Motion of drops on a surface induced by thermal gradient and vibration

It is well known that a liquid drop with a low contact angle (approximately 45 degrees ) and low wetting hysteresis moves toward the colder region of a temperature gradient substrate as a result of the thermal Marangoni force. A moderately sized water drop, however, usually does not move on such a surface because of the overwhelming effect of hysteresis. The water drop can, however, be forced to move when it is vibrated on a temperature gradient surface with its velocity exhibiting maxima at the respective Rayleigh frequencies. A simple model is presented that captures the dependence of drop velocity on hysteresis, vibration amplitude, and the forcing and resonance frequencies of vibration.