Mathematik-Gebäude, Raum 614/616

A new clarification is given for a seemingly paradoxical prediction of the behavior of an object with non-constant contact angle when dipped into a fluid. The method is then applied to the problem of determining the mutual attraction (or repulsion) of two parallel vertical plates dipped into an infinite liquid bath, subject to a downward gravity field. Criteria for attraction or repulsion of the plates are delineated, and exact expressions are obtained for the forces in all configurations. It is shown that the horizontal forces exerted on the plates by the fluid, and which act on the sides of the plates facing infinite domains, are independent of the contact angles on those sides; the horizontal force resultants on the plates can thus be characterized in terms only of the angles on the plate sides that face each other, and the plate separation distance. The behavior for fixed contact angles and varying plate separations can be exotic in some striking respects, and is suggestive for supporting experiments.

Prof. em. Robert Finn

Stanford University, Department of Mathematics, California, USA