Activated drops: Self-excited oscillation, critical speeding and noisy transport

A small drop (similar to 10 mu l) of water exhibits critical speeding dynamics on an inclined super-hydrophobic pillared surface, in that it moves very slowly at first, but speeds up rapidly after a critical velocity is reached. During the mobile phase, some of the natural vibration modes of the drops are self-excited on a pillared surface, but not on a smooth hydrophobic surface. Additional experiments were carried out with glycerin and the solutions of water and glycerin that allowed their density and surface tension to be held more or less constant, while their viscosity could be varied. The terminal velocities of these drops following the critical speeding did not exhibit the expected decrease with increasing viscosity, but showed a highly non-linear behavior, exhibiting a maximum at an intermediate viscosity. Any of these drops moves steadily on a sub-critically inclined pillared substrate when it is subjected to a mechanical noise, the dynamics of which is remarkably similar to that obtained from another designed experiment in which the drops were made to cross a physical barrier assisted by an external noise. The dynamics of the low viscosity (1 mPas to 5.3 mPas) drops are amenable to a Kramers-like transition rate in the low friction limit, although the overall dynamics is found to be sub-Arrhenius. This work highlights the importance of the fluctuation of a drop that is either self-excited or that induced by an external noise in its motion on a surface.