Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T13:48:03.024Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  25 September 2009

C. CLASEN ,
J. BICO ,
V. M. ENTOV  and
G. H. McKINLEY
C. CLASEN*
Affiliation:
Departement Chemische Ingenieurstechnieken, Katholieke Universiteit Leuven, 3001 Leuven, Belgium
J. BICO
Affiliation:
Physique et Mécanique des Milieux Hétérogènes (PMMH), CNRS UMR7636, ESPCI-ParisTech, Univ. Paris 6, Univ. Paris 7, 75005 Paris, France
V. M. ENTOV
Affiliation:
Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526Russia
G. H. McKINLEY
Affiliation:
Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 636 , 10 October 2009 , pp. 5 - 40
Copyright
Copyright © Cambridge University Press 2009

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

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

References

REFERENCES

Adamson, A. W. & Gast, A. P. 1997 Physical Chemistry of Surfaces, 6th edn. Wiley-Interscience.Google Scholar
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), 3558–3561.Google Scholar
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.Google Scholar
Anna, S. L. & McKinley, G. H. 2001 Elasto-capillary thinning and breakup of model elastic liquids. J. Rheol. 45 (1), 115–138.Google Scholar
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), 299–321.Google Scholar
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. 41–43. Elsevier Applied Science.Google Scholar
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), 716–726.Google Scholar
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. 44–46. Elsevier Applied Science.Google Scholar
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids. Volume 1: Fluid Mechanics, 2nd edn. Wiley Interscience.Google Scholar
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), 79–97.Google Scholar
Boys, C. V. 1958 Soap Bubbles: Their Colors and Forces Which Mold Them, Dover Publications.Google Scholar
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.Google Scholar
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), 9–26.Google Scholar
Clanet, C. & Lasheras, J. C. 1999 Transition from dripping to jetting. J. Fluid Mech. 383, 307–326.Google Scholar
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. 1–3. The Korean Society of Rheology.Google Scholar
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, 283–308.CrossRefGoogle Scholar
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), 849–881.Google Scholar
Coullet, P., Mahadevan, L. & Riera, C. S. 2005 Hydrodynamical models for the chaotic dripping faucet. J. Fluid Mech. 526, 1–17.Google Scholar
Craster, R. V., Matar, O. K. & Papageorgiou, D. T. 2005 On compound liquid threads with large viscosity contrasts. J. Fluid Mech. 533, 95–124.Google Scholar
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phy. 69 (3), 865–929.Google Scholar
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), 31–53.Google Scholar
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), 21–29.Google Scholar
Goldin, M., Yerushalmi, J., Pfeffer, R. & Shinnar, R. 1969 Breakup of a laminar capillary jet of a viscoelastic fluid. J. Fluid Mech. 38 (4), 689–711.Google Scholar
Griffith, A. A. 1926 The phenomena of rupture and flow in solids. Phil. Trans. R. Soc. Lond. Ser. A 221, 163–198.Google Scholar
Harkins, W. D. & Brown, F. E. 1919 The determination of surface tension and the weight of falling drops. J. Am. Chem. Soc. 41, 499–524.Google Scholar
Kliakhandler, I. L., Davis, S. H. & Bankoff, S. G. 2001 Viscous beads on vertical fibre. J. Fluid Mech. 429, 381–390.Google Scholar
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. 1–48. British Society of Rheology.Google Scholar
McKinley, G. H. & Sridhar, T. 2002 Filament-stretching rheometry of complex fluids. Annu. Rev. Fluid Mech. 34, 375–415.Google Scholar
McKinley, G. H. & Tripathi, A. 2000 How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer. J. Rheol. 44 (3), 653–670.Google Scholar
Middleman, S. 1965 Stability of a viscoelastic jet. Chem. Engng Sci. 20, 1037–1040.Google Scholar
Pearson, J. R. 1985 Mechanics of Polymer Processing. Springer.Google Scholar
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), 28–37.Google Scholar
Rayleigh, Lord 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. Ser. A 29, 71–79.Google Scholar
Rayleigh, Lord 1892 On the instability of a cylinder of viscous liquid under capillary forces. Phil. Mag. 34 (207), 145–154.Google Scholar
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, 275–297.Google Scholar
Rozhkov, A. N. 1983 Dynamics of threads of diluted polymer solutions. J. Engng Phys. Thermophys. 45 (1), 768–774.Google Scholar
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.CrossRefGoogle ScholarPubMed
Sauter, U. S. & Buggisch, H. W. 2005 Stability of initially slow viscous jets driven by gravity. J. Fluid Mech. 533, 237–257.Google Scholar
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.Google Scholar
Wagner, C., Amarouchene, Y., Bonn, D. & Eggers, J. 2005 Droplet detachment and satellite bead formation in viscoelastic fluids. Phys. Rev. Lett. 95 (16), 4.Google Scholar
Weber, C. 1931 Zum Zerfall eines Flüssigkeitsstrahls. Z. Angew. Math. Mech. 11 (2), 136–154.Google Scholar
Yarlanki, S. & Harlen, O. G. 2008 Jet breakup of polymeric liquids. In XXII International Congress of Theoretical and Applied Mechanics. Adeleide, Australia.Google Scholar
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), 17–37.Google Scholar