Bending and Buckling Instabilities of Free Liquid Jets: Experiments and General Quasi-One-Dimensional Model

  • A. L. YarinEmail author


This chapter deals with liquid jets bending due to the aerodynamic interaction with surrounding air or buckling due to the impingement on a solid wall. The experimental evidence is considered and linear and nonlinear theories describing perturbation growth developed in the framework of the quasi-one-dimensional equations of the dynamics of liquid jets moving in air are discussed. Jets of viscous Newtonian or rheologically complex liquids (in particular, viscoelastic polymeric liquids) are considered. In addition, bending instability of the electrified liquid jets (in particular, polymeric liquid jets in electrospinning) is considered. In the latter case, both the experimental and theoretical aspects are tackled.


Bending instability of liquid jets Buckling of liquid jets Electrified liquid jets Electrospinning Elongational rheology Newtonian and rheologically complex liquids Quasi-one-dimensional equations of the dynamics of liquid jets Small and finite perturbations Viscoelastic polymeric liquids 


  1. 1.
    Yarin, A. L. Free Liquid Jets and Films: Hydrodynamics and Rheology. Longman, Wiley & Sons; Harlow/New York: Longman/Wiley (1993).zbMATHGoogle Scholar
  2. 2.
    Weber, C. On the breakdown of a fluid jet, Zum Zerfall eines Flussigkeitsstrahles,Z. Angrew. Math und Mech., 11, 136–154 (1931).zbMATHCrossRefGoogle Scholar
  3. 3.
    Debye, P. & Daen, J. Stability considerations of nonviscous jets exhibiting surface or body tension. Phys. Fluids 2, 416–421 (1959).zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Grant, E. M. & Middleman, S. Newtonian jet stability. AIChE J. 12, 669–678 (1966).CrossRefGoogle Scholar
  5. 5.
    Entov, V. M. & Yarin, A. L.: Dynamical equations for a liquid jet. Fluid Dyn. 15, 644–649 (1980).zbMATHCrossRefGoogle Scholar
  6. 6.
    Entov, V. M. & Yarin, A. L. The dynamics of thin liquid jets in air. J. Fluid Mech. 140, 91–111 (1984).zbMATHCrossRefGoogle Scholar
  7. 7.
    Yarin, A. L. On the dynamical equations for liquid jets. Fluid Dyn. 18, 134–136 (1983).zbMATHCrossRefGoogle Scholar
  8. 8.
    Landau, L. D. & Lifshitz, E. M. Theory of Elasticity Pergamon, New York (1975).Google Scholar
  9. 9.
    Reneker, D. H. Yarin, A. L. Fong, H. & Koombhongse, S. Bending instability of electrically charged liquid jets of polymer solutions in electospinning. J. Appl. Phys. 87, 4531–4547 (2000).CrossRefGoogle Scholar
  10. 10.
    Yarin, A. L. Koombhongse, S. & Reneker, D. H. Bending instability in electrospinning of nanofibers. J. Appl. Phys. 89, 3018–3026 (2001).CrossRefGoogle Scholar
  11. 11.
    Reneker, D. H. Yarin, A. L. Zussman, E. & Xu, H. Electrospinning of nanofibers from polymer solutions and melts. Adv. Appl. Mech. 41, 43–195 (2007).CrossRefGoogle Scholar
  12. 12.
    Bresee R. R. & Ko, W. C. Fiber formation during melt blowing. Int. Nonwovens J., 21–28, Summer (2003).Google Scholar
  13. 13.
    Taylor, G. I. Instability of jets, threads and sheets of viscous fluid. In: Proceedings of the 12th International Congress Appl. Mech., Stanford, 1968. Stanford, pp. 382–388 (1969).Google Scholar
  14. 14.
    Taylor, G. I. Electrically driven jets. Proc. R. Soc. Lond. A313, 453–475 (1969).Google Scholar
  15. 15.
    Cruickshank J. O. & Munson, B.R. Viscous fluid buckling of plane and axisymmetric jets. J. Fluid Mech. 113, 221–239 (1981).CrossRefGoogle Scholar
  16. 16.
    Munson, B. R. Viscous buckling of slender horizontal jets. Phys. Fluids 24, 1780–1783 (1981).CrossRefGoogle Scholar
  17. 17.
    Tchavdarov, B. Yarin, A. L. & Radev, S. Buckling of thin liquid jets. J. Fluid Mech. 253, 593–615 (1993).zbMATHCrossRefGoogle Scholar
  18. 18.
    Yarin A. L. & Tchavdarov, B. Onset of folding in plane liquid films. J. Fluid Mech. 307, 85–99 (1996).zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Skorobogatiy M. & Mahadevan, L. Folding of viscous sheets and filaments. Europhys. Lett. 52, 532–538 (2000).CrossRefGoogle Scholar
  20. 20.
    Chiu-Webster S. & Lister, J. R. The fall of a viscous thread onto a moving surface: a ‘fluid-mechanical sewing machine’. J. Fluid Mech. 569, 89–111 (2006).zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Ribe, N. M. Lister, J. R. & Chiu-Webster, S. Stability of a dragged viscous thread: onset of ‘stitching’ in a fluid-mechanical ‘sewing machine’. Phys. Fluids 18, 124105 (2006).CrossRefGoogle Scholar
  22. 22.
    Han, T. Reneker, D. H. & Yarin, A. L. Buckling of jets in electrospinning. Polymer 48, 6064–6076 (2007).CrossRefGoogle Scholar
  23. 23.
    Yarin, A. L. Zussman, E. Wendorff, J. H. & Greiner, A. Material encapsulation in core-shell micro/nanofibers, polymer and carbon nanotubes and micro/nanochannels. J. Mater. Chem. 17, 2585–2599 (2007).CrossRefGoogle Scholar
  24. 24.
    Reneker D. H. & Yarin, A. L. Electrospinning jets and polymer nanofibers. Polymer 49, 2387–2425 (2008).CrossRefGoogle Scholar
  25. 25.
    Goren S. & Gavis, J. Transverse wave motion on a thin capillary jet of a viscoelastic liquid. Phys. Fluids 4, 575–579 (1961).zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Han, T. Yarin, A. L. & Reneker, D. H. Viscoelastic electrospun jets: initial stresses and elongational rheometry. Polymer 49, 1651–1658 (2008).CrossRefGoogle Scholar

Copyright information

© Springer US 2011

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringUniversity of Illinois at ChicagoChicagoUSA

Personalised recommendations