Abstract
As mentioned in the previous chapter, tip streaming can be categorized into two different classes: transient tip streaming and microdrip**/microjetting. This chapter reviews some transient tip streaming flows produced by hydrodynamics means. Specifically, we consider a surfactant-loaded droplet in a linear extensional flow, the viscous entrainment of selective withdrawal, and bubble bursting. The chapter closes by mentioning other examples that have received less attention.
We consider both the subcritical steady flow and the onset of tip streaming in a droplet submerged in a linear extensional flow, paying attention to the effect of a surfactant monolayer. We present the same analysis for the viscous entrainment of selective withdrawal. With respect to bubble bursting, we review the major results for simple liquids and summarize recent studies for liquids containing polymers and surfactants.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Taylor GI (1932) The viscosity of a fluid containing small drops of another fluid. Proc R Soc Lond A 138:41–48
Taylor GI (1964) Conical free surfaces and fluid interfaces. In: Gortler H (ed) Proceedings of the 11th international congress of applied mathematics. Springer, Heidelberg, pp 790–796
Taylor GI (1934) The formation of emulsions in definable fields of flow. Proc R Soc Lond Ser A 146:501–523
Rallison JM (1984) The deformation of small viscous drops and bubbles in shear flows. Annu Rev Fluid Mech 16:45–66
Stone HA (1994) Dynamics of drop deformation and breakup in viscous fluids. Ann Rev Fluid Mech 26:65–102
Buckmaster JD (1972) Pointed bubbles in slow viscous flow. J Fluid Mech 55:385–400
Eggers J, Courrech du Pont S (2009) Numerical analysis of tips in viscous flow. Phys Rev E 79(066):311
Courrech du Pont S, Eggers J (2020) Fluid interfaces with very sharp tips in viscous flow. Proc Natl Acad Sci 117:32,238–32,243
De Bruijn RA (1993) Tipstreaming of drops in simple shear flows. Chem Eng Sci 48:277–284
Eggers J (1997) Nonlinear dynamics and breakup of free-surface flows. Rev Mod Phys 69:865–929
Bentley BJ, Leal LG (1986) An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows. J Fluid Mech 167:241–283
Eggleton CD, Tsai TM, Stebe KJ (2001) Tip streaming from a drop in the presence of surfactants. Phys Rev Lett 87(048):302
Wang Q, Siegel M, Booty MR (2014) Numerical simulation of drop and bubble dynamics with soluble surfactant. Phys Fluids 26(052):102
Herrada MA, Ponce-Torres A, Rubio M, Eggers J, Montanero JM (2022) Stability and tip streaming of a surfactant-loaded drop in an extensional flow influence of surface viscosity. J Fluid Mech 934:A26
Vlahovska PM, Lawzdziewicz JB, Loewenberg M (2009) Small-deformation theory for a surfactant-covered drop in linear flows. J Fluid Mech 624:293–337
Scriven LE (1960) Dynamics of a fluid interface equation of motion for Newtonian surface fluids. Chem Eng Sci 12:98–108
Langevin D (2014) Rheology of adsorbed surfactant monolayers at fluid surfaces. Annu Rev Fluid Mech 46:4765
Kim K, Choi SQ, Zell ZA, Squires TM, Zasadzinski JA (2013) Effect of cholesterol nanodomains on monolayer morphology and dynamics. Proc Natl Acad Sci 110:E3054–E3060
Samaniuk JR, Mermant J (2014) Micro and macrorheology at fluid-fluid interfaces. Soft Matt 10:7023–7033
Zell ZA, Nowbahar A, Mansard V, Leal LG, Deshmukh SS, Mecca JM, Tucker CJ, Squires TM (2014) Surface shear inviscidity of soluble surfactants. Proc Natl Acad Sci 111:3677–3682
Ponce-Torres A, Rubio M, Herrada MA, Eggers J, Montanero JM (2020) Influence of the surface viscous stress on the pinch-off of free surfaces loaded with nearly-inviscid surfactants. Sci Rep 10(16):065
Rubio M, Montanero JM, Eggers J, Herrada MA (2024) Stable production of fluid jets with vanishing diameters via tip streaming. J Flui Mech 893: A4
Lister JR (1989) Selective withdrawal from a viscous two-layer system. J Fluid Mech 198:231–254
Cohen I, Li H, Hougland JL, Mrksich M, Nagel SR (2001) Using selective withdrawal to coat microparticles. Science 292:265–267
Case SC, Nagel SR (2007) Spout states in the selective withdrawal of immiscible fluids through a nozzle suspended above a two-fluid interface. Phys Rev Lett 98(114):501
Blanchette F, Zhang WW (2009) Force balance at the transition from selective withdrawal to viscous entrainment. Phys Rev Lett 102(144):501
Evangelio A, Campo-Cortés F, Gordillo JM (2015) Pressure gradient induced generation of microbubbles. J Fluid Mech 778:653–668
Cohen I, Nagel SR (2002) Scaling at the selective withdrawal transition through a tube suspended above the fluid surface. Phys Rev Lett 88(074):501
Cohen I (2004) Scaling and transition structure dependence on the fluid viscosity ratio in the selective withdrawal transition. Phys Rev E 70(026):302
Courrech du Pont S, Eggers J (2006) Sink flow deforms the interface between a viscous liquid and air into a tip singularity. Phys Rev Lett 96(034):501
Berkenbusch MK, Cohen I, Zhang WW (2008) Liquid interfaces in viscous straining flows: numerical studies of the selective withdrawal transition. J Fluid Mech 613:171–203
Eggers J, Courrech du Pont S (2010) Comment on force balance at the transition from selective withdrawal to viscous entrainment. Phys Rev Lett 105(089):401
Zhoua D, Feng JJ (2010) Selective withdrawal of polymer solutions: experiments. J Non-Newtonian Fluid Mech 165:829–838
Zhoua D, Feng JJ (2010) Selective withdrawal of polymer solutions: computations. J Non-Newtonian Fluid Mech 165:839–851
Rubio M, Montanero JM (2023) Influence of a soluble surfactant on the transition to tip streaming. Exp Therm Fluid Sci 141(110):776
Collins RT, Jones JJ, Harris MT, Basaran OA (2008) Electrohydrodynamic tip streaming and emission of charged drops from liquid cones. Nat Phys 4:149–154
Ferrera C, López-Herrera JM, Herrada MA, Montanero JM, Acero AJ (2013) Dynamical behavior of electrified pendant drops. Phys Fluids 25(012):104
Lhuissier H, Villermaux E (2012) Bursting bubble aerosols. J Fluid Mech 696:5–44
Jiang X, Rotily L, Villermaux E, Wang X (2022) Submicron drops from flap** bursting bubbles. Proc Natl Acad Sci 19:34
Villermaux E, Wang X, Deike L (2023) Bubbles spray aerosols: certitudes and mysteries. Proc Natl Acad Sci Nexus (in Press)
Duchemin L, Popinet S, Josserand C, Zaleski S (2002) Jet formation in bubbles bursting at a free surface. Phys Fluids 14:3000–3008
Ghabache E, Antkowiak A, Josserand C, Seon T (2014) On the physics of fizziness: How bubble bursting controls droplets ejection. Phys Fluids 26(121):701
Blanchard D, Syzdek L (1970) Mechanism for the water-to-air transfer and concentration of bacteria. Science 170:626–628
Boyce SG (1951) Source of atmospheric salts. Science 113:620–621
Deike L (2022) Mass transfer at the ocean-atmosphere interface: the role of wave breaking, droplets, and bubbles. Annu Rev Fluid Mech 54:191–224
MacIntyre F (1972) Flow patterns in breaking bubbles. J Geophys Res 77:5211–5228
Gañán-Calvo AM (2023) The ocean fine spray. Phys Fluids 35(023):317
Lee JS, Weon BM, Park SJ, Je JH, Fezzaa K, Lee WK (2011) Size limits the formation of liquid jets during bubble bursting. Nat Commun 2:367
Walls PLL, Henaux L, Bird JC (2015) Jet drops from bursting bubbles: how gravity and viscosity couple to inhibit droplet production. Phys Rev E 92(021):002(R)
Ji B, Yang Z, Feng J (2021) Compound jetting from bubble bursting at an air-oil-water interface. Nat Commun 12:6305
Ghabache E, Seon T (2016) Size of the top jet drop produced by bubble bursting. Phys Rev Fluids 1(051):901(R)
Gañán-Calvo AM (2017) Revision of bubble bursting: universal scaling laws of top jet drop size and speed. Phys Rev Lett 119(204):502
Gañán-Calvo AM, López-Herrera JM, Rebollo-Muñoz N, Montanero JM (2016) The onset of electrospray: the universal scaling laws of the first ejection. Sci Rep 6(32):357
Gañán-Calvo AM (2018) Scaling laws of top jet drop size and speed from bubble bursting including gravity and inviscid limit. Phys Rev Fluids 3(091):601(R)
Deike L, Ghabache E, Liger-Belair G, Das AK, Zaleski S, Popinet S, Seon T (2018) Dynamics of jets produced by bursting bubbles. Phys Rev Fluids 3(013):603
Berny A, Deike L, Seon T, Popinet S (2020) Role of all jet drops in mass transfer from bursting bubbles. Phys Rev Fluids 5(033):605
Gañán-Calvo AM, López-Herrera JM (2021) On the physics of transient ejection from bubble bursting. J Fluid Mech 929:A12
Yang Z, Ji B, Ault JT, Feng J (2023) Enhanced singular jet formation in oil-coated bubble bursting. Nat Phys 19:884–890
Berny A, Deike L, Seon T, Popinet S (2022) Size and speed of jet drops are robust to initial perturbations. Phys Rev Fluids 7(013):602
Lai CY, Eggers J, Deike L (2018) Bubble bursting: universal cavity and jet profiles. Phys Rev Lett 121(144):501
Gordillo JM, Rodriguez-Rodriguez J (2019) Capillary waves control the ejection of bubble bursting jets. J Fluid Mech 867:556–571
Blanco-Rodríguez FJ, Gordillo JM (2020) On the sea spray aerosol originated from bubble bursting jets. J Fluid Mech 886:R2
Feng J, Roché M, Vigolo D, Arnaudov LN, Stoyanov SD, Gurkov TD, Tsutsumanova GG, Stone HA (2014) Nanoemulsions obtained via bubble-bursting at a compound interface. Nat Phys 10:606–612
Dubitsky L, McRae O, Bird JC (2023) Enrichment of scavenged particles in jet drops determined by bubble size and particle position. Phys Rev Lett 130(054):001
Sanjay V, Lohse D, Jalaal M (2021) Bursting bubble in a viscoplastic medium. J Fluid Mech 922:A2
Neel B, Deike L (2021) Collective bursting of free-surface bubbles, and the role of surface contamination. J Fluid Mech 917:A46
Neel B, Erinin MA, Deike L (2021) Role of contamination in optimal droplet production by collective bubble bursting. Geophys Res Lett 49:e2021GL096,740
Constante-Amores CR, Kahouadji L, Batchvarov A, Shin S, Chergui J, Juric D, Matar O (2021) Dynamics of a surfactant-laden bubble bursting through an interface. J Fluid Mech 911:A57
Boulton-Stone JM (1995) The effect of surfactant on bursting gas bubbles. J Fluid Mech 302:231–257
Roche 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(264):501
Mayer HC, Krechetnikov R (2012) Landau-Levich flow visualization: revealing the flow topology responsible for the film thickening phenomena. Phys Fluids 24(052):103
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
Pierre J, Poujol M, Seon T (2022) Influence of surfactant concentration on drop production by bubble bursting. Phys Rev Fluids 7(073):602
Vega E, Montanero J (2024) Influence of a surfactant on bubble bursting. Exp Therm Fluid Sci 151(111):097
Rodríguez-Díaz P, Rubio A, Montanero JM, Gañán-Calvo A, Cabezas MG (2023) Bubble bursting in a weakly-viscoelastic liquid. Phys Fluids 35(102):107
Ji B, Yang Z, Wang Z, Ewoldt RH, Feng J (2023) Secondary bubble entrainment via primary bubble bursting at a viscoelastic surface. Phys Rev Lett 131(104):002
Zeff BW, Kleber B, Fineberg J, Lathrop DP (2000) Singularity dynamics in curvature collapse and jet eruption on a fluid surface. Nature 403:401–404
Antokowiak A, Bremond N, Le Dices S, Villermaux E (2007) Short-term dynamics of a density interface following an impact. J Fluid Mech 577:241–250
Bartolo D, Josserand C, Bonn D (2006) Singular jets and bubbles in drop impact. Phys Rev Lett 96(124):501
Andersen A, Bohr T, Stenum B, Rasmussen JJ, Lautrup B (2003) Anatomy of a bathtub vortex. Phys Rev Lett 91(104):502
Bergmann R, Andersen A, van der Meer D, Bohr T (2009) Bubble pinch-off in a rotating flow. Phys Rev Lett 102(104):502
Schroll RD, Wunenburger R, Casner A, Zhang WW, Delville JP (2007) Liquid transport due to light scattering. Phys Rev Lett 98(133):601
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Montanero, J.M. (2024). Hydrodynamic Transient Tip Streaming. In: Tip Streaming of Simple and Complex Fluids. Fluid Mechanics and Its Applications, vol 137. Springer, Cham. https://doi.org/10.1007/978-3-031-52768-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-031-52768-5_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-52767-8
Online ISBN: 978-3-031-52768-5
eBook Packages: EngineeringEngineering (R0)