The transport of small quantities of liquid on a solid surface is inhibited by the resistance to motion caused by the contact between the liquid and the solid. To overcome such resistance, motion can be externally driven through gradients in electric fields, but these all inconveniently involve the input of external energy. Alternatively, gradients in physical shape and wettability - the conical shape of cactus spines to create self-propelled motion. However, such self-propelled motion to date has limited success in overcoming the inherent resistance to motion of the liquid contact with the solid. Here we propose a simple solution in the form of shaped-liquid surface, where solid topographic structures at one length scale provides the base for a smaller length-scale liquid conformal layer. This dual-length scale render possible slippery surfaces with superhydrophobic properties. Combined to an heterogeneous topography, it provides a gradient in liquid-on-liquid wettability with minimal resistance to motion and long range directional self-propelled droplet transport. Moreover, the liquid-liquid contact enables impacting droplets to be captured and transported, even when the substrate is inverted. These design principles are highly beneficial for droplet transport in microfluidics, self-cleaning surfaces, fog harvesting and in heat transfer.
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