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
74/2009

On Young's Paradox, and the Attractions of Immersed Parallel Plates

Robert Finn

Abstract

A seemingly paradoxical prediction, for behavior of objects with non-constant contact angles when dipped into fluids, is clarified in a new way. The method is then applied to the problem of determining the attraction (or repulsion) of parallel vertical plates dipped into an infinite liquid bath. A criterion is given for determining whether the plates attract or repel each other, and estimates for the forces are obtained that are asymptotically exact for small plate separations. It is shown that the attracting force is asymptotically proportional inversely to the square of the distance between the plates, however the repelling force remains under a fixed bound in magnitude. In all cases the net forces are independent of the contact angles of the exterior fluid with the plates, although that is not the case for the individual forces ascribable to pressure differences and to surface tensions. It is shown that regardless of the data, each of the plates experiences the same net force as does the other. Finally a new and more precise and inclusive clarification is given for a phenomenon described in 1806 by Laplace, who noted conditions under which repelling forces can change abruptly into (much larger) attracting forces.

Received:
Dec 9, 2009
Published:
Dec 10, 2009
MSC Codes:
76B45
Keywords:
capillarity, surface tension

Related publications

Preprint
2009 Repository Open Access
Robert Finn

On Young's Paradox, and the attractions of immersed parallel plates