The viscous catenary: A poor man's approachF. Brochard-Wyart1 and P.-G. de Gennes2
1 Laboratoire PCC UMR 168 Institut Curie/CNRS - F-75231 Paris, Cedex 05, France
2 Institut Curie - 26 rue d'Ulm, F-75005 Paris, France
received 26 June 2007; accepted in final form 11 September 2007; published November 2007
published online 11 October 2007
The aim of the present paper is mainly tutorial. The original set up is an incompressible liquid thread, originally horizontal, and attached at both ends. Under its own weight, the thread sags and thins. A complete theoretical discussion was carried out three years ago by Teichman and Mahadevan -using rather complex mathematical tools. We show here how the main results can be obtained very simply. A single characteristic time td emerges. At t td the distortions is weak, with a fall amplitude growing like . At later times, the stretching is strong, and the stretched length diverges at a time ~ td. Extensions of these arguments are also quoted for various other cases: spinning filaments, filaments in a flowing fluid bath ...
68.03.Cd - Surface tension and related phenomena.
68.03.Kn - Dynamics (capillary waves).
67.40.Hf - Hydrodynamics in specific geometries, flow in narrow channels.
© Europhysics Letters Association 2007