Sessile Rayleigh drop instability

Rayleigh (1879) determined the mode shapes and frequencies of the inviscid motion of a free drop held by surface tension. We study the inviscid motions of a sessile Rayleigh drop -- a drop which rests on a planar solid and whose contact-line is free to move. Linear stability analysis gives the modes and frequencies of the droplet motions. In this talk, we focus on the ``walking instability,'' an unstable mode wherein the drop moves across a planar substrate in an inviscid rocking-like motion. The mode shape is non-axisymmetric. Although the experimental literature has hinted at such a mode, this is the first prediction from linear stability analysis, as far as we are aware. The ``walking instability'' of the drop converts energy stored in the liquid shape into the energy of liquid motion -- which represents a heretofore unknown pathway of energy conversion of potentially wide significance for a broad range of applications.