Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 18
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Perdigou, C. and Audoly, B. 2016. The viscous curtain: General formulation and finite-element solution for the stability of flowing viscous sheets. Journal of the Mechanics and Physics of Solids, Vol. 96, p. 291.

    Lhuissier, H. Néel, B. and Limat, L. 2014. Viscoelasticity Breaks the Symmetry of Impacting Jets. Physical Review Letters, Vol. 113, Issue. 19,

    Audoly, B. Clauvelin, N. Brun, P.-T. Bergou, M. Grinspun, E. and Wardetzky, M. 2013. A discrete geometric approach for simulating the dynamics of thin viscous threads. Journal of Computational Physics, Vol. 253, p. 18.

    Bhattacharya, S. Craster, R. V. and Flynn, M. R. 2013. Buckling of a thin, viscous film in an axisymmetric geometry. Physics of Fluids, Vol. 25, Issue. 4, p. 043102.

    Le Merrer, Marie Quéré, David and Clanet, Christophe 2012. Buckling of Viscous Filaments of a Fluid under Compression Stresses. Physical Review Letters, Vol. 109, Issue. 6,

    Ribe, Neil M. 2012. All bent out of shape: buckling of sheared fluid layers. Journal of Fluid Mechanics, Vol. 694, p. 1.

    Slim, Anja C. Teichman, Jeremy and Mahadevan, L. 2012. Buckling of a thin-layer Couette flow. Journal of Fluid Mechanics, Vol. 694, p. 5.

    Pfingstag, G. Audoly, B. and Boudaoud, A. 2011. Thin viscous sheets with inhomogeneous viscosity. Physics of Fluids, Vol. 23, Issue. 6, p. 063103.

    Pfingstag, G. Audoly, B. and Boudaoud, A. 2011. Linear and nonlinear stability of floating viscous sheets. Journal of Fluid Mechanics, Vol. 683, p. 112.

    Filippov, Andrey and Zheng, Zheming 2010. Dynamics and shape instability of thin viscous sheets. Physics of Fluids, Vol. 22, Issue. 2, p. 023601.

    Hunt, J.C.R. 2006. NONLINEAR AND WAVE THEORY CONTRIBUTIONS OF T. BROOKE BENJAMIN (1929–1995)*. Annual Review of Fluid Mechanics, Vol. 38, Issue. 1, p. 1.

    Ribe, Neil M. 2003. Periodic folding of viscous sheets. Physical Review E, Vol. 68, Issue. 3,

    Boudaoud, Arezki and Chaïeb, Sahraoui 2001. Singular thin viscous sheet. Physical Review E, Vol. 64, Issue. 5,

    Howell, P. D. 1996. Models for thin viscous sheets. European Journal of Applied Mathematics, Vol. 7, Issue. 04,

    Yarin, A. L. and Tchavdarov, B. M. 1996. Onset of folding in plane liquid films. Journal of Fluid Mechanics, Vol. 307, Issue. -1, p. 85.

    Fletcher, Raymond C. 1995. Three-dimensional folding and necking of a power-law layer: are folds cylindrical, and, if so, do we understand why?. Tectonophysics, Vol. 247, Issue. 1-4, p. 65.

    James, Andrew I. and Watkinson, A.John 1994. Initiation of folding and boudinage in wrench shear and transpression. Journal of Structural Geology, Vol. 16, Issue. 6, p. 883.

    Marshall, J. S. 1992. Buckling of a columnar vortex. Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue. 12, p. 2620.

  • Journal of Fluid Mechanics, Volume 195
  • October 1988, pp. 523-540

Buckling instabilities in layers of viscous liquid subjected to shearing

  • T. Brooke Benjamin (a1) and T. Mullin (a1)
  • DOI:
  • Published online: 01 April 2006

A theoretical and experimental investigation is reported dealing with the onset of buckling in a horizontal layer of highly viscous liquid. The layer floats on a heavier liquid with negligible viscosity, and at rest is stabilized by gravity and surface tension. When sheared at a sufficient rate, the flat configuration of the layer becomes unstable; and the aim of the investigation is to establish the relation between critical values of the shearing rate and values of the layer's thickness and other physical parameters.

A primitive theory based on membrane approximations is first reviewed and its deficiencies are appreciated. Then a more reliable theory is developed, providing estimates of values taken by a dimensionless shear stress f at the threshold of instability. The values fc are found to depend primarily on a dimensionless number H proportional to the thickness of the layer.

Experiments on sheared layers of silicone oil with various high viscosities are then described. Measured values of fc plotted against H over a wide range are shown to be in satisfactory agreement with the theory. Finally, discrepancies between previous experimental results and ours are discussed.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *