Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-22T09:26:49.343Z Has data issue: false hasContentIssue false
  • English
  • Français

Soft catenaries

Published online by Cambridge University Press:  08 December 2011

Ken Kamrin  and
L. Mahadevan
Ken Kamrin*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 01239, USA
L. Mahadevan*
Affiliation:
School of Engineering and Applied Sciences and Department of Physics, Harvard University, Cambridge, MA 02138, USA
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Using the classical catenary as a motivating example, we use slender-body theory to derive a general theory for thin filaments of arbitrary rheology undergoing large combined stretching and bending, which correctly accounts for the nonlinear geometry of deformation and uses integrated state variables to properly represent the complete deformation state. We test the theory for soft catenaries made of a Maxwell fluid and an elastic yield-stress fluid using a combination of asymptotic and numerical analyses to analyse the dynamics of transient sagging and arrest. We validate our results against three-dimensional finite element simulations of drooping catenaries, and show that our minimal models are easier and faster to solve, can capture all the salient behaviours of the full three-dimensional solution, and provide physical insights into the basic mechanisms involved.

JFM classification

Complex Fluids: Complex Fluids Nonlinear Dynamical Systems: Low-dimensional models Non-Newtonian Flows: Non-Newtonian Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 691 , 25 January 2012 , pp. 165 - 177
Copyright
Copyright © Cambridge University Press 2011

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.)

References

1. Brochard-Wyart, F. & de Gennes, P.-G. 2007 The viscous catenary: a poor man’s approach. Europhys. Lett. 80 (3), 36001.CrossRefGoogle Scholar
2. Gurtin, M., Fried, E. & Anand, L. 2010 The Mechanics and Thermodynamics of Continua. Cambridge University Press.CrossRefGoogle Scholar
3. Howell, P. D. 1996 Models for thin viscous sheets. Eur. J. Appl. Math. 7 (4), 321–343.CrossRefGoogle Scholar
4. Hult, J. A. 1966 Creep in Engineering Structures. Blaisdell Publishing Company.Google Scholar
5. Koulakis, J. P., Mitescu, C. D., Brochard-Wyart, F., de Gennes, P.-G. & Guyon, E. 2008 The viscous catenary revisited: experiments and theory. J. Fluid Mech. 609, 87–110.CrossRefGoogle Scholar
6. Kraus, H. 1980 Creep Analysis. Wiley.Google Scholar
7. Le Merrer, M., Seiwert, J., Quéré, D. & Clanet, C. 2008 Shapes of hanging viscous filaments. Europhys. Lett. 84 (5), 56004.CrossRefGoogle Scholar
8. Ribe, N. M. 2001 Bending and stretching of thin viscous sheets. J. Fluid Mech. 433, 135–160.CrossRefGoogle Scholar
9. Roy, A., Mahadevan, L. & Thiffeault, J.-L. 2006 Fall and rise of a viscoelastic filament. J. Fluid Mech. 563, 283–292.CrossRefGoogle Scholar
10. Teichman, J. & Mahadevan, L. 2003 The viscous catenary. J. Fluid Mech. 478, 71–80.CrossRefGoogle Scholar
11. Wang, C. Y. & Watson, L. T. 1982 The elastic catenary. Intl J. Mech. Sci. 24 (6), 349–357.CrossRefGoogle Scholar
12. Zylstra, A. & Mitescu, C. 2009 Regime transitions in the viscous catenary. Europhys. Lett. 87 (2), 26003.CrossRefGoogle Scholar