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.