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Instability and morphology of polymer solutions coating a fibre

Published online by Cambridge University Press:  03 July 2012

F. Boulogne ,
L. Pauchard  and
F. Giorgiutti-Dauphiné
F. Boulogne
Affiliation:
Université Pierre et Marie Curie–Paris 6, Université Paris-Sud, CNRS, F-91405, Lab. FAST, Bat. 502, Campus Universitaire, Orsay, F-91405, France
L. Pauchard
Affiliation:
Université Pierre et Marie Curie–Paris 6, Université Paris-Sud, CNRS, F-91405, Lab. FAST, Bat. 502, Campus Universitaire, Orsay, F-91405, France
F. Giorgiutti-Dauphiné*
Affiliation:
Université Pierre et Marie Curie–Paris 6, Université Paris-Sud, CNRS, F-91405, Lab. FAST, Bat. 502, Campus Universitaire, Orsay, F-91405, France
*
†Email address for correspondence: fred@fast.u-psud.fr
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Abstract

We report an experimental study on the dynamics of a thin film of polymer solution coating a vertical fibre. The liquid film has first a constant thickness and then undergoes the Plateau–Rayleigh instability, which leads to the formation of sequences of drops, separated by a thin film, moving down at a constant velocity. Different polymer solutions are used, i.e. xanthan solutions and polyacrylamide (PAAm) solutions. These solutions both exhibit shear-rate dependence of the viscosity, but for PAAm solutions, there are strong normal stresses in addition to the shear thinning effect. We characterize experimentally and separately the effects of these two non-Newtonian properties on the flow on the fibre. Thus, in the flat film observed before the emergence of the drops, only the shear-thinning effect plays a role, and tends to thin the film compared to the Newtonian case. The effect of the non-Newtonian rheology on the Plateau–Rayleigh instability is then investigated through the measurements of the growth rate and the wavelength of the instability. Results are in good agreement with linear stability analysis for a shear-thinning fluid. The effect of normal stress can be taken into account by considering an effective surface tension, which tends to decrease the growth rate of the instability. Finally, the dependence of the morphology of the drops on normal stress is investigated, and a simplified model including the normal stress within the lubrication approximation provides good quantitative results on the shape of the drops.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 704 , 10 August 2012 , pp. 232 - 250
Copyright
Copyright © Cambridge University Press 2012

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References

1. Bhat, P. P., Appathurai, S., Harris, M. T., Pasquali, M., McKinley, G. H. & Basaran, O. A. 2010 Formation of beads-on-a-string structures during break-up of viscoelastic filaments. Nature Phys. 6, 625–631.CrossRefGoogle Scholar
2. Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquid. Wiley.Google Scholar
3. Boudaoud, A. 2007 Non-Newtonian thin films with normal stresses: dynamics and spreading. Eur. Phys. J. E 22, 107–109.CrossRefGoogle ScholarPubMed
4. Boys, C. V. 1959 Soap Bubbles: Their Colors and Forces Which Mold Them. Thomas Y. Crowell Company.Google Scholar
5. Carroll, B. J. 1986 Equilibrium conformations of liquid drops on thin cylinders under forces of capillarity: a theory for the roll-up process. Langmuir 2, 248–250.CrossRefGoogle Scholar
6. Carroll, B. J. & Lucassen, J. 1974 Effect of surface dynamics on the process of droplet formation from supported and free liquid cylinders. J. Chem. Soc., Faraday Trans. 1 70, 1228–1239.CrossRefGoogle Scholar
7. Clasen, C., Eggers, J., Fontelos, M. A., LI, J. & McKinley, G. H. 2006 The beads-on-string structure of viscoelastic threads. J. Fluid Mech. 556, 283–308.CrossRefGoogle Scholar
8. Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81, 1131–1198.CrossRefGoogle Scholar
9. De Ryck, A. & Quéré, D. 1998 Fluid coating from a polymer solution. Langmuir 14, 1911–1914.CrossRefGoogle Scholar
10. Duprat, C., Giorgiutti-Dauphiné, F., Tseluiko, D., Saprykin, S. & Kalliadasis, S. 2009a Liquid film coating a fibre as a model system for the formation of bound states in active dispersive–dissipative nonlinear media. Phys. Rev. Lett. 103, 234501.CrossRefGoogle Scholar
11. Duprat, C., Ruyer-Quil, C. & Giorgiutti-Dauphiné, F. 2009b Spatial evolution of a film flowing down a fibre. Phys. Fluids 21, 042109.CrossRefGoogle Scholar
12. Duprat, C., Ruyer-Quil, C., Kalliadasis, S. & Giorgiutti-Dauphiné, F. 2007 Absolute and convective instabilities of a viscous film flowing down a vertical fibre. Phys. Rev. Lett. 98, 244502.CrossRefGoogle Scholar
13. Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.CrossRefGoogle Scholar
14. Fainerman, V. B., Miller, R. & Joos, P. 1994 The measurement of dynamic surface tension by the maximum bubble pressure method. Colloid Polym. Sci. 272, 731–739.CrossRefGoogle Scholar
15. Frenkel, A. L., Babchin, A. J., Levich, B. G., Shlang, T. & Sivashinsky, G. I. 1987 Annular flows can keep unstable films from breakup: nonlinear saturation of capillary instability. J. Colloid Interface Sci. 115, 225–233.CrossRefGoogle Scholar
16. Goren, S. L. 1962 The instability of an annular thread of fluid. J. Fluid Mech. 12, 309–319.CrossRefGoogle Scholar
17. Goren, S. L. 1964 The shape of a thread of liquid undergoing break-up. J. Colloid Sci. 19, 81–86.CrossRefGoogle Scholar
18. Goucher, F. S. & Ward, H. 1922 Films adhering to large wires upon withdrawal from liquid baths. Phil. Mag. 44, 1002.Google Scholar
19. Graham, M. D. 2003 Interfacial hoop stress and instability of viscoelastic free surface flows. Phys. Fluids 15, 1702–1710.CrossRefGoogle Scholar
20. Kalliadasis, S. & Chang, H. 1994 Drop formation during coating of vertical fibres. J. Fluid Mech. 261, 135–168.CrossRefGoogle Scholar
21. Kliakhandler, I. L., Davis, S. H. & Bankoff, S. G. 2001 Viscous beads on vertical fibre. J. Fluid Mech. 429, 381–390.CrossRefGoogle Scholar
22. Lindner, A. & Wagner, C. 2009 Viscoelastic surface instabilities. Comptes Rendus Physique 10, 712–727.CrossRefGoogle Scholar
23. Liu, Y., Jun, Y. & Steinberg, V. 2009 Concentration dependence of the longest relaxation times of dilute and semi-dilute polymer solutions. J. Rheol. 53, 1069–1085.CrossRefGoogle Scholar
24. Macosko, C. W. 1994 Rheology Principles, Measurements, and Applications. Wiley.Google Scholar
25. Quéré, D. 1990 Thin films flowing on vertical fibers. Europhys. Lett. 13, 721.CrossRefGoogle Scholar
26. Quéré, D. 1999 Fluid coating on a fiber. Annu. Rev. Fluid Mech. 31, 347–384.CrossRefGoogle Scholar
27. Rayleigh, Lord 1878 On the instability of jets. Proc. Lond. Math. Soc. s1–10, 4–13.CrossRefGoogle Scholar
28. Smolka, L. B., North, J. & Guerra, B. K. 2008 Dynamics of free surface perturbations along an annular viscous film. Phys. Rev. E 77, 036301.CrossRefGoogle ScholarPubMed
29. Wagner, C., Amarouchene, Y., Bonn, D. & Eggers, J. 2005 Droplet detachment and satellite bead formation in viscoelastic fluids. Phys. Rev. Lett. 95, 164504.CrossRefGoogle ScholarPubMed
30. White, D. A. & Tallmadge, J. A. 1966 A theory of withdrawal of cylinders from liquid baths. AIChE J. 12, 333–339.CrossRefGoogle Scholar
31. Wyatt, N. B. & Liberatore, M. W. 2009 Rheology and viscosity scaling of the polyelectrolyte xanthan gum. J. Appl. Polym. Sci. 114, 4076–4084.CrossRefGoogle Scholar
32. Zhang, J. Y., Wang, X. P., Liu, H. Y., Tang, J. A. & Jiang, L. 1998 Interfacial rheology investigation of polyacrylamide–surfactant interactions. Colloids Surf. A. Physicochemical and Engineering Aspects 132, 9–16.CrossRefGoogle Scholar