Abstract of Proposed Research Gerri Simonett
Over the last decades, the subject of free boundary problems has attracted increasing attention because of its theoretical interest, and because of its numerous applications in the natural and engineering sciences. Free boundary problems are important in many fields such as material sciences, fluid mechanics, hydrodynamics, thermo-mechanics, magneto-dynamics, solid state physics, geology, chemistry, and the biological and medical sciences. The appropriate numerical and analytical treatment is a major challenge, both to the engineer and to the mathematician. Typically, a free boundary problem consists of one or more partial differential equations which have to be solved in a domain that is a priori unknown and that has to be determined as part of the problem. Free boundary problems are in general harder to solve, both analytically and numerically, than the underlying differential equations would be in a prescribed domain. They have an inherent nonlinear structure, as two separate solutions cannot be superposed.
In this project, the PI proposes a systematic investigation of various free boundary problems with moving contact lines in the presence of surface tension. Moving contact lines occur in many situations, for example in processes such as the coating of solid surfaces by a viscous fluid, spin coating of micro chips, the displacement of one fluid by another fluid along a solid boundary, the spreading of drops on solid surfaces, the motion of a fluid (or a fluid-liquid system) in a container where the free surface is in contact with the wall of the container. The modeling and characterization of contact line motion is one of the major unsolved problems of capillary theory.
