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Three-dimensional response of unrelaxed tension to instability of viscoelastic jets

Published online by Cambridge University Press:  15 July 2011

AN-CHENG RUO ,
FALIN CHEN ,
CHIH-ANG CHUNG  and
MIN-HSING CHANG
AN-CHENG RUO
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei 107, Taiwan
FALIN CHEN*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei 107, Taiwan
CHIH-ANG CHUNG
Affiliation:
Department of Mechanical Engineering, National Central University, Jhongli 32001, Taiwan
MIN-HSING CHANG
Affiliation:
Department of Mechanical Engineering, Tatung University, Taipei 104, Taiwan
*
†Email address for correspondence: falin@iam.ntu.edu.tw
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Abstract

Understanding the cause of instability of viscoelastic liquid jets is of fundamental importance to realise practical applications such as ink-jet printing, fuel injection spraying, and fibre spinning. For common viscoelastic fluids, the elastic stresses caused by the stretching of entangled polymeric chains at the nozzle can persist along the jet for a long downstream distance far away from the exit. Unrelaxed elastic tension has been regarded as a factor responsible for the delay in the breakup of viscoelastic jets. The present study performs a complete linear stability analysis to obtain deeper insights into the response of unrelaxed elastic tension to the onset of three-dimensional instability in viscoelastic jets. Results show that the elastic effect is multidimensional. In the absence of the unrelaxed tension, the elastic force, characterised by a Deborah number, has a slightly destabilising influence on both axisymmetric and non-axisymmetric disturbances. However, when the unrelaxed tension arises, the elastic force begins to suppress the instabilities driven by surface tension and the wind-induced effect to a great extent. In particular, once the tension exceeds a threshold, some novel oscillating non-axisymmetric modes emerge because of stimulation by the relaxation of the elastic energy, causing a variety of asymmetrical deformations.

JFM classification

Instability: Absolute/convective instability Wakes/Jets: Jets Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 558 - 576
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Avital, E. 1995 Axisymmetric instability of a viscid capillary jet in an inviscid media. Phys. Fluids 7, 1162–1164.CrossRefGoogle Scholar
Basaran, O. A. 2002 Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J. 48, 1842–1848.CrossRefGoogle Scholar
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids, vol. 1, Fluid Mechanics, 2nd edn. Wiley.Google Scholar
Bird, R. B. & Wiest, J. M. 1995 Constitutive equations for polymeric liquids. Annu. Rev. Fluid Mech. 27, 169–193.CrossRefGoogle 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-Newtonian Fluid Mech. 21, 79–97.CrossRefGoogle Scholar
Boyd, J. P. 1989 Chebyshev and Fourier Spectral Methods. Springer.CrossRefGoogle Scholar
Brenn, G., Liu, Z. & Durst, F. 2000 Linear analysis of the temporal instability of axisymmetrical non-Newtonian liquid jets. Intl J. Multiphase Flow 26, 1621–1644.CrossRefGoogle Scholar
Eggers, J. 1993 Universal pinching of 3D axisymmetric free-surface flow. Phys. Rev. Lett. 71, 3458–3460.CrossRefGoogle ScholarPubMed
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.CrossRefGoogle Scholar
Goldin, M., Yerushalmi, J., Pfeffer, R. & Shinnar, R. 1969 Breakup of a laminar capillary jet of a viscoelastic fluid. J. Fluid Mech. 38, 689–711.CrossRefGoogle Scholar
Gordillo, J. M. & Perez-Saborid, M. 2005 Aerodynamic effects in the break-up of liquid jets: on the first wind-induced break-up regime. J. Fluid Mech. 541, 1–20.CrossRefGoogle Scholar
Gordon, M., Yerushalmi, J. & Shinnar, R. 1973 Instability of jets of non-Newtonian fluids. J. Rheol. 17, 303–324.Google Scholar
Goren, S. L. & Gottlieb, M. 1982 Surface-tension-driven breakup of viscoelastic liquid threads. J. Fluid Mech. 120, 245–266.CrossRefGoogle Scholar
Hoyt, J. W. & Taylor, J. J. 1977 Waves on the water jets. J. Fluid Mech. 83, 119–127.CrossRefGoogle Scholar
Ibrahim, E. A. 1997 Asymmetric instability of a viscous liquid jet. J. Colloid Interface Sci. 189, 181–183.CrossRefGoogle Scholar
James, D. F. 2009 Boger fluids. Annu. Rev. Fluid Mech. 41, 129–142.CrossRefGoogle Scholar
Kroesser, F. W. & Middleman, S. 1969 Viscoelastic jet stability. AICHE J. 15, 383–386.CrossRefGoogle Scholar
Larson, R. G. 1992 Instabilities in viscoelastic flows. Rheol. Acta 31, 213–263.CrossRefGoogle Scholar
Li, X. 1995 Mechanism of atomization of a liquid jet. Atomiz. Sprays 5, 89–105.CrossRefGoogle Scholar
Lin, S. P. 2003 Breakup of Liquid Sheets and Jets. Cambridge University Press.CrossRefGoogle Scholar
Lin, S. P. & Webb, R. 1994 Non-axisymmetric evanescent waves in a viscous-liquid jet. Phys. Fluids 6, 2545–2547.CrossRefGoogle Scholar
Liu, Z. & Liu, Z. 2006 Linear analysis of three-dimensional instability of non-Newtonian liquid jets. J. Fluid Mech. 559, 451–459.CrossRefGoogle Scholar
Mayer, W. O. H. & Branam, R. 2004 Atomization characteristics on the surface of a round liquid jet. Exp. Fluids 36, 528–539.CrossRefGoogle Scholar
Menard, T., Tanguy, S. & Berlemont, A. 2007 Coupling level set/VOF/ghost fluid methods: validation and application to 3D simulation of the primary break-up of a liquid jet. Intl J. Multiphase Flows 33, 510–524.CrossRefGoogle Scholar
Middleman, S. 1965 Stability of a viscoelastic jet. Chem. Engng Sci. 20, 1037–1040.CrossRefGoogle Scholar
Mun, R. P., Byars, J. A. & Boger, D. V. 1998 The effects of polymer concentration and molecular weight on the breakup of laminar capillary jets. J. Non-Newtonian Fluid Mech. 74, 285–297.CrossRefGoogle Scholar
Piau, J. M., Kissi, N. E. & Tremblay, B. 1990 Influence of upstream instabilities and wall slip on melt fracture and sharkskin phenomena during silicones extrusion through orifice dies. J. Non-Newtonian Fluid Mech. 34, 145–180.CrossRefGoogle Scholar
Quinzani, L. M., Mckinley, G. H., Brown, R. A. & Armstrong, R. C. 1990 Modeling the rheology of polyisobutylene solutions. J. Rheol. 34, 705–48.CrossRefGoogle Scholar
Rayleigh, Lord 1879 On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13.Google Scholar
Rayleigh, Lord 1892 On the instability of a cylinder of viscous liquid under capillary force. Phil. Mag. 34, 145–154.CrossRefGoogle Scholar
Reitz, R. D. & Bracco, F. V. 1982 Mechanism of atomization of a liquid jet. Phys. Fluids 25, 1730–1742.CrossRefGoogle Scholar
Ruo, A.-C., Chang, M.-H. & Chen, F. 2008 On the non-axisymmetric instability of round liquid jets. Phys. Fluids 20, 062105.CrossRefGoogle Scholar
Sallam, K. A., Dai, Z. & Faeth, G. M. 2002 Liquid breakup at the surface of turbulent round liquid jets in still gases. Intl J. Multiphase Flow 28, 427–449.CrossRefGoogle Scholar
Scardovelli, R. & Zaleski, S. 1999 Direct numerical simulation of free-surface and interfacial flow. Annu. Rev. Fluid Mech. 31, 567–603.CrossRefGoogle Scholar
Sornberger, G., Quantin, J. C., Fajolle, R., Vergnes, B. & Agassant, J. F. 1987 Experimental study of the sharkskin defect in linear low-density polyethylene. J. Non-Newtonian Fluid Mech. 23, 123–135.CrossRefGoogle Scholar
Weber, C. 1931 Zum Zerfall eines Flüssigkeitsstrahles. Z. Angew. Math. Mech. 11, 136–154.CrossRefGoogle Scholar