Dichotomous behavior of capillary surfaces in zero gravity

Abstract

A mathematical procedure is described for determining the behavior of the free surface of a fluid in static equilibrium and partly filling a cylindrical container with cross-section of general form in zero gravity. Either of two qualitatively distinct situations must prevail, depending on geometry and contact angle. Several illustrative examples are discussed, and the procedure is applied in detail to a container with a rectangular section on which the corners have been rounded, thereby determining the effect of rounding on the 'critical' contact angle that separates the two types of behavior. This last example is intended in part as a guide for application to general geometries.