Proposal for Exploratory Research

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Abstract: 9729817 Robert Finn The focus of this research is the study of capillarity phenomena of liquid surfaces. Capillarity effects are commonly observed in the shape of the surface of water or other liquid in a glass. For narrower containers, such as a test tube or drinking straw, the capillary forces make the surface of the liquid more curved and lift the liquid up the sides of the container. Interest is growing in this topic which has applications in areas as diverse as fluid management in low gravity, semiconductor manufacturing, behavior of liquids in porous rocks, and many other situations in which surface forces predominate over gravity. A significant parameter in capillarity phenomena is the angle that the liquid makes with a solid surface, this angle is called the contact angle. The angle depends on the liquid and the properties of the solid surface. The principle investigator has shown that in the presence of a corner, the height of the capillary surface in the corner depends, in a discontinuous way, on the relation between the angle of the corner and the contact angle. One aspect of this research will be applicable to finding new ways of determining the contact angle. The mathematical questions to be investigated will require new and as yet untested ideas for their resolution. The problems are exciting, relating formal mathematics directly to physics and leading to experimental verification. It is expected that the new results will display and clarify further exotic behavior of the surfaces.