(469c) Oscillations of a Sessile Drop with Moving Contact Line

The oscillation of a drop resting on a planar surface is of interest in applications where drop motion is induced by excitation (with or without a directional bias). We study the dynamic linear stability of a spherical-cap drop under a variety of contact line conditions, including a moving contact line modeled by a continuous contact-angle against speed relationship. Of special interest are those driving frequencies that are best for de-pinning the contact line in order to move drops along a substrate with a pre-established gradient in surface energy. A functional analytic approach is employed whereby ?mass', ?spring' and ?damping' functionals are derived and then solved using the Rayleigh-Ritz approach. Comparisons with previous analyses and available experiments are drawn where possible.