Self-propulsion of droplets by spatially-varying surface topography

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 theoretically that spatial texturing of the substrate topography may lead to spontaneous propulsion of droplets. Individual droplets tend to be 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 patterning the substrate with sinusoidal wrinkles 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 texturing of spatial topography with chemical or material patterning of the substrate.