Weakly-Damped Vibrating Sessile Rayleigh Drops

The natural frequencies and mode shapes for an inviscid free drop vibrating due to surface tension were reported by Rayleigh (1879).  In many applications, however, drops are constrained by a solid substrate which significantly influences both the frequencies and shapes of the Rayleigh spectrum, as we have recently reported.   In this talk, we focus on the influence of weak viscosity (small Ohnesorge number) and its role, in competition with dissipation arising from contact-line mobility, on the damping of forced oscillations of the sessile drop.  We report observations of a mechanically-excited sessile drop, driven in the plane-normal direction.  We compare experiment against prediction by a viscous potential theory extension of the inviscid linear stability results. Spectrum splitting and the broadening of resonance peaks of the inviscid spectrum are highlighted.