PROVIDENCE, RI -- Imagine a narrow glass test tube partly filled with water. The surface of the liquid will be not flat but curved, as if the liquid were climbing the walls of the tube. This is an example of a capillary surface, a boundary between a liquid and a gas, or between two liquids.
The shape of the surface depends on the gravity field and on the properties of the particular materials involved. In the case of a narrow test tube, the shape will be influenced strongly by the presence and by the shape of the solid walls of the tube.
Attempts to understand capillary phenomena go back to the time of Aristotle and have resulted in formidable scientific and mathematical challenges. The equations governing these phenomena are highly nonlinear and in general cannot be solved exactly. Further, the theory was difficult to confirm experimentally because capillary action can be masked by interference from other physical phenomena.
Recent mathematical discoveries have had an important impact on the study of capillary phenomena. Some of the discoveries led to predictions so surprising as to create doubts about the validity of the underlying physical theory. These doubts have been resolved by the dramatic results of NASA drop tower experiments and also recent experiments conducted on the NASA Space Shuttle and in the Russian Mir Space Station, confirming the predictions. The predictions indicate some ways in which a fuel tank can be designed, so as to make the fuel available in a specified location during space flight.
The article, "Capillary Surface Interfaces" by Robert Finn, to appear in the August 1999 issue of the NOTICES of the AMS, describes the history and current state of the mathematical theory of capillary phenomena. It can be accessed under the Journalists' Section at our website at www.ams.org. Professor Finn may be reached by email at finn@gauss.stanford.edu
Founded in 1888 to further mathematical research and scholarship, the 30,000-member AMS fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and everyday life.