Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-03T17:09:28.626Z Has data issue: false hasContentIssue false
  • English
  • Français

Surfactant-driven escape from endpinching during contraction of nearly inviscid filaments

Published online by Cambridge University Press:  24 July 2020

Pritish M. Kamat ,
Brayden W. Wagoner ,
Alfonso A. Castrejón-Pita Open the ORCID record for Alfonso A. Castrejón-Pita [Opens in a new window] ,
José R. Castrejón-Pita Open the ORCID record for José R. Castrejón-Pita [Opens in a new window] ,
Christopher R. Anthony  and
Osman A. Basaran Open the ORCID record for Osman A. Basaran [Opens in a new window]
Pritish M. Kamat
Affiliation:
Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN47907, USA
Brayden W. Wagoner
Affiliation:
Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN47907, USA
Alfonso A. Castrejón-Pita
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, OxfordOX1 3PJ, UK
José R. Castrejón-Pita
Affiliation:
School of Engineering and Material Science, Queen Mary University of London, Mile End Road, LondonE1 4NS, UK
Christopher R. Anthony
Affiliation:
Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN47907, USA
Osman A. Basaran*
Affiliation:
Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN47907, USA
*
†Email address for correspondence: obasaran@purdue.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Highly stretched liquid drops, or filaments, surrounded by a gas are routinely encountered in nature and industry. Such filaments can exhibit complex and unexpected dynamics as they contract under the action of surface tension. Instead of simply retracting to a sphere of the same volume, low-viscosity filaments exceeding a critical aspect ratio undergo localized pinch-off at their two ends resulting in a sequence of daughter droplets – a phenomenon called endpinching – which is an archetype breakup mode that is distinct from the classical Rayleigh–Plateau instability seen in jet breakup. It has been shown that endpinching can be precluded in filaments of intermediate viscosity, with the so-called escape from endpinching being understood heretofore only qualitatively as being caused by a viscous mechanism. Here, we show that a similar escape can also occur in nearly inviscid filaments when surfactants are present at the free surface of a recoiling filament. The fluid dynamics of the escape phenomenon is probed by numerical simulations. The computational results are used to show that the escape is driven by the action of Marangoni stress. Despite the apparently distinct physical origins of escape in moderately viscous surfactant-free filaments and that in nearly inviscid but surfactant-covered filaments, it is demonstrated that the genesis of all escape events can be attributed to a single cause – the generation of vorticity at curved interfaces. By analysing vorticity dynamics and the balance of vorticity in recoiling filaments, the manner in which surface tension gradients and concomitant Marangoni stresses can lead to escape from endpinching is clarified.

JFM classification

Drops and Bubbles: Drops Drops and Bubbles: Breakup/coalescence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A28
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

Present address: Dow, Inc., Lake Jackson, TX 77566, USA.

§

Present address: Convergent Science, Inc., Madison, WI 53719, USA.

References

REFERENCES

Ambravaneswaran, B. & Basaran, O. A. 1999 Effects of insoluble surfactants on the nonlinear deformation and breakup of stretching liquid bridges. Phys. Fluids 11 (5), 997–1015.CrossRefGoogle Scholar
Anthony, C. R., Kamat, P. M., Harris, M. T. & Basaran, O. A. 2019 Dynamics of contracting filaments. Phys. Rev. Fluids 4 (9), 093601.CrossRefGoogle Scholar
Apfel, R., Tian, Y., Jankovsky, J., Shi, T., Chen, X., Holt, R., Trinh, E., Croonquist, A., Thornton, K., Sacco, A. Jr, et al. 1997 Free oscillations and surfactant studies of superdeformed drops in microgravity. Phys. Rev. Lett. 78 (10), 1912–1915.CrossRefGoogle Scholar
Basaran, O. A. 1992 Nonlinear oscillations of viscous liquid drops. J. Fluid Mech. 241, 169–198.CrossRefGoogle Scholar
Basaran, O. A. 2002 Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J. 48 (9), 1842–1848.CrossRefGoogle Scholar
Basaran, O. A., Gao, H. & Bhat, P. P. 2013 Nonstandard inkjets. Annu. Rev. Fluid Mech. 45, 85–113.CrossRefGoogle Scholar
Basaran, O. A. & De Paoli, D. W. 1994 Nonlinear oscillations of pendant drops. Phys. Fluids 6 (9), 2923–2943.CrossRefGoogle Scholar
Brøns, M., Thompson, M. C., Leweke, T. & Hourigan, K. 2014 Vorticity generationand conservation for two-dimensional interfaces and boundaries. J. Fluid Mech. 758, 63–93.CrossRefGoogle Scholar
Castrejón-Pita, J. R., Baxter, W. R. S., Morgan, J., Temple, S., Martin, G. D. & Hutchings, I. M. 2013 Future, opportunities and challenges of inkjet technologies. Atomiz. Sprays 23 (6), 541–565.CrossRefGoogle Scholar
Castrejón-Pita, A. A., Castrejón-Pita, J. R. & Hutchings, I. M. 2012 Breakup of liquid filaments. Phys. Rev. Lett. 108 (7), 074506.CrossRefGoogle ScholarPubMed
Chen, Y. J. & Steen, P. H. 1997 Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge. J. Fluid Mech. 341, 245–267.CrossRefGoogle Scholar
Christodoulou, K. N. & Scriven, L. E. 1992 Discretization of free surface flows and other moving boundary problems. J. Comput. Phys. 99 (1), 39–55.CrossRefGoogle Scholar
Craster, R. V., Matar, O. K. & Papageorgiou, D. T. 2002 Pinchoff and satellite formation in surfactant covered viscous threads. Phys. Fluids 14 (4), 1364–1376.CrossRefGoogle Scholar
Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31 (6), 1128–1129.CrossRefGoogle Scholar
Day, R. F., Hinch, E. J. & Lister, J. R. 1998 Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80 (4), 704–707.CrossRefGoogle Scholar
Deen, W. M. 2012 Analysis of Transport Phenomena, 2nd edn. Oxford University Press.Google Scholar
Derby, B. 2010 Inkjet printing of functional and structural materials: fluid property requirements, feature stability, and resolution. Annu. Rev. Mater. Res. 40, 395–414.CrossRefGoogle Scholar
Driessen, T., Jeurissen, R., Wijshoff, H., Toschi, F. & Lohse, D. 2013 Stability of viscous long liquid filaments. Phys. Fluids 25 (6), 1–8.CrossRefGoogle Scholar
Eggers, J. 2005 Drop formation – an overview. Z. Angew. Math. Mech. 85 (6), 400–410.CrossRefGoogle Scholar
Eggers, J. & Dupont, T. F. 1994 Drop formation in a one-dimensional approximation of the Navier–Stokes equation. J. Fluid Mech. 262, 205–211.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71 (0001), 1–79.CrossRefGoogle Scholar
Fezzaa, K. & Wang, Y. 2008 Ultrafast x-ray phase-contrast imaging of the initial coalescence phase of two water droplets. Phys. Rev. Lett. 100 (10), 104501.CrossRefGoogle ScholarPubMed
Franses, E. I., Basaran, O. A. & Chang, C.-H. 1996 Techniques to measure dynamic surface tension. Curr. Opin. Colloid Interface Sci. 1 (2), 296–303.CrossRefGoogle Scholar
Fyrillas, M. M. & Szeri, A. J. 1995 Dissolution or growth of soluble spherical oscillating bubbles: the effect of surfactants. J. Fluid Mech. 289, 295–314.CrossRefGoogle Scholar
Glazman, R. E. 1984 Damping of bubble oscillations induced by transport of surfactants between the adsorbed film and the bulk solution. J. Acoust. Soc. Am. 76 (3), 890–896.CrossRefGoogle Scholar
Gresho, P. M., Lee, R. L. & Sani, R. C. 1979 On the time-dependent solution of the incompressible Navier–Stokes equations in two and three dimensions. In Recent Advances in Numerical Methods in Fluids (ed. Taylor, C. & Morgan, K.), vol. 1, pp. 27–79. Pineridge.Google Scholar
Hoepffner, J. & Paré, G. 2013 Recoil of a liquid filament: escape from pinch-off through creation of a vortex ring. J. Fluid Mech. 734, 183–197.CrossRefGoogle Scholar
Johnson, D. O. & Stebe, K. J. 1994 Oscillating bubble tensiometry: a method for measuring the surfactant adsorptive-desorptive kinetics and the surface dilatational viscosity. J. Colloid Interface Sci. 168 (1), 21–31.CrossRefGoogle Scholar
Kamat, P. M., Wagoner, B. W., Thete, S. S. & Basaran, O. A. 2018 Role of Marangoni stress during breakup of surfactant-covered liquid threads: reduced rates of thinning and microthread cascades. Phys. Rev. Fluids 3 (4), 043602.CrossRefGoogle Scholar
Liao, Y.-C., Basaran, O. A. & Franses, E. I. 2006 a Effects of dynamic surface tension and fluid flow on the oscillations of a supported bubble. Colloids Surf. A 282, 183–202.CrossRefGoogle Scholar
Liao, Y.-C., Franses, E. I. & Basaran, O. A. 2006 b Deformation and breakup of a stretching liquid bridge covered with an insoluble surfactant monolayer. Phys. Fluids 18 (2), 022101.CrossRefGoogle Scholar
Lighthill, M. J. 1963 Laminar Boundary Layers. Oxford University Press.Google Scholar
Lundgren, T. & Koumoutsakos, P. 1999 On the generation of vorticity at a free surface. J. Fluid Mech. 382, 351–366.CrossRefGoogle Scholar
Lundgren, T. S. & Mansour, N. N. 1988 Oscillations of drops in zero gravity with weak viscous effects. J. Fluid Mech. 194, 479–510.CrossRefGoogle Scholar
Martínez-Calvo, A., Rivero-Rodríguez, J., Scheid, B. & Sevilla, A. 2020 Natural break-up and satellite formation regimes of surfactant-laden liquid threads. J. Fluid Mech. 883, A35.CrossRefGoogle Scholar
Martínez-Calvo, A. & Sevilla, A. 2018 Temporal stability of free liquid threads with surface viscoelasticity. J. Fluid Mech. 846, 877–901.CrossRefGoogle Scholar
McGough, P. T. & Basaran, O. A. 2006 Repeated formation of fluid threads in breakup of a surfactant-covered jet. Phys. Rev. Lett. 96 (5), 054502.CrossRefGoogle ScholarPubMed
Milliken, W. J., Stone, H. A. & Leal, L. G. 1993 The effect of surfactant on the transient motion of Newtonian drops. Phys. Fluids A 5 (1), 69–79.CrossRefGoogle Scholar
Notz, P. K. & Basaran, O. A. 2004 Dynamics and breakup of a contracting liquid filament. J. Fluid Mech. 512, 223–256.CrossRefGoogle Scholar
Notz, P. K., Chen, A. U. & Basaran, O. A. 2001 Satellite drops: unexpected dynamics and change of scaling during pinch-off. Phys. Fluids 13 (3), 549–551.CrossRefGoogle Scholar
Patzek, T. W., Benner, R. E., Basaran, O. A. & Scriven, L. E. 1991 Nonlinear oscillations of inviscid free drops. J. Comput. Phys. 97 (2), 489–515.CrossRefGoogle Scholar
Planchette, C., Marangon, F., Hsiao, W.-K. & Brenn, G. 2019 Breakup of asymmetric liquid ligaments. Phys. Rev. Fluids 4 (12), 124004.CrossRefGoogle Scholar
Ponce-Torres, A., Montanero, J. M., Herrada, M. A., Vega, E. J. & Vega, J. M. 2017 Influence of the surface viscosity on the breakup of a surfactant-laden drop. Phys. Rev. Lett. 118 (2), 1–5.CrossRefGoogle ScholarPubMed
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 (26), 264501.CrossRefGoogle ScholarPubMed
Rood, E. P. 1994 Interpreting vortex interactions with a free surface. J. Fluids Engng 116, 91–94.CrossRefGoogle Scholar
Rosen, M. J. 2004 Surfactants and Interfacial Phenomena, 3rd edn. Wiley.CrossRefGoogle Scholar
Schulkes, R. M. S. M. 1996 The contraction of liquid filaments. J. Fluid Mech. 309, 277–300.CrossRefGoogle Scholar
Scriven, L. E. & Sternling, C. V. 1960 The Marangoni effects. Nature 187 (4733), 186–188.CrossRefGoogle Scholar
Stone, H. A. 1990 A simple derivation of the time-dependent convective-diffusion equation for surfactant transport along a deforming interface. Phys. Fluids A 2 (1), 111–112.CrossRefGoogle Scholar
Stone, H. A., Bentley, B. J. & Leal, L. G. 1986 An experimental study of transient effects in the breakup of viscous drops. J. Fluid Mech. 173, 131–158.CrossRefGoogle Scholar
Stone, H. A. & Leal, L. G. 1989 a Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399–427.CrossRefGoogle Scholar
Stone, H. A. & Leal, L. G. 1989 b The influence of initial deformation on drop breakup in subcritical time-dependent flows at low Reynolds numbers. J. Fluid Mech. 206, 223–263.CrossRefGoogle Scholar
Strang, G. & Fix, G. 1973 An Analysis of the Finite Element Method. Wellesley-Cambridge.Google Scholar
Taylor, G. I. 1959 The dynamics of thin theets of fluid. III. Disintegration of fluid sheets. Proc. R. Soc. Lond. A 253 (1274), 313–321.Google Scholar
Timmermans, M.-L. E. & Lister, J. R. 2002 The effect of surfactant on the stability of a liquid thread. J. Fluid Mech. 459, 289–306.CrossRefGoogle Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39 (1), 419–446.CrossRefGoogle Scholar
Wang, F, Contò, F. P., Naz, N., Castrejón-Pita, J. R., Castrejón-Pita, A. A., Bailey, C. G., Wang, W., Feng, J. J. & Sui, Y. 2019 A fate-alternating transitional regime in contracting liquid filaments. J. Fluid Mech. 860, 640–653.CrossRefGoogle Scholar
Wee, H., Wagoner, B. W., Kamat, P. M. & Basaran, O. A. 2020 Effects of surface viscosity on breakup of viscous threads. Phys. Rev. Lett. 124 (20), 204501.CrossRefGoogle ScholarPubMed
Wilkes, E. D. & Basaran, O. A. 1997 Forced oscillations of pendant (sessile) drops. Phys. Fluids 9 (6), 1512–1528.CrossRefGoogle Scholar
Xu, Q. 2007 Computational and theoretical analysis of ink-jets drop formation and breakup. PhD thesis, Purdue University.Google Scholar
Yeo, Y., Chen, A. U., Basaran, O. A. & Park, K. 2004 Solvent exchange method: a novel microencapsulation technique using dual microdispensers. Pharm. Res. 21 (8), 1419–1427.CrossRefGoogle ScholarPubMed
Zhang, X., Harris, M. T. & Basaran, O. A. 1994 Measurement of dynamic surface tension by a growing drop technique. J. Colloid Interface Sci. 168 (1), 47–60.CrossRefGoogle Scholar