Mathematical Modeling of Electro-Elastocapillary Systems

University Of Delaware, Newark DE

Investigators

Abstract

Pelesko 0807546 In this project, the investigator, his colleagues, and a team of undergraduate researchers study electrocapillary surfaces and electro-elastocapillary systems. Electrocapillary surfaces are capillary surfaces, i.e., surfaces which minimize surface energy subjected to a volume constraint, that are placed in an electric field. Electro-elastocapillary systems are electrocapillary surfaces that are additionally constrained to reside on a flexible elastic body. Mathematical models of these systems are developed via a variational principle. The resulting systems of coupled nonlinear partial differential equations are studied using tools from perturbation theory, nonlinear dynamics, and numerical analysis. In addition, experiments are carried out in the investigator's laboratory and the mathematical theory is compared with experimental data. Microelectromechanical systems (MEMS) operate at a scale where forces common to everyday experience, such as gravity and inertia, hold no sway. Rather, in the microworld, behavior is dominated by less familiar forces such as surface tension and the electrostatic force. Inspired and informed by recent advances in MEMS technology, this project develops the mathematical theory of systems dominated by the unique balance of capillary, electrostatic, and elastic forces. The development and analysis of this mathematical theory allows MEMS researchers to improve and optimize the design of MEMS devices. In turn, improved MEMS devices can be used in areas ranging from automotive safety to biomedical engineering. This project also focuses on outreach to mathematics faculty and students from local high schools. As part of this project, the investigator strengthens existing ties with several local high schools and help develop novel lab-based exercises to be integrated into the high school mathematics curriculum.