Fig. 3: Confirmation of the bidirectional motion of droplets on liquid-infused surfaces with topographical gradients.

a The colourmap describes the normalised driving force \(\tilde{F}\) provided in Eq. (10), with \({\theta }_{{\rm{wa}}| {\rm{s}}}^{{\rm{eff}}}\) and \({\theta }_{{\rm{wa}}| {\rm{o}}}^{{\rm{eff}}}\)the droplet apparent contact angle on a smooth solid surface and on a lubricant surface, respectively. The data points were obtained from simulations and experiments, in which the droplets were observed to move to the solid majority (blue) or the lubricant majority (red) surfaces. The symbols ⊕ , ⊲, ♢, × and ○ are from simulations, where we have used linear gradient of rectangular posts in b full 3D and c quasi 3D setups, stepwise gradient of d rectangular posts and e grooves in quasi 3D setups, and f 2D setups. Here, the solid and lubricant are coloured in yellow and orange, respectively. The symbols ⋆ and ⊳ are from experiments (the hollow symbols indicate the lubricant encapsulation case). They correspond to (g) stepwise gradient and (h) linear gradient of grooves. The solid and lubricant are represented in grey and orange, respectively.