first feature of our design, the microstructure consists of an interconnected frame that prevents the nanostructures from being removed by abradants that are larger than the frame size (Fig. 1b, c). The interconnectivity also enhances mechanical robustness, as observed for various natural structures including springtail skin and honeycomb. Additional design features must also be considered to ensure that the non-wettability of the surface is not compromised. Here we explore the relationship between the liquid–solid contact fraction f, the Young’s contact angle θY and the apparent contact angle θ* using the Cassie–Baxter model: