On the configuration manifold of a liquid bridge

✍ Scribed by Hans-Peter Kruse

• Book ID: 104343500
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 935 KB
• Volume: 29
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(98)00040-0

✦ Synopsis

We show that the configuration space of an inviscid incompressible liquid bridge connecting two parallel plates has the structure ofa Hilbert manifold. To construct this manifold structure we follow the general strategy of Ebin and Marsden [Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. Math. 92 (1970) 102-163], where a manifold structure has been introduced for an inviscid incompressible fluid which completely fills a domain with smooth boundary.

The fact that the liquid bridge has a non-smooth boundary requires extra considerations. In particular, we show how the use of Hodge theory as in the above mentioned reference can be avoided in the case of liquid bridges.