Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
18/2006

Variation of energy for capillary surfaces

John McCuan

Abstract

Well known first order necessary conditions for a liquid mass to be in equilibrium in contact with a fixed solid surface declare that the free surface interface has mean curvature prescribed in terms of the bulk accelerations acting on the liquid and meets the solid surface in a materially dependent contact angle. We derive first order necessary conditions for capillary surfaces in equilibrium in contact with solid surfaces which may also be allowed to move. These conditions consist of the same prescribed mean curvature equation for the interface, the same prescribed contact angle condition on the boundary, and an additional integral condition which may be said to involve, somewhat surprisingly, only the wetted region.

An example of the kind of system under consideration is that of a floating ball in a fixed container of liquid. We apply our first order conditions to this particular problem.

A brief introduction to the notation we use for surfaces containing a few useful formulae is given as an appendix at the end.

Received:
Feb 14, 2006
Published:
Feb 14, 2006

Related publications

Preprint
2006 Repository Open Access
John McCuan

Variation of energy for capillary surfaces