Proposal for Exploratory Research

摘要：9729817罗伯特·芬恩本研究的重点是研究液体表面的毛细现象。毛细效应通常以水或玻璃杯中其他液体的表面形状来观察。对于较窄的容器，如试管或吸管，毛细管力使液体表面更加弯曲，并将液体向上提起容器的侧面。人们对这一主题的兴趣与日俱增，它在各种领域都有应用，如低重力中的流体管理、半导体制造、液体在多孔岩石中的行为，以及许多其他表面力超过重力的情况。毛细现象中的一个重要参数是液体与固体表面的夹角，这个角度称为接触角。角度取决于液体和固体表面的性质。这位原理研究者已经证明，在有拐角的情况下，拐角处毛细管表面的高度以一种不连续的方式取决于拐角与接触角之间的关系。这项研究的一个方面将适用于寻找确定接触角的新方法。将要调查的数学问题将需要新的、尚未经过测试的想法来解决。这些问题令人兴奋，将形式数学与物理学直接联系起来，并导致了实验验证。预计新的结果将显示和澄清表面的进一步奇异行为。

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.