The mechanical stability of microst

The mechanical stability of microstructures is dominated by their geometry. To optimize the robustness, we adjusted the angle α between the sidewall and the substrate of the microstructures (Fig. 1e, f) while keeping the top contact area constant. From a structural mechanics viewpoint, increasing α is usually an effective way to strengthen the structural stability of the architecture. To confirm this principle, microstructures with different values of α were modelled and the stress distributions under fixed load were simulated using multipurpose finite-element analysis (Supplementary Fig. 2). The third principal stress (|σ|) reduces significantly, and therefore the stability of the microstructures improves markedly, as α increases (Fig. 1f). Conversely, the liquid–solid contact fraction of the microstructures, f orig micro, increases to f when half of the height is abraded (Fig. 1e, f, Supplementary Fig. 3, Supplementary Discussion section 2.2). The increase of Δf = f − f micro with α means that the liquid–solid contact area increases—that is, the liquid adhesion force increases—for larger values of α. As shown in Fig. 1f, an optimum regime emerges around α ≈ 120° in which both superhydrophobicity and mechanical stability can be balanced and guaranteed. The second and third design features of this strategy are therefore a low f micro and an α value of approximately 120°.