Papers

Soft catenaries

Ken Kamrin^a1 c1 and L. Mahadevan^a2 c1

^a1 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 01239, USA

^a2 School of Engineering and Applied Sciences and Department of Physics, Harvard University, Cambridge, MA 02138, USA

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.

(Received July 31 2011)

(Reviewed September 22 2011)

(Accepted October 19 2011)

(Online publication December 08 2011)

Key Words:

• complex fluids;
• low-dimensional models;
• non-Newtonian flows

Correspondence:

^c1 Email addresses for correspondence: kkamrin@mit.edu, lm@seas.harvard.edu