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‘Gobbling drops’: the jetting–dripping transition in flows of polymer solutions

  • C. CLASEN (a1), J. BICO (a2), V. M. ENTOV (a3) and G. H. McKINLEY (a4)

Abstract

This paper discusses the breakup of capillary jets of dilute polymer solutions and the dynamics associated with the transition from dripping to jetting. High-speed digital video imaging reveals a new scenario of transition and breakup via periodic growth and detachment of large terminal drops. The underlying mechanism is discussed and a basic theory for the mechanism of breakup is also presented. The dynamics of the terminal drop growth and trajectory prove to be governed primarily by mass and momentum balances involving capillary, gravity and inertial forces, whilst the drop detachment event is controlled by the kinetics of the thinning process in the viscoelastic ligaments that connect the drops. This thinning process of the ligaments that are subjected to a constant axial force is driven by surface tension and resisted by the viscoelasticity of the dissolved polymeric molecules. Analysis of this transition provides a new experimental method to probe the rheological properties of solutions when minute concentrations of macromolecules have been added.

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Corresponding author

Email address for correspondence: christian.clasen@cit.kuleuven.be

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This paper is dedicated to the memory of Vladimir M. Entov (1937–2008)

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References

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Adamson, A. W. & Gast, A. P. 1997 Physical Chemistry of Surfaces, 6th edn. Wiley-Interscience.
Amarouchene, Y., Bonn, D., Meunier, J. & Kellay, H. 2001 Inhibition of the finite-time singularity during droplet fission of a polymeric fluid. Phys. Rev. Lett. 86 (16), 35583561.
Ambravaneswaran, B., Subramani, H. J., Phillips, S. D. & Basaran, O. A. 2004 Dripping-jetting transitions in a dripping faucet. Phys. Rev. Lett. 93 (3), 034501.
Anna, S. L. & McKinley, G. H. 2001 Elasto-capillary thinning and breakup of model elastic liquids. J. Rheol. 45 (1), 115138.
Apelian, M. R., Armstrong, R. C. & Brown, R. A. 1988 Impact of the constitutive equation and singularity on the calculation of stick slip-flow – the modified upper-convected maxwell model (mucm). J. Non-Newton. Fluid Mech. 27 (3), 299321.
Bazilevskii, A. V., Entov, V. M. & Rozhkov, A. N. 1990 a Liquid filament microrheometer and some of its applications. In Third European Rheology Conference (ed. Oliver, D. R.), pp. 4143. Elsevier Applied Science.
Bazilevskii, A. V., Entov, V. M. & Rozhkov, A. N. 2001 Breakup of an oldroyd liquid bridge as a method for testing the rheological properties of polymer solutions. Vysokomol. Soedin. Ser. A 43 (7), 716726.
Bazilevskii, A. V., Entov, V. M., Rozhkov, A. N. & Yarin, A. L. 1990 b Polymeric jets, beads-on-string breakup and related phenomena. In Third European Rheology Conference (ed. Oliver, D. R.), pp. 4446. Elsevier Applied Science.
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids. Volume 1: Fluid Mechanics, 2nd edn. Wiley Interscience.
Bousfield, D. W., Keunings, R., Marrucci, G. & Denn, M. M. 1986 Nonlinear-analysis of the surface-tension driven breakup of viscoelastic filaments. J. Non-Newton. Fluid Mech. 21 (1), 7997.
Boys, C. V. 1958 Soap Bubbles: Their Colors and Forces Which Mold Them, Dover Publications.
Braithwaite, G. J. C. & Spiegelberg, S. H. 2001 A technique for characterizing complex polymer solutions in extensional flows. In Society of Rheology 72nd Meeting, EF2.
Christanti, Y. & Walker, L. M. 2001 Surface tension driven jet break up of strain-hardening polymer solutions. J. Non-Newton. Fluid Mech. 100 (1–3), 926.
Clanet, C. & Lasheras, J. C. 1999 Transition from dripping to jetting. J. Fluid Mech. 383, 307326.
Clasen, C., Bico, J., Entov, V. M. & McKinely, G. H. 2004 Video-rheology – studying the dripping, jetting, breaking, and “gobbling” of polymeric liquid threads. In The XIVth International Congress on Rheology (ed. Lee, J. W. & Lee, S. J.), vol. RE33, pp. 13. The Korean Society of Rheology.
Clasen, C., Eggers, J., Fontelos, M. A., Li, J. & McKinley, G. H. 2006 a The beads-on-string structure of viscoelastic threads. J. Fluid Mech. 556, 283308.
Clasen, C., Plog, J. P., Kulicke, W. M., Owens, M., Macosko, C., Scriven, L. E., Verani, M. & McKinley, G. H. 2006 b How dilute are dilute solutions in extensional flows? J. Rheol. 50 (6), 849881.
Coullet, P., Mahadevan, L. & Riera, C. S. 2005 Hydrodynamical models for the chaotic dripping faucet. J. Fluid Mech. 526, 117.
Craster, R. V., Matar, O. K. & Papageorgiou, D. T. 2005 On compound liquid threads with large viscosity contrasts. J. Fluid Mech. 533, 95124.
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phy. 69 (3), 865929.
Entov, V. M. & Hinch, E. J. 1997 Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid. J. Non-Newton. Fluid Mech. 72 (1), 3153.
Entov, V. M. & Yarin, A. L. 1984 Influence of elastic stresses on the capillary breakup of jets of dilute polymer solutions. Fluid Dyn. 19 (1), 2129.
Goldin, M., Yerushalmi, J., Pfeffer, R. & Shinnar, R. 1969 Breakup of a laminar capillary jet of a viscoelastic fluid. J. Fluid Mech. 38 (4), 689711.
Griffith, A. A. 1926 The phenomena of rupture and flow in solids. Phil. Trans. R. Soc. Lond. Ser. A 221, 163198.
Harkins, W. D. & Brown, F. E. 1919 The determination of surface tension and the weight of falling drops. J. Am. Chem. Soc. 41, 499524.
Kliakhandler, I. L., Davis, S. H. & Bankoff, S. G. 2001 Viscous beads on vertical fibre. J. Fluid Mech. 429, 381390.
McKinley, G. H. 2005 Visco-elasto-capillary thinning and breakup of complex fluids. In Annu. Rheol. Rev. (ed. Binding, D. M. & Walters, K.), vol. 3, pp. 148. British Society of Rheology.
McKinley, G. H. & Sridhar, T. 2002 Filament-stretching rheometry of complex fluids. Annu. Rev. Fluid Mech. 34, 375415.
McKinley, G. H. & Tripathi, A. 2000 How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer. J. Rheol. 44 (3), 653670.
Middleman, S. 1965 Stability of a viscoelastic jet. Chem. Engng Sci. 20, 10371040.
Pearson, J. R. 1985 Mechanics of Polymer Processing. Springer.
Plog, J. P., Kulicke, W. M. & Clasen, C. 2005 Influence of the molar mass distribution on the elongational behaviour of polymer solutions in capillary breakup. Appl. Rheol. 15 (1), 2837.
Rayleigh, Lord 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. Ser. A 29, 7179.
Rayleigh, Lord 1892 On the instability of a cylinder of viscous liquid under capillary forces. Phil. Mag. 34 (207), 145154.
Ribe, N. M., Huppert, H. E., Hallworth, M. A., Habibi, M. & Bonn, D. 2006 Multiple coexisting states of liquid rope coiling. J. Fluid Mech. 555, 275297.
Rozhkov, A. N. 1983 Dynamics of threads of diluted polymer solutions. J. Engng Phys. Thermophys. 45 (1), 768774.
Sattler, R., Wagner, C. & Eggers, J. 2008 Blistering pattern and formation of nanofibers in capillary thinning of polymer solutions. Phys. Rev. Lett. 100 (16), 164502.
Sauter, U. S. & Buggisch, H. W. 2005 Stability of initially slow viscous jets driven by gravity. J. Fluid Mech. 533, 237257.
Tirtaatmadja, V., McKinley, G. H. & Cooper-White, J. J. 2006 Drop formation and breakup of low viscosity elastic fluids: effects of molecular weight and concentration. Phys. Fluids 18 (4), 043101.
Wagner, C., Amarouchene, Y., Bonn, D. & Eggers, J. 2005 Droplet detachment and satellite bead formation in viscoelastic fluids. Phys. Rev. Lett. 95 (16), 4.
Weber, C. 1931 Zum Zerfall eines Flüssigkeitsstrahls. Z. Angew. Math. Mech. 11 (2), 136154.
Yarlanki, S. & Harlen, O. G. 2008 Jet breakup of polymeric liquids. In XXII International Congress of Theoretical and Applied Mechanics. Adeleide, Australia.
Yildirim, O. E. & Basaran, O. A. 2006 Dynamics of formation and dripping of drops of deformation-rate-thinning and -thickening liquids from capillary tubes. J. Non-Newton. Fluid Mech. 136 (1), 1737.
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