1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Fluid Mechanics
  4. Volume 55, 2023
  5. Article

Annual Review of Fluid Mechanics

Volume 55, 2023

Sharp Interface Methods for Simulation and Analysis of Free Surface Flows with Singularities: Breakup and Coalescence

Abstract

A common feature of many free surface flows—drop/bubble breakup or coalescence and film/sheet rupture—is the occurrence of hydrodynamic singularities. Accurately computing such flows with continuum mechanical, multidimensional free surface flow algorithms is a challenging task given these problems’ multiscale nature, which necessitates capturing dynamics occurring over disparate length scales across 5–6 orders of magnitude. In drop breakup, the thinning of fluid threads that form and eventually pinch-off must be simulated until the thread's radius is about 10 nm. When two drops approach one another, the thickness of the fluid film separating them must fall below 10 nm before coalescence is said to have occurred. If the initial drop radii are 1 mm, simulations must remain faithful to the physics as thread radius or film thickness falls from 10−3 m to below 10−8 m. Here we review significant findings in interfacial flows with hydrodynamic singularities spearheaded by sharp interface algorithms. These multidimensional algorithms can achieve resolution that to date has only been possible with the use of simple 1D evolution equations.

Keyword(s): breakup, coalescence, drops, filaments, finite elements, free surface flows, ink jet printing, jets, microfluidics, pinch-off, singularity, sprays
Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-120720-014714
2023-01-19
2024-04-20
Loading full text...

Full text loading...

/deliver/fulltext/fluid/55/1/annurev-fluid-120720-014714.html?itemId=/content/journals/10.1146/annurev-fluid-120720-014714&mimeType=html&fmt=ahah

Literature Cited

  1. Aarts DGAL, Lekkerkerker HNW, Guo H, Wegdam GH, Bonn D. 2005. Hydrodynamics of droplet coalescence. Phys. Rev. Lett. 95:164503
     [Google Scholar]
  2. Ambravaneswaran B, Basaran OA. 1999. Effects of insoluble surfactants on the nonlinear deformation and breakup of stretching liquid bridges. Phys. Fluids 11:997–1015
     [Google Scholar]
  3. Ambravaneswaran B, Phillips SD, Basaran OA. 2000. Theoretical analysis of a dripping faucet. Phys. Rev. Lett. 85:5332
     [Google Scholar]
  4. Ambravaneswaran B, Subramani HJ, Phillips SD, Basaran OA. 2004. Dripping-jetting transitions in a dripping faucet. Phys. Rev. Lett. 93:034501
     [Google Scholar]
  5. Anthony CR. 2017. Dynamics of retracting films and filaments near singularities PhD Thesis, Purdue Univ., West Lafayette, IN
  6. Anthony CR, Harris MT, Basaran OA. 2020. Initial regime of drop coalescence. Phys. Rev. Fluids 5:033608
     [Google Scholar]
  7. Anthony CR, Kamat PM, Harris MT, Basaran OA. 2019. Dynamics of contracting filaments. Phys. Rev. Fluids 4:093601
     [Google Scholar]
  8. Anthony CR, Kamat PM, Thete SS, Munro JP, Lister JR et al. 2017. Scaling laws and dynamics of bubble coalescence. Phys. Rev. Fluids 2:083601
     [Google Scholar]
  9. Aris R. 2012. Vectors, Tensors and the Basic Equations of Fluid Mechanics New York: Dover
  10. Basaran OA. 1992. Nonlinear oscillations of viscous liquid drops. J. Fluid Mech. 241:169–98
     [Google Scholar]
  11. Basaran OA. 2002. Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J. 48:1842–48
     [Google Scholar]
  12. Basaran OA, DePaoli DW. 1994. Nonlinear oscillations of pendant drops. Phys. Fluids 6:2923–43
     [Google Scholar]
  13. Basaran OA, Gao H, Bhat PP. 2013. Nonstandard inkjets. Annu. Rev. Fluid Mech. 45:85–113
     [Google Scholar]
  14. Berg JC. 2010. An Introduction to Interfaces & Colloids: the Bridge to Nanoscience Singapore: World Sci.
  15. Bhat PP, Basaran OA, Pasquali M. 2008. Dynamics of viscoelastic liquid filaments: low capillary number flows. J. Non-Newton. Fluid Mech. 150:211–25
     [Google Scholar]
  16. Brenn G, Kolobaric V. 2006. Satellite droplet formation by unstable binary drop collisions. Phys. Fluids 18:087101
     [Google Scholar]
  17. Brenner MP, Eggers J, Joseph K, Nagel SR, Shi XD. 1997. Breakdown of scaling in droplet fission at high Reynolds number. Phys. Fluids 9:1573–90
     [Google Scholar]
  18. Burton JC, Rutledge JE, Taborek P. 2004. Fluid pinch-off dynamics at nanometer length scales. Phys. Rev. Lett. 92:244505
     [Google Scholar]
  19. Cairncross RA, Schunk PR, Baer TA, Rao RR, Sackinger PA. 2000. A finite element method for free surface flows of incompressible fluids in three dimensions. Part I. Boundary fitted mesh motion. Int. J. Numer. Method. Fluids 33:375–403
     [Google Scholar]
  20. Case SC, Nagel SR. 2008. Coalescence in low-viscosity liquids. Phys. Rev. Lett. 100:084503
     [Google Scholar]
  21. Castrejón-Pita AA, Betton ES, Campbell N, Jackson N, Morgan J et al. 2021. Formulation, quality, cleaning, and other advances in inkjet printing. Atomization Sprays 31:57–79
     [Google Scholar]
  22. Castrejón-Pita AA, Castrejón-Pita JR, Hutchings IM 2012. Breakup of liquid filaments. Phys. Rev. Lett. 108:074506
     [Google Scholar]
  23. Castrejón-Pita JR, Baxter WRS, Morgan J, Temple S, Martin GD, Hutchings IM. 2013. Future, opportunities and challenges of inkjet technologies. Atomization Sprays 23:541–65
     [Google Scholar]
  24. Castrejón-Pita JR, Castrejón-Pita AA, Hinch EJ, Lister JR, Hutchings IM. 2012. Self-similar breakup of near-inviscid liquids. Phys. Rev. E 86:015301
     [Google Scholar]
  25. Castrejón-Pita JR, Castrejón-Pita AA, Thete SS, Sambath K, Hutchings IM et al. 2015. Plethora of transitions during breakup of liquid filaments. PNAS 112:4582–87
     [Google Scholar]
  26. Chen AU. 2002. Computational and experimental analysis of drop formation for MEMS applications PhD Thesis, Purdue Univ., West Lafayette, IN
  27. Chen AU, Notz PK, Basaran OA. 2002. Computational and experimental analysis of pinch-off and scaling. Phys. Rev. Lett. 88:174501
     [Google Scholar]
  28. Chen TY, Tsamopoulos J. 1993. Nonlinear dynamics of capillary bridges: theory. J. Fluid Mech. 255:373–409
     [Google Scholar]
  29. Chen YJ, Steen PH. 1997. Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge. J. Fluid Mech. 341:245–67
     [Google Scholar]
  30. Christodoulou KN, Scriven LE. 1992. Discretization of free surface flows and other moving boundary problems. J. Comput. Phys. 99:39–55
     [Google Scholar]
  31. Christov IC. 2021. Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits. J. Condens. Matter Phys. 34:063001
     [Google Scholar]
  32. Collins RT, Jones JJ, Harris MT, Basaran OA. 2008. Electrohydrodynamic tip streaming and emission of charged drops from liquid cones. Nat. Phys. 4:149–54
     [Google Scholar]
  33. Collins RT, Sambath K, Harris MT, Basaran OA. 2013. Universal scaling laws for the disintegration of electrified drops. PNAS 110:4905–10
     [Google Scholar]
  34. Craster RV, Matar OK, Papageorgiou DT. 2002. Pinchoff and satellite formation in surfactant covered viscous threads. Phys. Fluids 14:1364–76
     [Google Scholar]
  35. Cruz-Mazo F, Stone HA 2022. Pinch-off of liquid jets at the finite scale of an interface. Phys. Rev. Fluids 7:L012201
     [Google Scholar]
  36. Dallaston MC, Zhao C, Sprittles JE, Eggers J. 2021. Stability of similarity solutions of viscous thread pinch-off. Phys. Rev. Fluids 6:104004
     [Google Scholar]
  37. Day RF, Hinch EJ, Lister JR. 1998. Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80:704
     [Google Scholar]
  38. de Saint Vincent MR, Petit J, Aytouna M, Delville JP, Bonn D, Kellay H 2012. Dynamic interfacial tension effects in the rupture of liquid necks. J. Fluid Mech. 692:499–510
     [Google Scholar]
  39. Deblais A, Herrada MA, Hauner I, Velikov KP, Van Roon T et al. 2018. Viscous effects on inertial drop formation. Phys. Rev. Lett. 121:254501
     [Google Scholar]
  40. Driessen T, Jeurissen R, Wijshoff H, Toschi F, Lohse D. 2013. Stability of viscous long liquid filaments. Phys. Fluids 25:062109
     [Google Scholar]
  41. du Pont SC, Eggers J. 2020. Fluid interfaces with very sharp tips in viscous flow. PNAS 117:32238–43
     [Google Scholar]
  42. Edgerton HE, Hauser EA, Tucker WB. 1937. Studies in drop formation as revealed by the high-speed motion camera. J. Phys. Chem. 41:1017–28
     [Google Scholar]
  43. Eggers J. 1993. Universal pinching of 3D axisymmetric free-surface flow. Phys. Rev. Lett. 71:3458
     [Google Scholar]
  44. Eggers J. 1997. Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69:865–930
     [Google Scholar]
  45. Eggers J. 2001. Air entrainment through free-surface cusps. Phys. Rev. Lett. 86:4290
     [Google Scholar]
  46. Eggers J. 2005. Drop formation—an overview. Z. Angew. Math. Mech. 85:400–10
     [Google Scholar]
  47. Eggers J. 2021. Theory of bubble tips in strong viscous flows. Phys. Rev. Fluids 6:044005
     [Google Scholar]
  48. Eggers J, Dupont TF. 1994. Drop formation in a one-dimensional approximation of the Navier–Stokes equation. J. Fluid Mech. 262:205–21
     [Google Scholar]
  49. Eggers J, Fontelos MA. 2015. Singularities: Formation, Structure, and Propagation Cambridge, UK: Cambridge Univ. Press
  50. Eggers J, Herrada MA, Snoeijer JH. 2020. Self-similar breakup of polymeric threads as described by the Oldroyd-B model. J. Fluid Mech. 887:A19
     [Google Scholar]
  51. Eggers J, Lister JR, Stone HA. 1999. Coalescence of liquid drops. J. Fluid Mech. 401:293–310
     [Google Scholar]
  52. Eggers J, Villermaux E. 2008. Physics of liquid jets. Rep. Prog. Phys. 71:036601
     [Google Scholar]
  53. Eow JS, Ghadiri M, Sharif AO, Williams TJ. 2001. Electrostatic enhancement of coalescence of water droplets in oil: a review of the current understanding. Chem. Eng. J. 84:173–92
     [Google Scholar]
  54. Ettouney HM, Brown RA. 1983. Finite-element methods for steady solidification problems. J. Comput. Phys. 49:118–50
     [Google Scholar]
  55. Fezzaa K, Wang Y. 2008. Ultrafast X-ray phase-contrast imaging of the initial coalescence phase of two water droplets. Phys. Rev. Lett. 100:104501
     [Google Scholar]
  56. Fraggedakis D, Papaioannou J, Dimakopoulos Y, Tsamopoulos J. 2017. Discretization of three-dimensional free surface flows and moving boundary problems via elliptic grid methods based on variational principles. J. Comput. Phys. 344:127–50
     [Google Scholar]
  57. Franses EI, Basaran OA, Chang CH. 1996. Techniques to measure dynamic surface tension. Curr. Opin. Colloid Interface Sci. 1:296–303
     [Google Scholar]
  58. Friberg S, Larsson K, Sjöblom J. 2003. Food Emulsions Boca Raton, FL: CRC Press
  59. Frostad JM, Walter J, Leal LG. 2013. A scaling relation for the capillary-pressure driven drainage of thin films. Phys. Fluids 25:052108
     [Google Scholar]
  60. Gao H. 2012. Dynamics of yield stress fluids: drops, bubbles and foams PhD Thesis, Purdue Univ., West Lafayette, IN
  61. Garg V, Kamat PM, Anthony CR, Thete SS, Basaran OA. 2017. Self-similar rupture of thin films of power-law fluids on a substrate. J. Fluid Mech. 826:455–83
     [Google Scholar]
  62. Hauser EA, Edgerton HE, Holt BM, Cox JT Jr. 1936. The application of the high-speed motion picture camera to research on the surface tension of liquids. J. Phys. Chem. 40:973–88
     [Google Scholar]
  63. Heil M, Hazel A. 2006. Oomph-lib—an object-oriented multi-physics finite element library. Fluid-Structure Interaction: Modelling, Simulation, Optimisation HJ Bungartz, M Schäfer 75–198 Berlin: Springer
     [Google Scholar]
  64. Hernández-Sánchez JF, Lubbers LA, Eddi A, Snoeijer JH 2012. Symmetric and asymmetric coalescence of drops on a substrate. Phys. Rev. Lett. 109:184502
     [Google Scholar]
  65. Hoepffner J, Paré G. 2013. Recoil of a liquid filament: escape from pinch-off through creation of a vortex ring. J. Fluid Mech. 734:183–97
     [Google Scholar]
  66. Holterman HJ, Van De Zande JC, Porskamp HAJ, Huijsmans JFM. 1997. Modelling spray drift from boom sprayers. Comput. Electron. Agric. 19:1–22
     [Google Scholar]
  67. Hood P. 1976. Frontal solution program for unsymmetric matrices. Int. J. Numer. Methods Eng. 10:379–99
     [Google Scholar]
  68. Hsu AS, Roy A, Leal LG. 2008. Drop-size effects on coalescence of two equal-sized drops in a head-on collision. J. Rheol. 52:1291–310
     [Google Scholar]
  69. Huang KL, Pan KL, Josserand C. 2019. Pinching dynamics and satellite droplet formation in symmetrical droplet collisions. Phys. Rev. Lett. 123:234502
     [Google Scholar]
  70. Janssen PJA, Anderson PD. 2011. Modeling film drainage and coalescence of drops in a viscous fluid. Macromol. Mater. Eng. 296:238–48
     [Google Scholar]
  71. Kamat PM, Anthony CR, Basaran OA. 2020. Bubble coalescence in low-viscosity power-law fluids. J. Fluid Mech. 902:A8
     [Google Scholar]
  72. Kamat PM, Wagoner BW, Castrejón-Pita AA, Castrejón-Pita JR, Anthony CR, Basaran OA. 2020. Surfactant-driven escape from endpinching during contraction of nearly inviscid filaments. J. Fluid Mech. 899:A28
     [Google Scholar]
  73. Kamat PM, Wagoner BW, Thete SS, Basaran OA. 2018. Role of Marangoni stress during breakup of surfactant-covered liquid threads: reduced rates of thinning and microthread cascades. Phys. Rev. Fluids 3:043602
     [Google Scholar]
  74. Keller JB, Miksis MJ. 1983. Surface tension driven flows. SIAM J. Appl. Math. 43:268–77
     [Google Scholar]
  75. Kilpatrick PK. 2012. Water-in-crude oil emulsion stabilization: review and unanswered questions. Energy Fuels 26:4017–26
     [Google Scholar]
  76. Kistler SF, Scriven LE 1983. Coating flows. Computational Analysis of Polymer Processing JRA Pearson, SM Richardson 243–99 Dordrecht, Neth: Springer
     [Google Scholar]
  77. Kistler SF, Scriven LE. 1984. Coating flow theory by finite element and asymptotic analysis of the Navier-Stokes system. Int. J. Numer. Methods Fluids 4:207–29
     [Google Scholar]
  78. Kooij S, Sijs R, Denn MM, Villermaux E, Bonn D. 2018. What determines the drop size in sprays?. Phys. Rev. X 8:031019
     [Google Scholar]
  79. Kovalchuk NM, Nowak E, Simmons MJH. 2016. Effect of soluble surfactants on the kinetics of thinning of liquid bridges during drops formation and on size of satellite droplets. Langmuir 32:5069–77
     [Google Scholar]
  80. Leal LG. 2004. Flow induced coalescence of drops in a viscous fluid. Phys. Fluids 16:1833–51
     [Google Scholar]
  81. Lee MW, Kang DK, Yoon SS, Yarin AL. 2012. Coalescence of two drops on partially wettable substrates. Langmuir 28:3791–98
     [Google Scholar]
  82. Lenard P. 1887. Ueber die Schwingungen fallender Tropfen. Ann. Phys. 266:209–43
     [Google Scholar]
  83. Leppinen D, Lister JR. 2003. Capillary pinch-off in inviscid fluids. Phys. Fluids 15:568–78
     [Google Scholar]
  84. Li Y, Sprittles JE. 2016. Capillary breakup of a liquid bridge: identifying regimes and transitions. J. Fluid Mech. 797:29–59
     [Google Scholar]
  85. Liao YC. 2004. Adsorption dynamics and fluid mechanics of surfactant solutions PhD Thesis, Purdue Univ., West Lafayette, IN
  86. Lister JR, Stone HA. 1998. Capillary breakup of a viscous thread surrounded by another viscous fluid. Phys. Fluids 10:2758–64
     [Google Scholar]
  87. Loewenberg M, Hinch EJ. 1997. Collision of two deformable drops in shear flow. J. Fluid Mech. 338:299–315
     [Google Scholar]
  88. Lohse D. 2022. Fundamental fluid dynamics challenges in inkjet printing. Annu. Rev. Fluid Mech. 54:349–82
     [Google Scholar]
  89. Lohse D, Zhang X. 2020. Physicochemical hydrodynamics of droplets out of equilibrium. Nat. Rev. Phys. 2:426–43
     [Google Scholar]
  90. Martin GD, Hoath SD, Hutchings IM. 2008. Inkjet printing—the physics of manipulating liquid jets and drops. J. Phys. Conf. Ser. 105:012001
     [Google Scholar]
  91. Martínez-Calvo A, Sevilla A. 2020. Universal thinning of liquid filaments under dominant surface forces. Phys. Rev. Lett. 125:114502
     [Google Scholar]
  92. McGough PT, Basaran OA. 2006. Repeated formation of fluid threads in breakup of a surfactant-covered jet. Phys. Rev. Lett. 96:054502
     [Google Scholar]
  93. Munro JP, Anthony CR, Basaran OA, Lister JR. 2015. Thin-sheet flow between coalescing bubbles. J. Fluid Mech. 773:R3
     [Google Scholar]
  94. Notz PK, Basaran OA. 2004. Dynamics and breakup of a contracting liquid filament. J. Fluid Mech. 512:223–56
     [Google Scholar]
  95. Notz PK, Chen AU, Basaran OA. 2001. Satellite drops: unexpected dynamics and change of scaling during pinch-off. Phys. Fluids 13:549–52
     [Google Scholar]
  96. Papageorgiou DT. 1995. On the breakup of viscous liquid threads. Phys. Fluids 7:1529–44
     [Google Scholar]
  97. 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. PNAS 109:6857–61
     [Google Scholar]
  98. Paulsen JD, Carmigniani R, Kannan A, Burton JC, Nagel SR. 2014. Coalescence of bubbles and drops in an outer fluid. Nat. Commun. 5:3182
     [Google Scholar]
  99. Peregrine DH, Shoker G, Symon A. 1990. The bifurcation of liquid bridges. J. Fluid Mech. 212:25–39
     [Google Scholar]
  100. Pettas D, Dimakopoulos Y, Tsamopoulos J. 2020. Steady flow of a viscoelastic film over an inclined plane featuring periodic slits. J. Non-Newton. Fluid Mech. 278:104243
     [Google Scholar]
  101. Ristenpart WD, McCalla PM, Roy RV, Stone HA. 2006. Coalescence of spreading droplets on a wettable substrate. Phys. Rev. Lett. 97:064501
     [Google Scholar]
  102. Robinson ND, Steen PH. 2001. Observations of singularity formation during the capillary collapse and bubble pinch-off of a soap film bridge. J. Colloid Interface Sci. 241:448–58
     [Google Scholar]
  103. Roché M, Aytouna M, Bonn D, Kellay H. 2009. Effect of surface tension variations on the pinch-off behavior of small fluid drops in the presence of surfactants. Phys. Rev. Lett. 103:264501
     [Google Scholar]
  104. Ruschak KJ. 1980. A method for incorporating free boundaries with surface tension in finite element fluid-flow simulators. Int. J. Numer. Methods Eng. 15:639–48
     [Google Scholar]
  105. Ruschak KJ. 1982. Boundary conditions at a liquid/air interface in lubrication flows. J. Fluid Mech. 119:107–20
     [Google Scholar]
  106. Saito H, Scriven LE. 1981. Study of coating flow by the finite element method. J. Comput. Phys. 42:53–76
     [Google Scholar]
  107. Sambath K, Garg V, Thete SS, Subramani HJ, Basaran OA. 2019. Inertial impedance of coalescence during collision of liquid drops. J. Fluid Mech. 876:449–80
     [Google Scholar]
  108. Schulkes RMSM. 1994. The evolution and bifurcation of a pendant drop. J. Fluid Mech. 278:83–100
     [Google Scholar]
  109. Schulkes RMSM. 1996. The contraction of liquid filaments. J. Fluid Mech. 309:277–300
     [Google Scholar]
  110. Scriven LE. 1960. Dynamics of a fluid interface equation of motion for Newtonian surface fluids. Chem. Eng. Sci. 12:98–108
     [Google Scholar]
  111. Scriven LE, Sternling CV. 1960. The Marangoni effects. Nature 187:186–88
     [Google Scholar]
  112. Shi XD, Brenner MP, Nagel SR. 1994. A cascade of structure in a drop falling from a faucet. Science 265:219–22
     [Google Scholar]
  113. Sprittles JE, Shikhmurzaev YD. 2012. Coalescence of liquid drops: different models versus experiment. Phys. Fluids 24:122105
     [Google Scholar]
  114. Sprittles JE, Shikhmurzaev YD. 2014a. Dynamics of liquid drops coalescing in the inertial regime. Phys. Rev. E 89:063008
     [Google Scholar]
  115. Sprittles JE, Shikhmurzaev YD. 2014b. A parametric study of the coalescence of liquid drops in a viscous gas. J. Fluid Mech. 753:279–306
     [Google Scholar]
  116. Stone HA, Bentley BJ, Leal LG. 1986. An experimental study of transient effects in the breakup of viscous drops. J. Fluid Mech. 173:131–58
     [Google Scholar]
  117. Subramani HJ, Yeoh HK, Suryo R, Xu Q, Ambravaneswaran B, Basaran OA. 2006. Simplicity and complexity in a dripping faucet. Phys. Fluids 18:032106
     [Google Scholar]
  118. Suryo R. 2006. Breakup of simple and compound drops and bubbles PhD Thesis, Purdue Univ., West Lafayette, IN
  119. Suryo R, Basaran OA. 2006. Local dynamics during pinch-off of liquid threads of power law fluids: scaling analysis and self-similarity. J. Non-Newton. Fluid Mech. 138:134–60
     [Google Scholar]
  120. Taylor GI. 1934. The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A 146:501–23
     [Google Scholar]
  121. Teske ME, Bird SL, Esterly DM, Curbishley TB, Ray SL, Perry SG. 2002. AgDrift®: a model for estimating near-field spray drift from aerial applications. Environ. Toxicol. Chem. 21:659–71
     [Google Scholar]
  122. Thete SS, Anthony CR, Doshi P, Harris MT, Basaran OA. 2016. Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids. Phys. Fluids 28:092101
     [Google Scholar]
  123. Thoroddsen ST, Etoh TG, Takehara K. 2008. High-speed imaging of drops and bubbles. Annu. Rev. Fluid Mech. 40:257–85
     [Google Scholar]
  124. Thoroddsen ST, Takehara K, Etoh TG. 2005. The coalescence speed of a pendent and a sessile drop. J. Fluid Mech. 527:85–114
     [Google Scholar]
  125. Timmermans ME, Lister JR. 2002. The effect of surfactant on the stability of a liquid thread. J. Fluid Mech. 459:289–306
     [Google Scholar]
  126. Tsamopoulos J, Chen TY, Borkar A. 1992. Viscous oscillations of capillary bridges. J. Fluid Mech. 235:579–609
     [Google Scholar]
  127. Tsiveriotis K, Brown RA. 1992. Boundary-conforming mapping applied to computations of highly deformed solidification interfaces. Int. J. Numer. Methods Fluids 14:981–1003
     [Google Scholar]
  128. Tsiveriotis K, Brown RA. 1993. Solution of free-boundary problems using finite-element/Newton methods and locally refined grids: application to analysis of solidification microstructure. Int. J. Numer. Methods Fluids 16:827–43
     [Google Scholar]
  129. Van Der Meulen MJ, Reinten H, Wijshoff H, Versluis M, Lohse D, Steen P. 2020. Nonaxisymmetric effects in drop-on-demand piezoacoustic inkjet printing. Phys. Rev. Appl. 13:054071
     [Google Scholar]
  130. Van Dyke M. 1982. An Album of Fluid Motion Stanford, CA: Parabolic Press
  131. Vaynblat D, Lister JR, Witelski TP. 2001. Rupture of thin viscous films by van der Waals forces: evolution and self-similarity. Phys. Fluids 13:1130–40
     [Google Scholar]
  132. Villermaux E. 2020. Fragmentation versus cohesion. J. Fluid Mech. 898:P1
     [Google Scholar]
  133. Villermaux E, Marmottant PH, Duplat J. 2004. Ligament-mediated spray formation. Phys. Rev. Lett. 92:074501
     [Google Scholar]
  134. Wagoner BW, Vlahovska PM, Harris MT, Basaran OA. 2020. Electric-field-induced transitions from spherical to discocyte and lens-shaped drops. J. Fluid Mech. 904:R4
     [Google Scholar]
  135. Wagoner BW, Vlahovska PM, Harris MT, Basaran OA. 2021. Electrohydrodynamics of lenticular drops and equatorial streaming. J. Fluid Mech. 925:A36
     [Google Scholar]
  136. Wang F, Contò FP, Naz N, Castrejón-Pita JR, Castrejón-Pita AA et al. 2019. A fate-alternating transitional regime in contracting liquid filaments. J. Fluid Mech. 860:640–53
     [Google Scholar]
  137. Wang Y, Im KS, Fezzaa K. 2008. Similarity between the primary and secondary air-assisted liquid jet breakup mechanisms. Phys. Rev. Lett. 100:154502
     [Google Scholar]
  138. Wee H, Wagoner BW, Basaran OA 2022. Absence of scaling transitions in breakup of liquid jets caused by surface viscosity. Phys. Rev. Fluids 7:074001
     [Google Scholar]
  139. Wee H, Wagoner BW, Garg V, Kamat PM, Basaran OA. 2021. Pinch-off of a surfactant-covered jet. J. Fluid Mech. 908:A38
     [Google Scholar]
  140. Wee H, Wagoner BW, Kamat PM, Basaran OA. 2020. Effects of surface viscosity on breakup of viscous threads. Phys. Rev. Lett. 124:204501
     [Google Scholar]
  141. Weinstein SJ, Ruschak KJ. 2004. Coating flows. Annu. Rev. Fluid Mech. 36:29–53
     [Google Scholar]
  142. Wilkes ED, Basaran OA. 1997. Forced oscillations of pendant (sessile) drops. Phys. Fluids 9:1512–28
     [Google Scholar]
  143. Wilkes ED, Basaran OA. 2001. Drop ejection from an oscillating rod. J. Colloid Interface Sci. 242:180–201
     [Google Scholar]
  144. Wilkes ED, Phillips SD, Basaran OA. 1999. Computational and experimental analysis of dynamics of drop formation. Phys. Fluids 11:3577–98
     [Google Scholar]
  145. Xu Q, Liao YC, Basaran OA. 2007. Can surfactant be present at pinch-off of a liquid filament?. Phys. Rev. Lett. 98:054503
     [Google Scholar]
  146. Yildirim OE, Xu Q, Basaran OA. 2005. Analysis of the drop weight method. Phys. Fluids 17:062107
     [Google Scholar]
  147. Yoon Y, Baldessari F, Ceniceros HD, Leal LG. 2007. Coalescence of two equal-sized deformable drops in an axisymmetric flow. Phys. Fluids 19:102102
     [Google Scholar]
  148. Yoon Y, Borrell M, Park CC, Leal LG. 2005. Viscosity ratio effects on the coalescence of two equal-sized drops in a two-dimensional linear flow. J. Fluid Mech. 525:355–79
     [Google Scholar]
  149. Zhang WW, Lister JR. 1999. Similarity solutions for van der Waals rupture of a thin film on a solid substrate. Phys. Fluids 11:2454–62
     [Google Scholar]
  150. Zhang X, Basaran OA. 1995. An experimental study of dynamics of drop formation. Phys. Fluids 7:1184–203
     [Google Scholar]
  151. Zhang X, Basaran OA, Wham RM. 1995. Theoretical prediction of electric field-enhanced coalescence of spherical drops. AIChE J. 41:1629–39
     [Google Scholar]
  152. Zhang X, Harris MT, Basaran OA. 1994. Measurement of dynamic surface tension by a growing drop technique. J. Colloid Interface Sci. 168:47–60
     [Google Scholar]
/content/journals/10.1146/annurev-fluid-120720-014714
Loading
Sharp Interface Methods for Simulation and Analysis of Free Surface Flows with Singularities: Breakup and Coalescence
Annual Review of Fluid Mechanics 55, 707 (2023); https://doi.org/10.1146/annurev-fluid-120720-014714
/content/journals/10.1146/annurev-fluid-120720-014714
/content/journals/10.1146/annurev-fluid-120720-014714
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error