This project is devoted to understanding physical phenomena in liquids at small length scales. One main challenge is to characterize the dynamics of contact lines through novel applications of asymptotic and variational techniques. The role of surfactants, surface defects, and electrostatic control will be explored. Instability-driven pattern formation and coarsening behavior will be another focus of study. Finally, numerical methods based on boundary integral and finite element techniques will be developed both for experimentation and technological applications.
The behavior of fluids at small scales poses a set of challenging scientific problems, with applications to subjects as diverse as industrial coatings, microscopic mechanical devices, and collective bacterial motion. The proposed projects are intended to not only extend fundamental theoretical knowledge, but to develop models and algorithms that have predictive capabilities. These will be crucial for engineering present day and cutting edge microfluidic applications.
