Self-Propulsion of Droplets by Spatially-Varying Roughness

Under partial wetting conditions, making a substrate uniformly rougher enhances the wetting characteristics of the corresponding smooth substrate {--} hydrophilic systems become even more hydrophilic and hydrophobic systems even more hydrophobic. Here we show that spatial texturing of the roughness may lead to spontaneous propulsion of droplets. Individual droplets are driven toward regions of maximal roughness for intrinsically hydrophilic systems and toward regions of minimal roughness for intrinsically hydrophobic systems. Spatial texturing can be achieved by wrinkling the substrate with sinusoidal grooves whose wavelength varies in one direction (inhomogeneous wrinkling) or lithographically etching a radial pattern of fractal (Koch curve) grooves on the substrate. Richer energy landscapes for droplet trajectories can be designed by combining roughness texturing with chemical or material patterning of the substrate.