The focus of Professor Davis’ research is the development of mathematical models to provide a fundamental understanding of microscale fluid dynamics on heterogeneous surfaces.This heterogeneity results from chemical patterning, topographical variations, and differential heating of the substrate, all of which lead to significant deviations from fluidic behavior on uniform surfaces. Flows over these non-uniform surfaces are crucial to applications that include microfluidic analytical devices and sensors, micro-electro-mechanical systems, and micro-fabrication processes. This research has two major thrusts: (1) free-surface flows on heterogeneous surfaces that enable improved performance and fabrication of micro-devices and (2) particle dynamics in flow over nanotextured surfaces that form the basis for biomimetic sensors.