems have received a great deal of attention, the active matter’s behavior in a fluid–fluid interface is equally intriguing and essential. In this particular review, we study the interactions of such active matter at the interface of two fluids, for example, air and water. The associated motion is termed as surfing, as opposed to swimming which is essentially a bulk phenomenon. We discuss the various aspects of surfing which are caused by an imbalance of different stresses arising from a host of causes like surface tension, temperature, heterogeneity of the interface, unbalanced chemical reactions, surface acoustic waves, etc. We study the division, fusion, and coalescence of liquid drops under the influence of various gradients. Furthermore, we describe in detail the motion of particles in the presence of an externally applied uniform electric as well as a magnetic field. We also discuss the fundamental structure, various methods of synthesization, dynamics, and critical applications of half-coated self-propelled active Janus particles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

Data availability statement

No data associated in the manuscript

References

  1. A. Zöttl, H. Stark, Periodic and quasiperiodic motion of an elongated microswimmer in poiseuille flow. Eur. Phys. J. E 36(1), 1–10 (2013)

    Google Scholar 

  2. A. Zöttl, H. Stark, Hydrodynamics determines collective motion and phase behavior of active colloids in quasi-two-dimensional confinement. Phys. Rev. Lett. 112(11), 118101 (2014)

    ADS  Google Scholar 

  3. R. Golestanian, T.B. Liverpool, A. Ajdari, Propulsion of a molecular machine by asymmetric distribution of reaction products. Phys. Rev. Lett. 94(22), 220801 (2005)

    ADS  Google Scholar 

  4. J.R. Howse, R.A. Jones, A.J. Ryan, T. Gough, R. Vafabakhsh, R. Golestanian, Self-motile colloidal particles: from directed propulsion to random walk. Phys. Rev. Lett. 99(4), 048102 (2007)

    ADS  Google Scholar 

  5. A. Walther, A.H. Müller, Janus particles. Soft Matter 4(4), 663–668 (2008)

    ADS  Google Scholar 

  6. S. Thutupalli, R. Seemann, S. Herminghaus, Swarming behavior of simple model squirmers. New J. Phys. 13(7), 073021 (2011)

    ADS  Google Scholar 

  7. M. Schmitt, H. Stark, Swimming active droplet: A theoretical analysis. EPL (Europhysics Letters) 101(4), 44008 (2013)

    ADS  Google Scholar 

  8. I. Theurkauff, C. Cottin-Bizonne, J. Palacci, C. Ybert, L. Bocquet, Dynamic clustering in active colloidal suspensions with chemical signaling. Phys. Rev. Lett. 108(26), 268303 (2012)

    ADS  Google Scholar 

  9. J. Palacci, S. Sacanna, A.P. Steinberg, D.J. Pine, P.M. Chaikin, Living crystals of light-activated colloidal surfers. Science 339(6122), 936–940 (2013)

    ADS  Google Scholar 

  10. U.M. Córdova-Figueroa, J.F. Brady, Osmotic propulsion: the osmotic motor. Phys. Rev. Lett. 100(15), 158303 (2008)

    ADS  Google Scholar 

  11. B. Ezhilan, R. Alonso-Matilla, D. Saintillan, On the distribution and swim pressure of run-and-tumble particles in confinement. Journal of Fluid Mechanics 781 (2015)

  12. F. Smallenburg, H. Löwen, Swim pressure on walls with curves and corners. Phys. Rev. E 92(3), 032304 (2015)

    ADS  Google Scholar 

  13. A. Snezhko, I.S. Aranson, Magnetic manipulation of self-assembled colloidal asters. Nat. Mater. 10(9), 698–703 (2011)

    ADS  Google Scholar 

  14. M. Sapozhnikov, Y.V. Tolmachev, I. Aranson, W.K. Kwok, Dynamic self-assembly and patterns in electrostatically driven granular media. Phys. Rev. Lett. 90(11), 114301 (2003)

    ADS  Google Scholar 

  15. M.E. Leunissen, H.R. Vutukuri, A. van Blaaderen, Directing colloidal self-assembly with biaxial electric fields. Adv. Mater. 21(30), 3116–3120 (2009)

    Google Scholar 

  16. B.P. Binks, S. Lumsdon, Influence of particle wettability on the type and stability of surfactant-free emulsions. Langmuir 16(23), 8622–8631 (2000)

    Google Scholar 

  17. Y. Karasawa, S. Oshima, T. Nomoto, T. Toyota, M. Fujinami, Simultaneous measurement of surface tension and its gradient around moving camphor boat on water surface. Chem. Lett. 43(7), 1002–1004 (2014)

    Google Scholar 

  18. Z. Izri, M.N. Van Der Linden, S. Michelin, O. Dauchot, Self-propulsion of pure water droplets by spontaneous marangoni-stress-driven motion. Phys. Rev. Lett. 113(24), 248302 (2014)

    ADS  Google Scholar 

  19. S. Nakata, Y. Iguchi, S. Ose, M. Kuboyama, T. Ishii, K. Yoshikawa, Self-rotation of a camphor scraping on water: new insight into the old problem. Langmuir 13(16), 4454–4458 (1997)

    Google Scholar 

  20. S. Nakata, Y. Iguchi, S. Ose, T. Ishii, ph-sensitive self-motion of a solid scraping on an aqueous phase. J. Phys. Chem. B 102(38), 7425–7427 (1998)

    Google Scholar 

  21. S. Nakata, Y. Hayashima, H. Komoto, Spontaneous switching of camphor motion between two chambers. Phys. Chem. Chem. Phys. 2(10), 2395–2399 (2000)

    Google Scholar 

  22. S. Nakata, M.I. Kohira, Y. Hayashima, Mode selection of a camphor boat in a dual-circle canal. Chem. Phys. Lett. 322(5), 419–423 (2000)

    ADS  Google Scholar 

  23. M.I. Kohira, Y. Hayashima, M. Nagayama, S. Nakata, Synchronized self-motion of two camphor boats. Langmuir 17(22), 7124–7129 (2001)

    Google Scholar 

  24. Y. Hayashima, M. Nagayama, S. Nakata, A camphor grain oscillates while breaking symmetry. J. Phys. Chem. B 105(22), 5353–5357 (2001)

    Google Scholar 

  25. Y. Hayashima, M. Nagayama, Y. Doi, S. Nakata, M. Kimura, M. Iida, Self-motion of a camphoric acid boat sensitive to the chemical environment. Phys. Chem. Chem. Phys. 4(8), 1386–1392 (2002)

    Google Scholar 

  26. S. Nakata, S. Hiromatsu, Intermittent motion of a camphor float. Colloids Surf., A 224(1–3), 157–163 (2003)

    Google Scholar 

  27. M. Nagayama, S. Nakata, Y. Doi, Y. Hayashima, A theoretical and experimental study on the unidirectional motion of a camphor disk. Physica D 194(3–4), 151–165 (2004)

    ADS  MATH  Google Scholar 

  28. S. Nakata, S. Hiromatsu, Self-motion of soap at an oil-water interface. Chem. Phys. Lett. 405(1–3), 39–42 (2005)

    ADS  Google Scholar 

  29. N. Bassik, B.T. Abebe, D.H. Gracias, Solvent driven motion of lithographically fabricated gels. Langmuir 24(21), 12158–12163 (2008)

    Google Scholar 

  30. F. Takabatake, N. Magome, M. Ichikawa, K. Yoshikawa, Spontaneous mode-selection in the self-propelled motion of a solid/liquid composite driven by interfacial instability. J. Chem. Phys. 134(11), 114704 (2011)

    ADS  Google Scholar 

  31. R. Seemann, J.B. Fleury, C.C. Maass, Self-propelled droplets. The European Physical Journal Special Topics 225(11), 2227–2240 (2016)

    ADS  Google Scholar 

  32. Y.J. Chen, Y. Nagamine, K. Yoshikawa, Self-propelled motion of a droplet induced by marangoni-driven spreading. Phys. Rev. E 80(1), 016303 (2009)

    ADS  Google Scholar 

  33. G. Jayaraman, S. Ramachandran, S. Ghose, A. Laskar, M.S. Bhamla, P.S. Kumar, R. Adhikari, Autonomous motility of active filaments due to spontaneous flow-symmetry breaking. Phys. Rev. Lett. 109(15), 158302 (2012)

    ADS  Google Scholar 

  34. J.W. Bush, D.L. Hu, Walking on water: biolocomotion at the interface. Annu. Rev. Fluid Mech. 38(1), 339–369 (2006)

    ADS  MathSciNet  MATH  Google Scholar 

  35. F.D. Dos Santos, T. Ondarcuhu, Free-running droplets. Phys. Rev. Lett. 75(16), 2972 (1995)

    ADS  Google Scholar 

  36. K. Ichimura, S.K. Oh, M. Nakagawa, Light-driven motion of liquids on a photoresponsive surface. Science 288(5471), 1624–1626 (2000)

    ADS  Google Scholar 

  37. S. Daniel, M.K. Chaudhury, J.C. Chen, Fast drop movements resulting from the phase change on a gradient surface. Science 291(5504), 633–636 (2001)

    ADS  Google Scholar 

  38. M.L. Cordero, D.R. Burnham, C.N. Baroud, D. McGloin, Thermocapillary manipulation of droplets using holographic beam shaping: Microfluidic pin ball. Appl. Phys. Lett. 93(3), 034107 (2008)

    ADS  Google Scholar 

  39. N.J. Cira, A. Benusiglio, M. Prakash, Vapour-mediated sensing and motility in two-component droplets. Nature 519(7544), 446–450 (2015)

    ADS  Google Scholar 

  40. F. Brochard, Motions of droplets on solid surfaces induced by chemical or thermal gradients. langmuir 5(2), 432–438 (1989)

    Google Scholar 

  41. P. Carles, A. Cazabat, Spreading involving the marangoni effect: some preliminary results. Colloids Surf. 41, 97–105 (1989)

    Google Scholar 

  42. M. Santiago-Rosanne, M. Vignes-Adler, M.G. Velarde, On the spreading of partially miscible liquids. J. Colloid Interface Sci. 234(2), 375–383 (2001)

    ADS  Google Scholar 

  43. E. Saiz, A.P. Tomsia, Atomic dynamics and marangoni films during liquid-metal spreading. Nat. Mater. 3(12), 903–909 (2004)

    ADS  Google Scholar 

  44. S. Thakur, P.S. Kumar, N. Madhusudana, P.A. Pullarkat, Mode selection in the spontaneous motion of an alcohol droplet. Phys. Rev. Lett. 97(11), 065301 (2005)

    Google Scholar 

  45. H. Kitahata, N. Yoshinaga, K.H. Nagai, Y. Sumino, Spontaneous motion of a belousov-zhabotinsky reaction droplet coupled with a spiral wave. Chem. Lett. 41(10), 1052–1054 (2012)

    Google Scholar 

  46. H. Hu, R.G. Larson, Analysis of the effects of marangoni stresses on the microflow in an evaporating sessile droplet. Langmuir 21(9), 3972–3980 (2005)

    Google Scholar 

  47. M.M. Hanczyc, T. Toyota, T. Ikegami, N. Packard, T. Sugawara, Fatty acid chemistry at the oil- water interface: Self-propelled oil droplets. J. Am. Chem. Soc. 129(30), 9386–9391 (2007)

    Google Scholar 

  48. W. Ristenpart, P. Kim, C. Domingues, J. Wan, H.A. Stone, Influence of substrate conductivity on circulation reversal in evaporating drops. Phys. Rev. Lett. 99(23), 234502 (2007)

    ADS  Google Scholar 

  49. V. Pimienta, M. Brost, N. Kovalchuk, S. Bresch, O. Steinbock, Complex shapes and dynamics of dissolving drops of dichloromethane. Angew. Chem. Int. Ed. 50(45), 10728–10731 (2011)

    Google Scholar 

  50. L. Keiser, H. Bense, P. Colinet, J. Bico, E. Reyssat, Marangoni bursting: evaporation-induced emulsification of binary mixtures on a liquid layer. Phys. Rev. Lett. 118(7), 074504 (2017)

    ADS  Google Scholar 

  51. S. Oshima, T. Nomoto, T. Toyota, M. Fujinami, Surface tension gradient around an alcohol droplet moving spontaneously on a water surface. Anal. Sci. 30(4), 441–444 (2014)

    Google Scholar 

  52. Y. Tsoumpas, S. Dehaeck, A. Rednikov, P. Colinet, Effect of marangoni flows on the shape of thin sessile droplets evaporating into air. Langmuir 31(49), 13334–13340 (2015)

    Google Scholar 

  53. J.F. Hernández-Sánchez, A. Eddi, J.H. Snoeijer, Marangoni spreading due to a localized alcohol supply on a thin water film. Phys. Fluids 27(3), 032003 (2015)

    ADS  Google Scholar 

  54. K.H. Nagai, K. Tachibana, Y. Tobe, M. Kazama, H. Kitahata, S. Omata, M. Nagayama, Mathematical model for self-propelled droplets driven by interfacial tension. J. Chem. Phys. 144(11), 114707 (2016)

    ADS  Google Scholar 

  55. S. Hardt, J. Hartmann, S. Zhao, A. Bandopadhyay, Electric-field-induced pattern formation in layers of dna molecules at the interface between two immiscible liquids. Phys. Rev. Lett. 124(6), 064501 (2020)

    ADS  Google Scholar 

  56. R. Seyboldt, F. Jülicher, Role of hydrodynamic flows in chemically driven droplet division. New J. Phys. 20(10), 105010 (2018)

    ADS  Google Scholar 

  57. P.A. Bachmann, P. Walde, P.L. Luisi, J. Lang, Self-replicating micelles: aqueous micelles and enzymatically driven reactions in reverse micelles. J. Am. Chem. Soc. 113(22), 8204–8209 (1991)

    Google Scholar 

  58. P.A. Bachmann, P. Walde, P.L. Luisi, J. Lang, Self-replicating reverse micelles and chemical autopoiesis. J. Am. Chem. Soc. 112(22), 8200–8201 (1990)

    Google Scholar 

  59. F. Caschera, S. Rasmussen, M.M. Hanczyc, An oil droplet division-fusion cycle. ChemPlusChem 78(1), 52–54 (2013)

    Google Scholar 

  60. I. Derényi, I. Lagzi, Fatty acid droplet self-division driven by a chemical reaction. Phys. Chem. Chem. Phys. 16(10), 4639–4641 (2014)

    Google Scholar 

  61. Y. Sumino, H. Kitahata, H. Seto, K. Yoshikawa, Dynamical blebbing at a droplet interface driven by instability in elastic stress: a novel self-motile system. Soft Matter 7(7), 3204–3212 (2011)

    ADS  Google Scholar 

  62. P. Constantin, T.F. Dupont, R.E. Goldstein, L.P. Kadanoff, M.J. Shelley, S.M. Zhou, Droplet breakup in a model of the hele-shaw cell. Phys. Rev. E 47(6), 4169 (1993)

    ADS  MathSciNet  Google Scholar 

  63. Y. Sumino, H. Kitahata, H. Seto, K. Yoshikawa, Blebbing dynamics in an oil-water-surfactant system through the generation and destruction of a gel-like structure. Phys. Rev. E 76(5), 055202 (2007)

    ADS  Google Scholar 

  64. Y. Sumino, H. Kitahata, H. Seto, S. Nakata, K. Yoshikawa, Spontaneous deformation of an oil droplet induced by the cooperative transport of cationic and anionic surfactants through the interface. J. Phys. Chem. B 113(48), 15709–15714 (2009)

    Google Scholar 

  65. K.P. Browne, D.A. Walker, K.J. Bishop, B.A. Grzybowski, Self-division of macroscopic droplets: Partitioning of nanosized cargo into nanoscale micelles. Angew. Chem. Int. Ed. 49(38), 6756–6759 (2010)

    Google Scholar 

  66. Y. Sumino, H. Kitahata, Y. Shinohara, N.L. Yamada, H. Seto, Formation of a multiscale aggregate structure through spontaneous blebbing of an interface. Langmuir 28(7), 3378–3384 (2012)

    Google Scholar 

  67. Y. Sumino, N.L. Yamada, M. Nagao, T. Honda, H. Kitahata, Y.B. Melnichenko, H. Seto, Mechanism of spontaneous blebbing motion of an oil-water interface: Elastic stress generated by a lamellar-lamellar transition. Langmuir 32(12), 2891–2899 (2016)

    Google Scholar 

  68. D. Zwicker, R. Seyboldt, C.A. Weber, A.A. Hyman, F. Jülicher, Growth and division of active droplets provides a model for protocells. Nat. Phys. 13(4), 408–413 (2017)

    Google Scholar 

  69. M. Okada, Y. Sumino, H. Ito, H. Kitahata, Spontaneous deformation and fission of oil droplets on an aqueous surfactant solution. Phys. Rev. E 102(4), 042603 (2020)

    ADS  Google Scholar 

  70. S.N. Jadhav, U. Ghosh, Thermocapillary effects on eccentric compound drops in poiseuille flows. Physical Review Fluids 6(7), 073602 (2021)

    ADS  Google Scholar 

  71. S.N. Jadhav, U. Ghosh, Effect of interfacial kinetics on the settling of a drop in a viscous medium. Phys. Fluids 34(4), 042007 (2022)

    ADS  Google Scholar 

  72. S.N. Jadhav, U. Ghosh, Effect of surfactant on the settling of a drop towards a wall. Journal of Fluid Mechanics 912 (2021)

  73. L. Rayleigh, The influence of electricity on colliding water drops. Proc. R. Soc. Lond. 28, 405–409 (1878)

    Google Scholar 

  74. S.P. Reynolds, Continuum spectra of collimated, ionized stellar winds. Astrophys J 304, 713–720 (1986)

    ADS  Google Scholar 

  75. D.G. Aarts, H.N. Lekkerkerker, H. Guo, G.H. Wegdam, D. Bonn, Hydrodynamics of droplet coalescence. Phys. Rev. Lett. 95(16), 164503 (2005)

    ADS  Google Scholar 

  76. W. Yao, H. Maris, P. Pennington, G. Seidel, Coalescence of viscous liquid drops. Phys. Rev. E 71(1), 016309 (2005)

    ADS  Google Scholar 

  77. D. Katoshevski, A. Nenes, J.H. Seinfeld, A study of processes that govern the maintenance of aerosols in the marine boundary layer. J. Aerosol Sci. 30(4), 503–532 (1999)

    ADS  Google Scholar 

  78. J.C. Lasheras, E. Hopfinger, Liquid jet instability and atomization in a coaxial gas stream. Annu. Rev. Fluid Mech. 32(1), 275–308 (2000)

    ADS  MATH  Google Scholar 

  79. D. Rosenfeld, Suppression of rain and snow by urban and industrial air pollution. science 287(5459), 1793–1796 (2000)

    ADS  Google Scholar 

  80. J.J. Thomson, H.F. Newall, V. on the formation of vortex rings by drops falling into liquids, and some allied phenomena. Proceedings of the royal society of London 39(239-241), 417–436 (1886)

  81. A. Menchaca-Rocha, A. Martínez-Dávalos, R. Nunez, S. Popinet, S. Zaleski, Coalescence of liquid drops by surface tension. Phys. Rev. E 63(4), 046309 (2001)

    ADS  Google Scholar 

  82. L. Duchemin, J. Eggers, C. Josserand, Inviscid coalescence of drops. J. Fluid Mech. 487, 167–178 (2003)

    ADS  MATH  Google Scholar 

  83. M. Wu, T. Cubaud, C.M. Ho, Scaling law in liquid drop coalescence driven by surface tension. Phys. Fluids 16(7), L51–L54 (2004)

    ADS  MATH  Google Scholar 

  84. J. Frenkel, Viscous flow of crystalline bodies under the action of surface tension. J. Phys. 9, 385 (1945)

    Google Scholar 

  85. R.W. Hopper, Plane stokes flow driven by capillarity on a free surface. J. Fluid Mech. 213, 349–375 (1990)

    ADS  MathSciNet  MATH  Google Scholar 

  86. R.W. Hopper, Stokes flow of a cylinder and half-space driven by capillarity. J. Fluid Mech. 243, 171–181 (1992)

    ADS  MATH  Google Scholar 

  87. R.W. Hopper, Coalescence of two viscous cylinders by capillarity: Part i, theory. J. Am. Ceram. Soc. 76(12), 2947–2952 (1993)

    Google Scholar 

  88. J. Eggers, J.R. Lister, H.A. Stone, Coalescence of liquid drops. J. Fluid Mech. 401, 293–310 (1999)

    ADS  MathSciNet  MATH  Google Scholar 

  89. K. Fezzaa, Y. Wang, Ultrafast x-ray phase-contrast imaging of the initial coalescence phase of two water droplets. Phys. Rev. Lett. 100(10), 104501 (2008)

    ADS  Google Scholar 

  90. J.D. Paulsen, R. Carmigniani, A. Kannan, J.C. Burton, S.R. Nagel, Coalescence of bubbles and drops in an outer fluid. Nat. Commun. 5(1), 1–7 (2014)

    Google Scholar 

  91. S. Nudurupati, M. Janjua, P. Singh, N. Aubry, Electrohydrodynamic removal of particles from drop surfaces. Phys. Rev. E 80(1), 010402 (2009)

    ADS  Google Scholar 

  92. S. Nudurupati, M. Janjua, P. Singh, N. Aubry, Effect of parameters on redistribution and removal of particles from drop surfaces. Soft Matter 6(6), 1157–1169 (2010)

    ADS  Google Scholar 

  93. T.B. Jones, M. Washizu, Multipolar dielectrophoretic and electrorotation theory. J. Electrostat. 37(1–2), 121–134 (1996)

    Google Scholar 

  94. H.A. Pohl, Dielectrophoresis. The behavior of neutral matter in nonuniform electric fields (1978)

  95. A. Ramos, H. Morgan, N.G. Green, A. Castellanos, The role of electrohydrodynamic forces in the dielectrophoretic manipulation and separation of particles. J. Electrostat. 47(1–2), 71–81 (1999)

    Google Scholar 

  96. N.G. Green, A. Ramos, H. Morgan, Numerical solution of the dielectrophoretic and travelling wave forces for interdigitated electrode arrays using the finite element method. J. Electrostat. 56(2), 235–254 (2002)

    Google Scholar 

  97. T. Heida, W. Rutten, E. Marani, Understanding dielectrophoretic trapping of neuronal cells: modelling electric field, electrode-liquid interface and fluid flow. J. Phys. D Appl. Phys. 35(13), 1592 (2002)

    ADS  Google Scholar 

  98. A. Mikkelsen, K. Khobaib, F.K. Eriksen, K.J. Måløy, Z. Rozynek, Particle-covered drops in electric fields: drop deformation and surface particle organization. Soft Matter 14(26), 5442–5451 (2018)

    ADS  Google Scholar 

  99. E. Amah, K. Shah, I. Fischer, P. Singh, Electrohydrodynamic manipulation of particles adsorbed on the surface of a drop. Soft Matter 12(6), 1663–1673 (2016)

    ADS  Google Scholar 

  100. S. Nudurupati, M. Janjua, N. Aubry, P. Singh, Concentrating particles on drop surfaces using external electric fields. Electrophoresis 29(5), 1164–1172 (2008)

    Google Scholar 

  101. S. Torza, R. Cox, S. Mason, Electrohydrodynamic deformation and bursts of liquid drops. Philosophical Transactions of the Royal Society of London.Series A, Mathematical and Physical Sciences 269(1198), 295–319 (1971)

    ADS  Google Scholar 

  102. R. Allan, S. Mason, Particle behaviour in shear and electric fields i. deformation and burst of fluid drops. Proc. R. Soc. Lond. A 267(1328), 45–61 (1962)

    ADS  Google Scholar 

  103. P.G. De Gennes, F. Brochard-Wyart, D. Quéré, et al., Capillarity and wetting phenomena: drops, bubbles, pearls, waves, vol. 315 (Springer, 2004)

  104. J.D. Paulsen, J.C. Burton, S.R. Nagel, S. Appathurai, M.T. Harris, O.A. Basaran, The inexorable resistance of inertia determines the initial regime of drop coalescence. Proc. Natl. Acad. Sci. 109(18), 6857–6861 (2012)

    ADS  Google Scholar 

  105. G.I. Taylor, Disintegration of water drops in an electric field. Proc. R. Soc. Lond. A 280(1382), 383–397 (1964)

    ADS  MATH  Google Scholar 

  106. D. Saville, Electrohydrodynamics: the taylor-melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29(1), 27–64 (1997)

    ADS  MathSciNet  Google Scholar 

  107. H.A. Stone, J.R. Lister, M.P. Brenner, Drops with conical ends in electric and magnetic fields. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 455(1981), 329–347 (1999)

    ADS  MATH  Google Scholar 

  108. L. Oddershede, S.R. Nagel, Singularity during the onset of an electrohydrodynamic spout. Phys. Rev. Lett. 85(6), 1234 (2000)

    ADS  Google Scholar 

  109. R.T. Collins, J.J. Jones, M.T. Harris, O.A. Basaran, Electrohydrodynamic tip streaming and emission of charged drops from liquid cones. Nat. Phys. 4(2), 149–154 (2008)

    Google Scholar 

  110. J.C. Bird, W.D. Ristenpart, A. Belmonte, H.A. Stone, Critical angle for electrically driven coalescence of two conical droplets. Phys. Rev. Lett. 103(16), 164502 (2009)

    ADS  Google Scholar 

  111. J. Melcher, Electrohydrodynamics: a review of the role of interfacial shear stresses. Ann. Rev. Fluid Mech. 1, 111–146 (1969)

    ADS  Google Scholar 

  112. J. Fernández de La Mora, The fluid dynamics of taylor cones. Annu. Rev. Fluid Mech. 39, 217–243 (2007)

    ADS  MathSciNet  MATH  Google Scholar 

  113. Y. Amarouchene, G. Cristobal, H. Kellay, Noncoalescing drops. Phys. Rev. Lett. 87(20), 206104 (2001)

    ADS  Google Scholar 

  114. R. Aveyard, B.P. Binks, J.H. Clint, Emulsions stabilised solely by colloidal particles. Adv. Coll. Interface. Sci. 100, 503–546 (2003)

    Google Scholar 

  115. J. Burton, J. Rutledge, P. Taborek, Fluid pinch-off dynamics at nanometer length scales. Phys. Rev. Lett. 92(24), 244505 (2004)

    ADS  Google Scholar 

  116. K. Ahn, J. Agresti, H. Chong, M. Marquez, D.A. Weitz, Electrocoalescence of drops synchronized by size-dependent flow in microfluidic channels. Appl. Phys. Lett. 88(26), 264105 (2006)

    ADS  Google Scholar 

  117. J. Burton, P. Taborek, Role of dimensionality and axisymmetry in fluid pinch-off and coalescence. Phys. Rev. Lett. 98(22), 224502 (2007)

    ADS  Google Scholar 

  118. S.C. Case, S.R. Nagel, Coalescence in low-viscosity liquids. Phys. Rev. Lett. 100(8), 084503 (2008)

    ADS  Google Scholar 

  119. S.C. Case, Coalescence of low-viscosity fluids in air. Phys. Rev. E 79(2), 026307 (2009)

    ADS  Google Scholar 

  120. A. Lukyanets, H. Kavehpour, Effect of electric fields on the rest time of coalescing drops. Appl. Phys. Lett. 93(19), 194101 (2008)

    ADS  Google Scholar 

  121. J.D. Paulsen, J.C. Burton, S.R. Nagel, Viscous to inertial crossover in liquid drop coalescence. Phys. Rev. Lett. 106(11), 114501 (2011)

    ADS  Google Scholar 

  122. J.D. Paulsen, Approach and coalescence of liquid drops in air. Phys. Rev. E 88(6), 063010 (2013)

    ADS  Google Scholar 

  123. M. Belkin, A. Snezhko, I. Aranson, W.K. Kwok, Driven magnetic particles on a fluid surface: Pattern assisted surface flows. Phys. Rev. Lett. 99(15), 158301 (2007)

    ADS  Google Scholar 

  124. A. Snezhko, I. Aranson, W.K. Kwok, Surface wave assisted self-assembly of multidomain magnetic structures. Phys. Rev. Lett. 96(7), 078701 (2006)

    ADS  Google Scholar 

  125. P.A. Kralchevsky, K. Nagayama, Capillary forces between colloidal particles. Langmuir 10(1), 23–36 (1994)

    Google Scholar 

  126. D. Vella, L. Mahadevan, The “cheerios effect’’. Am. J. Phys. 73(9), 817–825 (2005)

    ADS  Google Scholar 

  127. M. Golosovsky, Y. Saado, D. Davidov, Self-assembly of floating magnetic particles into ordered structures: A promising route for the fabrication of tunable photonic band gap materials. Appl. Phys. Lett. 75(26), 4168–4170 (1999)

    ADS  Google Scholar 

  128. G. Grosjean, G. Lagubeau, A. Darras, M. Hubert, G. Lumay, N. Vandewalle, Remote control of self-assembled microswimmers. Sci. Rep. 5(1), 1–8 (2015)

    Google Scholar 

  129. A. Snezhko, M. Belkin, I. Aranson, W.K. Kwok, Self-assembled magnetic surface swimmers. Phys. Rev. Lett. 102(11), 118103 (2009)

    ADS  Google Scholar 

  130. M. Berhanu, A. Kudrolli, Heterogeneous structure of granular aggregates with capillary interactions. Phys. Rev. Lett. 105(9), 098002 (2010)

    ADS  Google Scholar 

  131. G. Lumay, N. Obara, F. Weyer, N. Vandewalle, Self-assembled magnetocapillary swimmers. Soft Matter 9(8), 2420–2425 (2013)

    ADS  Google Scholar 

  132. M.N. Popescu, W.E. Uspal, S. Dietrich, Self-diffusiophoresis of chemically active colloids. The European Physical Journal Special Topics 225(11), 2189–2206 (2016)

    ADS  Google Scholar 

  133. S. Michelin, E. Lauga, D. Bartolo, Spontaneous autophoretic motion of isotropic particles. Phys. Fluids 25(6), 061701 (2013)

    ADS  Google Scholar 

  134. K. Dietrich, D. Renggli, M. Zanini, G. Volpe, I. Buttinoni, L. Isa, Two-dimensional nature of the active brownian motion of catalytic microswimmers at solid and liquid interfaces. New J. Phys. 19(6), 065008 (2017)

    ADS  Google Scholar 

  135. K. Dietrich, G. Volpe, M.N. Sulaiman, D. Renggli, I. Buttinoni, L. Isa, Active atoms and interstitials in two-dimensional colloidal crystals. Phys. Rev. Lett. 120(26), 268004 (2018)

    ADS  Google Scholar 

  136. P. Malgaretti, M. Popescu, S. Dietrich, Self-diffusiophoresis induced by fluid interfaces. Soft Matter 14(8), 1375–1388 (2018)

    ADS  Google Scholar 

  137. X. Wang, M. In, C. Blanc, M. Nobili, A. Stocco, Enhanced active motion of janus colloids at the water surface. Soft Matter 11(37), 7376–7384 (2015)

    ADS  Google Scholar 

  138. X. Wang, M. In, C. Blanc, A. wurger, M. Nobili, A. Stocco, Janus colloids actively rotating on the surface of water. Langmuir 33(48), 13766–13773 (2017)

    Google Scholar 

  139. H.R. Jiang, N. Yoshinaga, M. Sano, Active motion of a janus particle by self-thermophoresis in a defocused laser beam. Phys. Rev. Lett. 105(26), 268302 (2010)

    ADS  Google Scholar 

  140. C. Casagrande, Janus beads-realization and 1st observation of interfacial properties. CR Acad. Sci. Ser. II(306), 1423–1425 (1998)

    Google Scholar 

  141. C. Casagrande, P. Fabre, E. Raphael, M. Veyssié, “janus beads’’: realization and behaviour at water/oil interfaces. EPL (Europhysics Letters) 9(3), 251 (1989)

    ADS  Google Scholar 

  142. L. Hong, S. Jiang, S. Granick, Simple method to produce janus colloidal particles in large quantity. Langmuir 22(23), 9495–9499 (2006)

    Google Scholar 

  143. K.H. Roh, D.C. Martin, J. Lahann, Biphasic janus particles with nanoscale anisotropy. Nat. Mater. 4(10), 759–763 (2005)

    ADS  Google Scholar 

  144. T. Nisisako, T. Torii, T. Takahashi, Y. Takizawa, Synthesis of monodisperse bicolored janus particles with electrical anisotropy using a microfluidic co-flow system. Adv. Mater. 18(9), 1152–1156 (2006)

    Google Scholar 

  145. T. Nisisako, T. Torii, Formation of biphasic janus droplets in a microfabricated channel for the synthesis of shape-controlled polymer microparticles. Adv. Mater. 19(11), 1489–1493 (2007)

    Google Scholar 

  146. R.F. Shepherd, J.C. Conrad, S.K. Rhodes, D.R. Link, M. Marquez, D.A. Weitz, J.A. Lewis, Microfluidic assembly of homogeneous and janus colloid-filled hydrogel granules. Langmuir 22(21), 8618–8622 (2006)

    Google Scholar 

  147. D. Dendukuri, D.C. Pregibon, J. Collins, T.A. Hatton, P.S. Doyle, Continuous-flow lithography for high-throughput microparticle synthesis. Nat. Mater. 5(5), 365–369 (2006)

    ADS  Google Scholar 

  148. Z. Nie, W. Li, M. Seo, S. Xu, E. Kumacheva, Janus and ternary particles generated by microfluidic synthesis: design, synthesis, and self-assembly. J. Am. Chem. Soc. 128(29), 9408–9412 (2006)

    Google Scholar 

  149. M. Seo, Z. Nie, S. Xu, M. Mok, P.C. Lewis, R. Graham, E. Kumacheva, Continuous microfluidic reactors for polymer particles. Langmuir 21(25), 11614–11622 (2005)

    Google Scholar 

  150. A. Perro, S. Reculusa, S. Ravaine, E. Bourgeat-Lami, E. Duguet, Design and synthesis of janus micro-and nanoparticles. J. Mater. Chem. 15(35–36), 3745–3760 (2005)

    Google Scholar 

  151. C.J. Behrend, J.N. Anker, B.H. McNaughton, R. Kopelman, Microrheology with modulated optical nanoprobes (moons). J. Magn. Magn. Mater. 293(1), 663–670 (2005)

    ADS  Google Scholar 

  152. C.J. Behrend, J.N. Anker, R. Kopelman, Brownian modulated optical nanoprobes. Appl. Phys. Lett. 84(1), 154–156 (2004)

    ADS  Google Scholar 

  153. C.J. Behrend, J.N. Anker, B.H. McNaughton, M. Brasuel, M.A. Philbert, R. Kopelman, Metal-capped brownian and magnetically modulated optical nanoprobes (moons): micromechanics in chemical and biological microenvironments. J. Phys. Chem. B 108(29), 10408–10414 (2004)

    Google Scholar 

  154. J.N. Anker, C. Behrend, R. Kopelman, Aspherical magnetically modulated optical nanoprobes (magmoons). J. Appl. Phys. 93(10), 6698–6700 (2003)

    ADS  Google Scholar 

  155. J.N. Anker, C.J. Behrend, H. Huang, R. Kopelman, Magnetically-modulated optical nanoprobes (magmoons) and systems. J. Magn. Magn. Mater. 293(1), 655–662 (2005)

    ADS  Google Scholar 

  156. J. Choi, Y. Zhao, D. Zhang, S. Chien, Y.H. Lo, Patterned fluorescent particles as nanoprobes for the investigation of molecular interactions. Nano Lett. 3(8), 995–1000 (2003)

    ADS  Google Scholar 

  157. N. Glaser, D.J. Adams, A. Böker, G. Krausch, Janus particles at liquid- liquid interfaces. Langmuir 22(12), 5227–5229 (2006)

    Google Scholar 

  158. B. Binks, P. Fletcher, Particles adsorbed at the oil- water interface: A theoretical comparison between spheres of uniform wettability and “janus’’ particles. Langmuir 17(16), 4708–4710 (2001)

    Google Scholar 

  159. Y. Nonomura, S. Komura, K. Tsujii, Adsorption of disk-shaped janus beads at liquid- liquid interfaces. Langmuir 20(26), 11821–11823 (2004)

    Google Scholar 

  160. J. Palacci, C. Cottin-Bizonne, C. Ybert, L. Bocquet, Sedimentation and effective temperature of active colloidal suspensions. Phys. Rev. Lett. 105(8), 088304 (2010)

    ADS  Google Scholar 

  161. I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, T. Speck, Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles. Phys. Rev. Lett. 110(23), 238301 (2013)

    ADS  Google Scholar 

  162. J.L. Anderson, Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 21(1), 61–99 (1989)

    ADS  MATH  Google Scholar 

  163. A. Sen, M. Ibele, Y. Hong, D. Velegol, Chemo and phototactic nano/microbots. Faraday Discuss. 143, 15–27 (2009)

    ADS  Google Scholar 

  164. P.E. Lammert, V.H. Crespi, A. Nourhani, Bypassing slip velocity: rotational and translational velocities of autophoretic colloids in terms of surface flux. J. Fluid Mech. 802, 294–304 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  165. J.F. Brady, Particle motion driven by solute gradients with application to autonomous motion: continuum and colloidal perspectives. J. Fluid Mech. 667, 216–259 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  166. H. Masoud, H.A. Stone, The reciprocal theorem in fluid dynamics and transport phenomena. Journal of Fluid Mechanics 879 (2019)

  167. H. Brenner, The stokes resistance of an arbitrary particle-iv arbitrary fields of flow. Chem. Eng. Sci. 19(10), 703–727 (1964)

    Google Scholar 

  168. S. Kim, Ellipsoidal microhydrodynamics without elliptic integrals and how to get there using linear operator theory. Industrial & Engineering Chemistry Research 54(42), 10497–10501 (2015)

    Google Scholar 

  169. A. Ajdari, H.A. Stone, A note on swimming using internally generated traveling waves. Phys. Fluids 11(5), 1275–1277 (1999)

    ADS  MATH  Google Scholar 

  170. O.S. Pak, L. Zhu, L. Brandt, E. Lauga, Micropropulsion and microrheology in complex fluids via symmetry breaking. Phys. Fluids 24(10), 103102 (2012)

    ADS  Google Scholar 

  171. D. Papavassiliou, G.P. Alexander, The many-body reciprocal theorem and swimmer hydrodynamics. EPL (Europhysics Letters) 110(4), 44001 (2015)

    ADS  Google Scholar 

  172. G.J. Elfring, G. Goyal, The effect of gait on swimming in viscoelastic fluids. J. Nonnewton. Fluid Mech. 234, 8–14 (2016)

    MathSciNet  Google Scholar 

  173. G.J. Elfring, Force moments of an active particle in a complex fluid. Journal of Fluid Mechanics 829 (2017)

  174. K. Shoele, P.S. Eastham, Effects of nonuniform viscosity on ciliary locomotion. Physical Review Fluids 3(4), 043101 (2018)

    ADS  Google Scholar 

  175. A. Nourhani, P.E. Lammert, V.H. Crespi, A. Borhan, A general flux-based analysis for spherical electrocatalytic nanomotors. Phys. Fluids 27(1), 012001 (2015)

    ADS  Google Scholar 

  176. A. Mozaffari, N. Sharifi-Mood, J. Koplik, C. Maldarelli, Self-diffusiophoretic colloidal propulsion near a solid boundary. Phys. Fluids 28(5), 053107 (2016)

    ADS  Google Scholar 

  177. F. Schweitzer, J.D. Farmer, Brownian agents and active particles: collective dynamics in the natural and social sciences, vol. 1 (Springer, 2003)

  178. J.K. Dhont, An introduction to dynamics of colloids (Elsevier, 1996)

    Google Scholar 

  179. F. Schweitzer, W. Ebeling, B. Tilch, Complex motion of brownian particles with energy depots. Phys. Rev. Lett. 80(23), 5044 (1998)

    ADS  Google Scholar 

  180. S.E. Spagnolie, E. Lauga, Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations. J. Fluid Mech. 700, 105–147 (2012)

    ADS  MathSciNet  MATH  Google Scholar 

  181. C. Pozrikidis et al., Boundary integral and singularity methods for linearized viscous flow (Cambridge university press, 1992)

    MATH  Google Scholar 

  182. S. Kim, S. Karrila. Microhydrodynamics butterworth (1991)

  183. J. Gb, The motion of ellipsoidal particles in a viscous fluid. Proc Roy Soc (London), Ser A-Containing Papers Mathematical Physical Character 102, 161–179 (1922)

    Google Scholar 

  184. E. Hinch, L. Leal, Rotation of small non-axisymmetric particles in a simple shear flow. J. Fluid Mech. 92(3), 591–607 (1979)

    ADS  MathSciNet  MATH  Google Scholar 

  185. G. Pucci, E. Fort, M.B. Amar, Y. Couder, Mutual adaptation of a faraday instability pattern with its flexible boundaries in floating fluid drops. Phys. Rev. Lett. 106(2), 024503 (2011)

    ADS  Google Scholar 

  186. G. Pucci, M.B. Amar, Y. Couder, Faraday instability in floating liquid lenses: the spontaneous mutual adaptation due to radiation pressure. J. Fluid Mech. 725, 402–427 (2013)

    ADS  MATH  Google Scholar 

  187. A. Eddi, E. Sultan, J. Moukhtar, E. Fort, M. Rossi, Y. Couder, Information stored in faraday waves: the origin of a path memory. J. Fluid Mech. 674, 433–463 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  188. S. Dehe, M. Hartmann, A. Bandopadhyay, S. Hardt, The spatial structure of electrostatically forced faraday waves. Journal of Fluid Mechanics 939 (2022)

  189. D. Beaglehole, Capillary waves on the liquid-vapour interface, and propagation near boundaries. Physica A 200(1–4), 696–707 (1993)

    ADS  Google Scholar 

  190. K.J. Målo/y, J. Feder, T. Jo/ssang, An experimental technique for measurements of capillary waves. Review of scientific instruments 60(3), 481–486 (1989)

  191. A.E. Ismail, G.S. Grest, M.J. Stevens, Capillary waves at the liquid-vapor interface and the surface tension of water. J. Chem. Phys. 125(1), 014702 (2006)

    ADS  Google Scholar 

  192. L. Shen, F. Denner, N. Morgan, B. van Wachem, D. Dini, Capillary waves with surface viscosity. J. Fluid Mech. 847, 644–663 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  193. H. Ding, E. Li, F. Zhang, Y. Sui, P.D. Spelt, S.T. Thoroddsen, Propagation of capillary waves and ejection of small droplets in rapid droplet spreading. J. Fluid Mech. 697, 92–114 (2012)

    ADS  MATH  Google Scholar 

  194. D.P. Häder, R. Hemmersbach, M. Lebert et al., Gravity and the behavior of unicellular organisms, vol. 40 (Cambridge University Press, 2005)

    Google Scholar 

  195. F. Behroozi, N. Podolefsky, Capillary-gravity waves and the navier-stokes equation. Eur. J. Phys. 22(6), 587 (2001)

    MATH  Google Scholar 

  196. F. Behroozi, B. Lambert, B. Buhrow, Direct measurement of the attenuation of capillary waves by laser interferometry: Noncontact determination of viscosity. Appl. Phys. Lett. 78(16), 2399–2401 (2001)

    ADS  Google Scholar 

  197. F. Behroozi, N. Podolefsky, Dispersion of capillary-gravity waves: a derivation based on conservation of energy. Eur. J. Phys. 22(3), 225 (2001)

    MATH  Google Scholar 

  198. M. Debiane, C. Kharif, A new way for the calculation of steady periodic capillary-gravity waves on deep water. European journal of mechanics. B, Fluids 16(2), 257–275 (1997)

    MATH  Google Scholar 

  199. H. Ebata, M. Sano, Swimming droplets driven by a surface wave. Sci. Rep. 5(1), 1–7 (2015)

    Google Scholar 

  200. J. Walker, Drops of liquid can be made to float on liquid-what enables them to do so. Sci. Am. 238(6), 151 (1978)

    Google Scholar 

  201. Y. Couder, E. Fort, C.H. Gautier, A. Boudaoud, From bouncing to floating: noncoalescence of drops on a fluid bath. Phys. Rev. Lett. 94(17), 177801 (2005)

    ADS  Google Scholar 

  202. S.C. Varma, A. Saha, S. Mukherjee, A. Bandopadhyay, A. Kumar, S. Chakraborty, Universality in coalescence of polymeric fluids. Soft Matter 16(48), 10921–10927 (2020)

    ADS  Google Scholar 

  203. S.C. Varma, A. Saha, A. Kumar, Coalescence of polymeric sessile drops on a partially wettable substrate. Phys. Fluids 33(12), 123101 (2021)

    ADS  Google Scholar 

  204. A. Rahimzadeh, M.R. Ahmadian-Yazdi, M. Eslamian, Experimental study on the characteristics of capillary surface waves on a liquid film on an ultrasonically vibrated substrate. Fluid Dyn. Res. 50(6), 065510 (2018)

    ADS  Google Scholar 

  205. J. Saylor, A. Szeri, G. Foulks, Measurement of surfactant properties using a circular capillary wave field. Exp. Fluids 29(6), 509–518 (2000)

    Google Scholar 

  206. R. Carmigniani, S. Lapointe, S. Symon, B. McKeon, Influence of a local change of depth on the behavior of walking oil drops. Exp. Thermal Fluid Sci. 54, 237–246 (2014)

    Google Scholar 

  207. Y.D. Chashechkin, A.Y. Ilinykh, in Doklady physics, vol. 60 (Springer, 2015), pp. 548–554

  208. Y. Couder, A. Boudaoud, S. Protière, E. Fort, Walking droplets, a form of wave-particle duality at macroscopic scale? Europhys. News 41(1), 14–18 (2010)

    ADS  Google Scholar 

  209. J. Whitehill, A. Neild, T.W. Ng, S. Martyn, J. Chong, Droplet spreading using low frequency vibration. Appl. Phys. Lett. 98(13), 133503 (2011)

    ADS  Google Scholar 

  210. B. Filoux, M. Hubert, N. Vandewalle, Strings of droplets propelled by coherent waves. Phys. Rev. E 92(4), 041004 (2015)

    ADS  Google Scholar 

  211. E. Bormashenko, Y. Bormashenko, R. Grynyov, H. Aharoni, G. Whyman, B.P. Binks, Self-propulsion of liquid marbles: Leidenfrost-like levitation driven by marangoni flow. The Journal of Physical Chemistry C 119(18), 9910–9915 (2015)

    ADS  Google Scholar 

  212. A.P. Wallenberger, D.R. Lyzenga, Measurement of the surface tension of water using microwave backscatter from gravity-capillary waves. IEEE Trans. Geosci. Remote Sens. 28(6), 1012–1016 (1990)

    ADS  Google Scholar 

  213. T. Bohanon, J. Mikrut, B. Abraham, J. Ketterson, P. Dutta, Fiber-optic detection system for capillary waves: an apparatus for studying liquid surfaces and spread monolayers. Rev. Sci. Instrum. 62(12), 2959–2962 (1991)

    ADS  Google Scholar 

  214. J. Earnshaw, C. Hughes, High-frequency capillary waves on the clean surface of water. Langmuir 7(11), 2419–2421 (1991)

    Google Scholar 

  215. A. Belmonte, J.M. Flesselles, Experimental determination of the dispersion relation for spiral waves. Phys. Rev. Lett. 77(6), 1174 (1996)

    ADS  Google Scholar 

  216. G. Weisbuch, F. Garbay, Light scattering by surface tension waves. Am. J. Phys. 47(4), 355–56 (1979)

    ADS  Google Scholar 

  217. W. Klipstein, J. Radnich, S. Lamoreaux, Thermally excited liquid surface waves and their study through the quasielastic scattering of light. Am. J. Phys. 64(6), 758–765 (1996)

    ADS  Google Scholar 

  218. D.R. Howell, B. Buhrow, T. Heath, C. McKenna, W. Hwang, M.F. Schatz, Measurements of surface-wave damping in a container. Phys. Fluids 12(2), 322–326 (2000)

    ADS  MATH  Google Scholar 

  219. R. Miao, Z. Yang, J. Zhu, C. Shen, Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction. Appl. Phys. Lett. 80(17), 3033–3035 (2002)

    ADS  Google Scholar 

  220. F. Behroozi, B. Lambert, B. Buhrow, Noninvasive measurement of viscosity from damping of capillary waves. ISA Trans. 42(1), 3–8 (2003)

    Google Scholar 

  221. F. Behroozi. Apparatus and method for measurement of fluid viscosity (2003). US Patent 6,563,588

  222. D. Chowdhury, S. Bhunia, T.K. Barik, Study the liquid surface capillary wave profile by optical method. Int. J. Soft Comput. Eng 2, 386 (2013)

    Google Scholar 

  223. F. Zhu, R. Miao, C. Xu, Z. Cao, Measurement of the dispersion relation of capillary waves by laser diffraction. Am. J. Phys. 75(10), 896–898 (2007)

    ADS  Google Scholar 

  224. F. Behroozi, A. Perkins, Direct measurement of the dispersion relation of capillary waves by laser interferometry. Am. J. Phys. 74(11), 957–961 (2006)

    ADS  Google Scholar 

  225. R. Bahadur, L.M. Russell, S. Alavi, Surface tensions in nacl- water- air systems from md simulations. J. Phys. Chem. B 111(41), 11989–11996 (2007)

    Google Scholar 

  226. D. Nikolić, L. Nešić, Determination of surface tension coefficient of liquids by diffraction of light on capillary waves. Eur. J. Phys. 33(6), 1677 (2012)

    Google Scholar 

  227. C. Pigot, A. Hibara, Surface tension measurement at the microscale by passive resonance of capillary waves. Anal. Chem. 84(5), 2557–2561 (2012)

    Google Scholar 

  228. S. Yang, X. He, H. Wang, S. Li, G. Wang, E. Wu, K. Zhou, in Symposium on Computer Animation (2016), pp. 29–36

  229. O. Shomina, I. Kapustin, S. Ermakov, Damping of gravity-capillary waves on the surface of turbulent fluid. Exp. Fluids 61(8), 1–12 (2020)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Aditya Bandopadhyay.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Panday, P.N., Bandopadhyay, A. & Das, P.K. Surfing of particles and droplets on the free surface of a liquid: a review. Eur. Phys. J. Spec. Top. 232, 735–768 (2023). https://doi.org/10.1140/epjs/s11734-022-00726-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-022-00726-z

Navigation