Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
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.