Capillarity is the phenomena of fluid rise against a solid vertical wall. For our research, we consider bounded cases of intermediate corner angles ( p/2< a + g < p/2+2 g ), where g is the angle of contact and 2a is the wedge angle. The Laplace-Young Capillary equations are used to determine the rise of the fluid, especially at corners. While there exist asymptotic expansions for the height rise occurring at the corner of an intermediate angle, not all coefficients are known analytically. Therefore, numerical solutions are necessary, even though only a few numerical methods have been published. We explain our least-squares finite element method used in determining solutions to the Laplace-Young Capillary equations, and then give our numerical results.

Author Bio

Genevieve is a senior at the University of Notre Dame and will graduate in May of 2009 with a degree in mathematics. The REU at Wabash was her first experience in mathematical research, and she has had the opportunity to present the research at various conferences. Originally from Montana, she plans to continue on into graduate work in development statistics.

Jessica is a senior at the University of Puerto Rico at Humacao, pursuing mathematics. As her second REU, Wabash provided an opportunity to study applied mathematics. From San Juan, Puerto Rico, Jessica looks forward to what she will do after graduation.