Superomniphobic textures are at the frontier of surface design for vast arrays of applications. Despite recent substantial advances in fabrication methods for reentrant and doubly reentrant microstructures, design optimization remains a major challenge. We overcome this in two stages. First, we develop readily generalizable computational methods to systematically survey three key wetting properties: contact angle hysteresis, critical pressure, and minimum energy wetting barrier. For each, we uncover multiple competing mechanisms, leading to the development of quantitative models and correction of inaccurate assumptions in prevailing models. Second, we combine these analyses simultaneously, demonstrating the power of this strategy by optimizing structures that are designed to overcome challenges in two emerging applications: membrane distillation and digital microfluidics. As the wetting properties are antagonistically coupled, this multifaceted approach is essential for optimal design. When large surveys are impractical, we show that genetic algorithms enable efficient optimization, offering speedups of up to 10,000 times.

The fundamental impacts of surface geometry on the stability of wetting states, and the transitions between them are elucidated for square posts and reentrant structures in three dimensions. We identify three principal outcomes of particular importance for future surface design of liquid-repellent surfaces. Firstly, we demonstrate and quantify how capillary condensation and vapour cavitation affect wetting state stabilities. At high contact angles, cavitation is enhanced about wide, closely-spaced square posts, leading to the existence of suspended states without an associated collapsed state. At low contact angles, narrow reentrant pillars suppress condensation and enable the suspension of even highly wetting liquids. Secondly, two distinct collapse mechanisms are observed for 3D reentrant geometries, base contact and pillar contact, which are operative at different pillar heights. As well as morphological differences in the interface of the penetrating liquid, each mechanism is affected differently by changes in the contact angle with the solid. Finally, for highly-wetting liquids, condensates are shown to critically modify the transition pathways in both the base contact and pillar contact modes.

Liquid infused surfaces with partially wetting lubricants have recently been exploited for numerous intriguing applications. Here, we study the factors that control the pinning force and the contact angle hysteresis of liquid droplets on liquid infused surfaces.

Even for relatively simple thin shell morphologies, many different buckled configurations can be stable simultaneously. Which state is observed in practice is highly sensitive to both environmental perturbations and shell imperfections. The complexity and unpredictability of postbuckling responses has therefore raised great challenges to emerging technologies exploiting buckling transitions. Here we show how the buckling landscapes can be explored through a comprehensive survey of the stable states and the transition mechanisms between them, which we demonstrate for cylindrical shells. This is achieved by combining a simple and versatile triangulated lattice model with efficient high-dimensional free-energy minimisation and transition path finding algorithms. We then introduce the method of landscape biasing to show how the landscapes can be exploited to exert control over the postbuckling response, and develop structures which are resistant to lateral perturbations. These methods now offer the potential for studying complex buckling phenomena on a range of elastic shells.