Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published 1993 | Published
Book Section - Chapter Open

On uniformly rotating fluid drops trapped between two parallel plates

Abstract

This contribution is about the dynamics of a liquid bridge between two fixed parallel plates. We consider a mathematical model and present some results from the doctoral thesis [10] of the first author. He showed that there is a Poisson bracket and a corresponding Hamiltonian, so that the model equations are in Hamiltonian form. The result generalizes previous results of Lewis et al. on the dynamics of free boundary problems for "free" liquid drops to the case of a drop between two parallel plates, including, especially the effect of capillarity and the angle of contact between the plates and the free fluid surface. Also, we prove the existence of special solutions which represent uniformly rotating fluid ridges, and we present specific stability conditions for these solutions. These results extend work of Concus and Finn [2] and Vogel [18],[19] on static capillarity problems (see also Finn [5]). Using the Hamiltonian structure of the model equations and symmetries of the solutions, the stability conditions can be derived in a systematic way. The ideas that are described will be useful for other situations involving capillarity and free boundary problems as well.

Additional Information

© 1993 American Mathematical Society. Partially supported by a Humboldt award at the University of Hamburg and by DOE Contract DE-FG03-88ER25064. This paper is in final form and no version of it will be submitted for publication elsewhere.

Attached Files

Published - KrMaSc1993.pdf

Files

KrMaSc1993.pdf
Files (623.4 kB)
Name Size Download all
md5:dade1153bf22c5d6aac9ee61b49918b6
623.4 kB Preview Download

Additional details

Created:
August 20, 2023
Modified:
January 13, 2024