Depinning-Induced Capillary Wave during the Sliding of a Droplet on a Textured Surface

Surfaces covered with hydrophobic micro-/nanoscale textures can allow water droplets to slide easily because of low contact angle hysteresis. In contrast to the case of a droplet sliding on a smooth surface, when a droplet slides on a textured surface, it must recede from the textures at its rear edge and the resultant depinning events induce a capillary wave on the surface of the droplet. Although this depinning-induced capillary wave can be observed to some extent through high-speed imaging, important parameters of the wave, such as the wavelength and frequency, and the factors that determine these parameters are not fully understood. We report direct measurements of this depinning-induced capillary wave using microelectromechanical systems (MEMS)-based force sensors fabricated on a textured surface. Such sensor measurements reveal the frequency of the vibration occurring on the surface of the droplet, from which it is possible to calculate the wavelength of the capillary wave. We show that the frequency and wavelength of the depinning-induced capillary wave during the sliding of a water droplet on a micropillar array depend upon neither the size of the droplet nor its sliding velocity. However, the frequency (wavelength) decreases (increases) as the pitch of the micropillar array increases. We argue that the wavelength of the depinning-induced capillary wave is equal to the maximum length of the liquid bridges that develop at the micropillars before depinning. This hypothesis is confirmed by comparing the wavelengths obtained from the sensor measurements to the maximum liquid-bridge lengths calculated from observations using a high-speed camera.