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NJIT Applied Mathematics Colloquium

Friday, April 1st 2011, 11:30am
Cullimore Lecture Hall II
New Jersey Institute of Technology

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Stability of a planar-extensional flow and an axisymmetric thin film flow

Linda Smolka

Bucknell

We derive from the Navier-Stokes equations a time-dependent exact solution of the free surface problem that describes the planar extensional motion of a viscous sheet driven by inertia. The linear stability of the exact solution to one- and two-dimensional symmetric perturbations is examined in the inviscid and viscous limits within the framework of the slender body approximation. Both transient and long-time asymptotic stability are considered. We show the flow is most unstable to transverse perturbations. In a second problem, we consider the motion and stability of a gravity-driven contact line of a thin viscous film traveling down the outside of a vertical cylinder. We derive a lubrication model and examine the influence of substrate curvature on the fingering instability along the contact line. We find the wavelength and number of fingers that form along the contact line predicted from stability theory are in excellent agreement to experimental data.