A capillary surface is an interface between two fluids whose shape is determined primarily by surface tension. Sessile drops, liquid bridges, rivulets, and liquid drops on fibers are all examples of capillary shapes influenced by contact with a solid. Capillary shapes can reconfigure spontaneously or exhibit natural oscillations, reflecting static or dynamic instabilities, respectively. Both instabilities are related, and a review of static stability precedes the dynamic case. The focus of the dynamic case here is the hydrodynamic stability of capillary surfaces subject to constraints of () volume conservation, () contact-line boundary conditions, and () the geometry of the supporting surface.


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Literature Cited

  1. Almeida ME, Teixeira HF, Koester LS. 2008. Preparation of submicron emulsions: theoretical aspects about the methods employed today. Lat. Am. J. Pharm. 27:780–88 [Google Scholar]
  2. Attinger D, Moore C, Donaldson A, Jafari A, Stone HA. 2013. Fluid dynamics topics in bloodstain pattern analysis: comparative review and research opportunities. Forensic Sci. Int. 231:375–96 [Google Scholar]
  3. Barz DPJ, Steen PH. 2013. A dynamic model of the electroosmotic droplet switch. Phys. Fluids 25:097104 [Google Scholar]
  4. Basaran OA. 2002. Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J. 48:1842–48 [Google Scholar]
  5. Basaran OA, DePaoli D. 1994. Nonlinear oscillations of pendant drops. Phys. Fluids 6:2923–43 [Google Scholar]
  6. Bauer H, Chiba M. 2004. Oscillations of captured spherical drop of frictionless liquid. J. Sound Vib. 274:725–46 [Google Scholar]
  7. Benilov E. 2009. On the stability of shallow rivulets. J. Fluid Mech. 636:455–74 [Google Scholar]
  8. Benilov E, Billingham J. 2011. Drops climbing uphill on an oscillating substrate. J. Fluid Mech. 674:93–119 [Google Scholar]
  9. Benjamin TB, Scott JC. 1979. Gravity-capillary waves with edge constraints. J. Fluid Mech. 92:241–67 [Google Scholar]
  10. Berthier E, Warrick J, Yu H, Beebe DJ. 2008. Managing evaporation for more robust microscale assays. Part 2. Characterization of convection and diffusion for cell biology. Lab Chip 8:860–64 [Google Scholar]
  11. Bigioni TP, Lin XM, Nguyen TT, Corwin EI, Witten TA, Jaeger HM. 2006. Kinetically driven self assembly of highly ordered nanoparticle monolayers. Nat. Mater. 5:265–70 [Google Scholar]
  12. Bisch C, Lasek A, Rodot H. 1982. Compartement hydrodynamique de volumes liquides spheriques semi-libres en apesanteur simulee. J. Mec. Theor. Appl. 1:165–84 [Google Scholar]
  13. Bolza O. 1904. Lectures on the Calculus of Variations Chicago: Univ. Chicago Press [Google Scholar]
  14. Borkar A, Tsamopoulos J. 1991. Boundary-layer analysis of the dynamics of axisymmetric capillary bridges. Phys. Fluids A 3:2866–74 [Google Scholar]
  15. Bostwick JB, Steen PH. 2009. Capillary oscillations of a constrained liquid drop. Phys. Fluids 21:032108 [Google Scholar]
  16. Bostwick JB, Steen PH. 2010. Stability of constrained cylindrical interfaces and the torus lift of Plateau-Rayleigh. J. Fluid Mech. 647:201–19 [Google Scholar]
  17. Bostwick JB, Steen PH. 2013a. Coupled oscillations of deformable spherical-cap droplets. Part 1. Inviscid motions. J. Fluid Mech. 714:312–35 [Google Scholar]
  18. Bostwick JB, Steen PH. 2013b. Coupled oscillations of deformable spherical-cap droplets. Part 2. Viscous motions. J. Fluid Mech. 714:336–60 [Google Scholar]
  19. Bostwick JB, Steen PH. 2014. Dynamics of sessile drops. Part 1. Inviscid theory. J. Fluid Mech. 7605–38 [Google Scholar]
  20. Boudaoud A, Patricio P, Ben Amar M. 1999. The helicoid versus the catenoid: geometrically induced bifurcations. Phys. Rev. Lett. 83:3836–39 [Google Scholar]
  21. Boys C. 1959 (1890). Soap Bubbles, Their Colours and the Forces Which Mold Them New York: Dover [Google Scholar]
  22. Brakke KA. 1992. The surface evolver. Exp. Math. 1:141–65 [Google Scholar]
  23. Brown RA, Scriven LE. 1980a. On the multiple equilibrium shapes and stability of an interface pinned on a slot. J. Colloid Interface Sci. 78:528–42 [Google Scholar]
  24. Brown RA, Scriven LE. 1980b. The shape and stability of rotating liquid drops. Proc. R. Soc. Lond. A 371:331–57 [Google Scholar]
  25. Chandrasekhar S. 1987. Ellipsoidal Figures of Equilibrium New York: Dover [Google Scholar]
  26. Chang C, Bostwick JB, Steen PH, Daniel S. 2013. Substrate constraint modifies the Rayleigh spectrum of vibrating sessile drops. Phys. Rev. E 88:023015 [Google Scholar]
  27. Chen TY, Tsamopoulos J. 1993. Nonlinear dynamics of capillary bridges: theory. J. Fluid Mech. 255:373–409 [Google Scholar]
  28. Collicott SH, Weislogel MM. 2004. Computing existence and stability of capillary surfaces using surface evolver. AIAA J. 42:289–95 [Google Scholar]
  29. Courant R, Hilbert D. 1953. Methods of Mathematical Physics I New York: Wiley Intersci. [Google Scholar]
  30. Culkin JB, Davis SH. 1983. Meandering of water rivulets. AIChE J. 30:263–67 [Google Scholar]
  31. Daniel S, Sircar S, Gliem J, Chaudhury M. 2004. Ratcheting motion of liquid drops on gradient surfaces. Langmuir 20:4085–92 [Google Scholar]
  32. Davis SH. 1980. Moving contact lines and rivulet instabilities. Part 1. The static rivulet. J. Fluid Mech. 98:225–42Introduces the mobility parameter and shows that the CL speed condition leads to an effective dissipation, even for inviscid fluids. [Google Scholar]
  33. de Gennes P. 1985. Wetting: statics and dynamics. Rev. Mod. Phys. 57:827–63 [Google Scholar]
  34. de Gennes P, Brochard-Wyart F, Quéré D. 2010. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves New York: Springer [Google Scholar]
  35. Souza EJ, Gao L, McCarthy TJ, Arzt E, Crosby AJ. De 2008. Effect of contact angle hysteresis on the measurement of capillary forces. Langmuir 24:1391–96 [Google Scholar]
  36. Delaunay C. 1841. Sur la surface de révolution dont la courbure moyenne est constante. J. Math. Pure Appl. 16:309–21 [Google Scholar]
  37. Dodds S, Carvalho MS, Kumar S. 2012. The dynamics of three-dimensional liquid bridges with pinned and moving contact lines. J. Fluid Mech. 707:521–40 [Google Scholar]
  38. Doedel EJ, Oldeman BE. 2009. AUTO-07P: continuation and bifurcation software for ordinary differential equations. http://www.macs.hw.ac.uk/∼gabriel/auto07/auto.html
  39. Dupré A. 1869. Théorie Méchanique de La Chaleur Paris: Gauthier-Villars [Google Scholar]
  40. Dussan V. E. 1979. On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11:371–400 [Google Scholar]
  41. Dyson D. 1988. Contact line stability at edges: comments on Gibbs's inequalities. Phys. Fluids 31:229–32 [Google Scholar]
  42. Edwards WS, Fauve S. 1994. Patterns and quasi-patterns in the Faraday experiment. J. Fluid Mech. 278:123–48 [Google Scholar]
  43. Eggers J. 1997. Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69:865–929 [Google Scholar]
  44. El-Genk MS, Saber HH. 2001. Minimum thickness of a flowing down liquid film on a vertical surface. Int. J. Heat Mass Transf. 44:2809–25 [Google Scholar]
  45. Erle M, Gillette R, Dyson D. 1970. Stability of interfaces of revolution with constant surface tension: the case of the catenoid. Chem. Eng. J. 1:97–109 [Google Scholar]
  46. Faraday M. 1831. On a peculiar class of acoustical figures, and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Philos. Trans. R. Soc. Lond. 121:299–340 [Google Scholar]
  47. Fayzrakhmanova I, Straube A. 2009. Stick-slip dynamics of an oscillated sessile drop. Phys. Fluids 21:072104 [Google Scholar]
  48. Finn R. 1999. Capillary surface interfaces. Not. AMS 46:770–81 [Google Scholar]
  49. Gauss CF. 1830. Principia generalia Theoriae Figurae Fluidorum in statu Aequilibrii Göttingen: Dieterichs [Google Scholar]
  50. Gibbs JW. 1906. The Scientific Papers of J. Willard Gibbs 1 London: Longmans, Green & Co. [Google Scholar]
  51. Gillette R, Dyson D. 1971. Stability of fluid interfaces of revolution between equal solid circular plates. Chem. Eng. J. 2:44–54 [Google Scholar]
  52. Gillette R, Dyson D. 1972. Stability of axisymmetric liquid-fluid interfaces towards general disturbances. Chem. Eng. J. 3:196–99 [Google Scholar]
  53. Gillette R, Dyson D. 1974. Stability of static configurations with applications to the theory of capillarity. Arch. Ration. Mech. Anal. 53:150–77 [Google Scholar]
  54. Graham-Eagle J. 1983. A new method for calculating eigenvalues with applications to gravity-capillary waves with edge constraints. Math. Proc. Camb. Philos. Soc. 94:553–64 [Google Scholar]
  55. Grand-Piteira NL, Daerr A, Limat L. 2006. Meandering rivulets on a plane: a simple balance between inertia and capillarity. Phys. Rev. Lett. 96:254503 [Google Scholar]
  56. Harder PM, Shedd TA, Colburn M. 2008. Static and dynamic wetting characteristics of nano-patterned surfaces. J. Adhes. Sci. Technol. 22:1931–48 [Google Scholar]
  57. Henderson DM, Miles JW. 1994. Surface-wave damping in a circular cylinder with a fixed contact line. J. Fluid Mech. 275:285–99 [Google Scholar]
  58. Hirsa AH, López CA, Laytin M, Vogel MJ, Steen PH. 2005. Low-dissipation capillary switches at small scales. Appl. Phys. Lett. 86:014106 [Google Scholar]
  59. Hocking L. 1987. The damping of capillary-gravity waves at a rigid boundary. J. Fluid Mech. 179:253–66 [Google Scholar]
  60. Hormann G. 1887. Untersuchung über die Grenzen, zwischen welchen Unduloide und Nodoide, die von zwei festen Parallelkreisflächen begrenzt sind, bei gegebenem Volumen ein Minimum der Oberfläche besitzen PhD Thesis, George-Augustus Univ., Göttingen [Google Scholar]
  61. Howe W. 1887. Die Rotationsflächen, welche bei vorgeschriebener Flächengröße ein möglichst großes oder kleines Volumen enthalten. PhD Thesis, Friedrich-Wilhelms Univ., Berlin [Google Scholar]
  62. Jain A, Toombes GE, Hall LM, Mahajan S, Garcia CB. et al. 2005. Direct access to bicontinuous skeletal inorganic plumber's nightmare networks from block copolymers. Angew. Chem. Int. Ed. Engl. 44:1226–29 [Google Scholar]
  63. Johns L, Narayanan R. 2002. Interfacial Instability New York: Springer [Google Scholar]
  64. Katz J. 1978. On the number of unstable modes of an equilibrium. Mon. Not. R. Astron. Soc. 183:765–70 [Google Scholar]
  65. Katz J. 1979. On the number of unstable modes of an equilibrium—II. Mon. Not. R. Astron. Soc. 189:817–22 [Google Scholar]
  66. Kidambi R. 2011. Frequency and damping of non-axisymmetric surface oscillations of a viscous cylindrical liquid bridge. J. Fluid Mech. 681:597–621 [Google Scholar]
  67. Kim H, Kim J, Kang B. 2004. Meandering instability of a rivulet. J. Fluid Mech. 498:245–56 [Google Scholar]
  68. Ko SH, Lee H, Kang KH. 2008. Hydrodynamic flows in electrowetting. Langmuir 24:1094–101 [Google Scholar]
  69. Kralchevsky PA, Denkov ND. 2001. Capillary forces and structuring in layers of colloid particles. Curr. Opin. Colloid Interface Sci. 6:383–401 [Google Scholar]
  70. Kumar S. 2015. Liquid transfer in printing processes: liquid bridges with moving contact lines. Annu. Rev. Fluid Mech. 47:67–94 [Google Scholar]
  71. Lafuma A, Quéré D. 2003. Superhydrophobic states. Nat. Mater. 2:457–60 [Google Scholar]
  72. Lamb H. 1932. Hydrodynamics Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  73. Langbein D. 1990. The shape and stability of liquid menisci at solid edges. J. Fluid Mech. 213:251–65 [Google Scholar]
  74. Langbein D. 2002. Capillary Surfaces: Shape – Stability – Dynamics, in Particular Under Weightlessness. Berlin: Springer-VerlagPlaces the stability of capillary interfaces into the context of low-gravity experiments. [Google Scholar]
  75. Laplace R. 1806. An Essay on the Cohesion of Fluids Paris: Coureier [Google Scholar]
  76. Lappa M. 2005. Thermal convection and related instabilities in models of crystal growth from the melt on earth and in microgravity: past history and current status. Cryst. Res. Technol. 40:531–49 [Google Scholar]
  77. López CA, Lee C, Hirsa AH. 2005. Electrochemically activated adaptive liquid lens. Appl. Phys. Lett. 87:134102 [Google Scholar]
  78. Lowry B, Steen PH. 1995. Capillary surfaces: stability from families of equilibria with application to the liquid bridge. Proc. R. Soc. Lond. A 449:411–39 [Google Scholar]
  79. Lowry B, Steen PH. 1997. Stability of slender liquid bridges subjected to axial flows. J. Fluid Mech. 330:189–213 [Google Scholar]
  80. Lowry B, Thiessen D. 2007. Fixed contact line helical interfaces in zero gravity. Phys. Fluids 19:022102 [Google Scholar]
  81. Luzzatto-Fegiz P, Williamson CHK. 2012. Determining the stability of steady two-dimensional flows through imperfect velocity-impulse diagrams. J. Fluid Mech. 706:323–50 [Google Scholar]
  82. Lynden-Bell D, Wood R. 1968. The gravo-thermal catastrophe in isothermal spheres and the onset of red-giant structure for stellar systems. Mon. Not. R. Astron. Soc. 138:495–525 [Google Scholar]
  83. Lyubimov DV, Lyubimova TP, Shklyaev SV. 2004. Non-axisymmetric oscillations of a hemispheric drop. Fluid Dyn. 39:851–62 [Google Scholar]
  84. Lyubimov DV, Lyubimova TP, Shklyaev SV. 2006. Behavior of a drop on an oscillating solid plate. Phys. Fluids 18:012101 [Google Scholar]
  85. Maddocks JH. 1987. Stability and folds. Arch. Ration. Mech. Anal. 99:301–28Develops TP theorems for isoperimetric problems that are related to pressure and volume disturbances for capillary surfaces. [Google Scholar]
  86. Maddocks JH, Sachs RL. 1995. Constrained variational principles and stability in Hamiltonian systems. Hamiltonian Dynamical Systems H Dumas, K Meyer, D Schmidt 231–64 New York: Springer [Google Scholar]
  87. Malouin B, Vogel MJ, Hirsa AH. 2010. Electromagnetic control of coupled droplets. Appl. Phys. Lett. 96:214104 [Google Scholar]
  88. Mampallil D, van den Ende D, Mugele F. 2011. Controlling flow patterns in oscillating sessile drops by breaking azimuthal symmetry. Appl. Phys. Lett. 99:154102 [Google Scholar]
  89. Matar O, Craster R. 2009. Dynamics of surfactant-assisted spreading. Soft Matter 5:3801–9 [Google Scholar]
  90. Matsumoto T, Nogi K. 2008. Wetting in soldering and microelectronics. Annu. Rev. Mater. Res. 38:251–73 [Google Scholar]
  91. Maugis D. 2000. Contact, Adhesion and Rupture of Elastic Solids New York: Springer [Google Scholar]
  92. Maxwell J. 1898. Encyclopedia Britannica Edinburgh: Adam & Charles Black, 9th ed.. [Google Scholar]
  93. May H, Lowry B. 2008. Microgravity/microscale double-helical fluid containment. Proc. R. Soc. A 464:855–75 [Google Scholar]
  94. McKinley GH, Sridhar T. 2002. Filament-stretching rheometry of complex fluids. Annu. Rev. Fluid Mech. 34:375–415 [Google Scholar]
  95. Michael D. 1981. Meniscus stability. Annu. Rev. Fluid Mech. 13:189–215 [Google Scholar]
  96. Miles J, Henderson D. 1990. Parametrically forced surface waves. Annu. Rev. Fluid Mech. 22:143–65 [Google Scholar]
  97. Milne A, Defez B, Cabrerizo-Vílchez M, Amirfazli A. 2014. Understanding (sessile/constrained) bubble and drop oscillations. Adv. Colloid Interface Sci. 203:22–36 [Google Scholar]
  98. Mollot D, Tsamopoulos J, Chen T, Ashgriz N. 1993. Nonlinear dynamics of capillary bridges: experiments. J. Fluid Mech. 255:411–35 [Google Scholar]
  99. Muralidharan S, Voorhees PW, Davis SH. 2013. Nonaxisymmetric droplet unpinning in vapor-liquid-solid-grown nanowires. J. Appl. Phys. 114:114305 [Google Scholar]
  100. Myshkis A, Babskii V, Slobozhanin N, Tyuptsov A. 1987. Low-Gravity Fluid Mechanics New York: SpringerSets forth the mathematical approach to the stability of capillary surfaces, motivated by the low-gravity application and with a large number of references. [Google Scholar]
  101. Nakagawa T, Nakagawa R. 1996. A novel oscillation phenomenon of the water rivulet on a smooth hydrophobic surface. Acta Mech. 115:27–37 [Google Scholar]
  102. Nakagawa T, Scott J. 1992. Rivulet meanders on a smooth hydrophobic surface. Int. J. Multiphase Flow 18:455–63 [Google Scholar]
  103. Nguyem-Thu-Lam K, Caps H. 2011. Effect of a capillary meniscus on the Faraday instability threshold. Eur. Phys. J. E 34:112 [Google Scholar]
  104. Noblin X, Buguin A, Brochard-Wyart F. 2004. Vibrated sessile drops: transition between pinned and mobile contact lines. Eur. Phys. J. E 14:395–404 [Google Scholar]
  105. Noblin X, Buguin A, Brochard-Wyart F. 2005. Triplon modes of puddles. Phys. Rev. Lett. 94:166102 [Google Scholar]
  106. Noblin X, Kofman R, Celestini F. 2009. Ratchet-like motion of a shaken drop. Phys. Rev. Lett. 19:194504 [Google Scholar]
  107. Oh JM, Ko SH, Kang KH. 2008. Shape oscillation of a drop in ac electrowetting. Langmuir 24:8379–86 [Google Scholar]
  108. Oron A, Davis SH, Bankoff SG. 1997. Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69:931–80 [Google Scholar]
  109. Paulsen JD, Burton JC, Nagel SR, Appathurai S, Harris MT, Basaran OA. 2012. The inexorable resistance of inertia determines the initial regime of drop coalescence. Proc. Natl. Acad. Sci. USA 109:6857–61 [Google Scholar]
  110. Perlin M, Schultz WW. 2000. Capillary effects on surface waves. Annu. Rev. Fluid Mech. 32:241–74 [Google Scholar]
  111. Plateau J. 1863. Experimental and theoretical researches on the figures on equilibrium of a liquid mass withdrawn from the action of gravity, etc. Annual Report of the Board of Regents of the Smithsonian Institution207–85 Washington, DC: Smithsonian Inst. [Google Scholar]
  112. Poincaré H. 1885. Sur l'équilibre d'une masse fluide animée d'un mouvement de rotation. Acta Math. 7:259–380 [Google Scholar]
  113. Prosperetti A. 2012. Linear oscillations of constrained drops, bubbles, and plane liquid surfaces. Phys. Fluids 24:032109 [Google Scholar]
  114. Quéré D. 1999. Fluid coating on a fiber. Annu. Rev. Fluid Mech. 31:347–84 [Google Scholar]
  115. Ramalingam SK, Basaran OA. 2010. Axisymmetric oscillation modes of a double droplet system. Phys. Fluids 22:112111 [Google Scholar]
  116. Ramalingam SK, Ramkrishna D, Basaran OA. 2012. Free vibrations of a spherical drop constrained at an azimuth. Phys. Fluids 24:082102 [Google Scholar]
  117. Rayleigh L. 1879. On the capillary phenomenon of jets. Proc. R. Soc. Lond. 29:71–97 [Google Scholar]
  118. Rowlinson J, Widom B. 2002. Molecular Theory of Capillarity New York: Dover [Google Scholar]
  119. Roy R, Schwartz L. 1999. On the stability of liquid ridges. J. Fluid Mech. 391:293–318 [Google Scholar]
  120. Rücker AW. 1886. On the critical mean curvature of liquid surfaces of revolution. Philos. Mag. 23:35–45 [Google Scholar]
  121. Russo MJ, Steen PH. 1986. Instability of rotund capillary bridges to general disturbances: experiment and theory. J. Colloid Interface Sci. 113:154–63 [Google Scholar]
  122. Sambath K, Basaran OA. 2014. Electrohydrostatics of capillary switches. AIChE J. 60:1451–59 [Google Scholar]
  123. Sariola V, Jääskeläinen M, Zhou Q. 2010. Hybrid microassembly combining robotics and water droplet self-alignment. IEEE Trans. Robot. 26:965–77 [Google Scholar]
  124. Schmuki P, Laso M. 1990. On the stability of rivulet flow. J. Fluid Mech. 215:125–43 [Google Scholar]
  125. Schrödinger E. 1915. Notiz über den kapillardruck in gasblasen. Ann. Phys. 46:1413–18 [Google Scholar]
  126. Seetharaman S, Teng L, Hayashi M, Wang L. 2013. Understanding the properties of slags. ISIJ Int. 53:1–8 [Google Scholar]
  127. Segner J. 1751. De figuris superficierum fluidarum. Soc. Reg. Goetting. 1:301–72 [Google Scholar]
  128. Shahraz A, Borhan A, Fichthorn KA. 2012. A theory for the morphological dependence of wetting on a physically patterned solid surface. Langmuir 28:14227–37 [Google Scholar]
  129. Sharp J. 2012. Resonant properties of sessile droplets: contact angle dependence of the resonant frequency and width in glycerol/water mixtures. Soft Matter 8:399–407 [Google Scholar]
  130. Sharp J, Farmer D, Kelly J. 2011. Contact angle dependence of the resonant frequency of sessile water droplets. Langmuir 27:9367–71 [Google Scholar]
  131. Shikhmurzaev YD. 2007. Capillary Flows with Forming Interfaces Boca Raton, FL: Chapman & Hall/CRC [Google Scholar]
  132. Slater DM, Vogel MJ, Macner AM, Steen PH. 2012. Beetle-inspired adhesion by capillary-bridge arrays: pull-off detachment. J. Adhes. Sci. Technol. 28:273–89 [Google Scholar]
  133. Slobozhanin LA, Alexander JID. 2003. Stability diagrams for disconnected capillary surfaces. Phys. Fluids 15:3532–45 [Google Scholar]
  134. Slobozhanin LA, Alexander JID, Resnick AH. 1997. Bifurcation of the equilibrium states of a weightless liquid bridge. Phys. Fluids 9:1893–905 [Google Scholar]
  135. Slobozhanin LA, Shevtsova VM, Alexander JID, Meseguer J, Montanero JM. 2012. Stability of liquid bridges between coaxial equidimensional disks to axisymmetric finite perturbations: a review. Microgravity Sci. Technol. 24:65–77 [Google Scholar]
  136. Snoeijer JH, Andreotti B. 2013. Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45:269–92 [Google Scholar]
  137. Steiner J. 1882. Gesammelte Werke Berlin: Reimer [Google Scholar]
  138. Strani M, Sabetta F. 1984. Free vibrations of a drop in partial contact with a solid support. J. Fluid Mech. 141:233–47Shows that the introduction of a spherical-bowl constraint introduces a new low-frequency mode not present for free drops. [Google Scholar]
  139. Sui Y, Ding H, Spelt PD. 2014. Numerical simulations of flows with moving contact lines. Annu. Rev. Fluid Mech. 46:97–119 [Google Scholar]
  140. Theisen EA, Vogel MJ, López CA, Hirsa AH, Steen PH. 2007. Capillary dynamics of coupled spherical-cap droplets. J. Fluid Mech. 580:495–505 [Google Scholar]
  141. Thiessen DB, Marr-Lyon MJ, Marston PL. 2002. Active electrostatic stabilization of liquid bridges in low gravity. J. Fluid Mech. 457:285–94 [Google Scholar]
  142. Thomas EL, Anderson DM, Henkee CS, Hoffman D. 1988. Periodic area-minimizing surfaces in block copolymers. Nature 334:598–601 [Google Scholar]
  143. Thompson J. 1979. Stability predictions through a succession of folds. Philos. Trans. R. Soc. Lond. A 292:1–23 [Google Scholar]
  144. Tsamopoulos J, Chen TY, Borkar A. 1992. Viscous oscillations of capillary bridges. J. Fluid Mech. 235:579–609 [Google Scholar]
  145. Tuteja A, Choi W, Ma M, Mabry JM, Mazzella SA. et al. 2007. Designing superoleophobic surfaces. Science 318:1618–22 [Google Scholar]
  146. van Lengerich HB, Steen PH. 2012. Energy dissipation and the contact-line region of a spreading bridge. J. Fluid Mech. 703:111–41 [Google Scholar]
  147. van Lengerich HB, Vogel MJ, Steen PH. 2010. Coarsening of capillary drops coupled by conduit networks. Phys. Rev. E 82:066312 [Google Scholar]
  148. Vejrazka J, Vobecka L, Tihon J. 2013. Linear oscillations of a supported bubble or drop. Phys. Fluids 25:062102 [Google Scholar]
  149. Vogel MJ, Ehrhard P, Steen PH. 2005. The electroosmotic droplet switch: countering capillarity with electrokinetics. Proc. Natl. Acad. Sci. USA 102:11974–79 [Google Scholar]
  150. Vogel MJ, Steen PH. 2010. Capillarity-based switchable adhesion. Proc. Natl. Acad. Sci. USA 107:3377–81 [Google Scholar]
  151. Vukasinovic B, Smith M, Glezer A. 2007. Dynamics of a sessile drop in forced vibration. J. Fluid Mech. 587:395–423 [Google Scholar]
  152. Weiland RH, Davis SH. 1981. Moving contact lines and rivulet instabilities. Part 2. Long waves on flat rivulets. J. Fluid Mech. 107:261–80 [Google Scholar]
  153. Wente HC. 1999. A surprising bubble catastrophe. Pac. J. Math. 189:339–75 [Google Scholar]
  154. Xu XM, Vereecke G, van den Hoogen E, Smeers J, Armini S. et al. 2013. Wetting challenges in cleaning of high aspect ratio nano-structures. Solid State Phenom. 195:235–38 [Google Scholar]
  155. Young GW, Davis SH. 1987. Rivulet instabilities. J. Fluid Mech. 176:1–31 [Google Scholar]
  156. Young T. 1805. An essay on the cohesion of fluids. Philos. Trans. R. Soc. Lond. 95:65–87 [Google Scholar]

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