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- My general research interests include mathematical modeling of problems motivated by physical processes and phenomena in fluid mechanics and materials science. Currently my research program is focused on the motion and stability of free surface and thin film flows in cylindrical and planar geometries. Free surface and thin film flows in planar and cylindrical geometries appear in a wide variety of industrial applications, such as ink-jet printing, fiber-spinning, agricultural and industrial sprays, film coating and curtain coating. It is common for these flows to undergo some form of instability, a feature that may or may not be desired. In either case, controlling instabilities is paramount to maintaining quality control in applications. My research seeks to develop a fundamental understanding of the role that: fluid properties (specifically, surface tension, viscosity and elasticity); flow conditions (Stokes versus inertial flows); and flow geometry (planar versus cylindrical), play on hydrodynamic stability. Particular problems of interest include: (1) the motion and stability of time-dependent extensional flows of viscous and viscoelastic fluids; (2) the dynamics of free surface perturbations that form as an annular jet of fluid flows down the outside of a thin vertical fiber; and (3) the stability of a gravity-driven contact line of thin film flowing down a solid substrate. Another field of interest is in quantifying how the choice of governing equations, that is, the full 3-D Navier-Stokes equations versus slender 1-D equations, influence stability predictions of time-dependent extensional free surface flows. This last topic is critical to developing accurate predictions for free surface breakup. My research is interdisciplinary in scope with theoretical, numerical and experimental components involved. Experiments are conducted in my applied math (fluid mechanics) laboratory at Bucknell University.