Proposal for Exploratory Research

摘要：9729817 罗伯特·芬恩 本研究的重点是液体表面毛细现象的研究。 毛细效应通常在玻璃杯中水或其他液体的表面形状中观察到。对于较窄的容器，如试管或吸管，毛细作用力使液体的表面更加弯曲，并将液体从容器的侧面提升。 人们对这一主题的兴趣越来越大，它在低重力下的流体管理、半导体制造、多孔岩石中液体的行为以及表面力占主导地位的许多其他情况下都有应用。 毛细现象中的一个重要参数是液体与固体表面形成的角度，这个角度称为接触角。 该角度取决于液体和固体表面的性质。 主要研究者已经表明，在存在拐角的情况下，拐角中的毛细管表面的高度以不连续的方式取决于拐角的角度与接触角之间的关系。本研究的一个方面将适用于寻找新的方法来确定接触角。 要研究的数学问题将需要新的、尚未经过检验的思想来解决。 这些问题令人兴奋，将形式数学直接与物理学联系起来，并导致实验验证。 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.