The viscous catenary: A poor man's approach

• Published in: Europhysics letters 2007-11, Vol.80 (3), p.36001-36001(p5)
• Main Authors: Brochard-Wyart, F, de Gennes, P.-G
• Format: Article
• Language: English
• Subjects: 67.40.Hf; 68.03.Cd; 68.03.Kn
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/0295-5075/80/36001

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 $t^{\frac{1}{3}} $. 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 ...