Hierarchical Surface Patterns via Global Wrinkling on Curved Substrate for Fluid Drag Control

In this paper, the results of an investigation on the global wrinkling of stiff coatings resting on curved compliant substrates are presented. It is found that the overall stiffness of the corrugated coatings can dominate the deformation mode and induce the global wrinkling when the coating thickness exceeds certain critical value. It is demonstrated that hierarchical wrinkling patterns with small wrinkles superposing on large wrinkles, either parallel or perpendicularly, can be generated via the global wrinkling processes. Through a combination of theoretical model, experimental studies, and numerical simulations, the formation mechanism and controlling parameters of the hierarchical wrinkling patterns are systematically investigated. The quantitative expression of the critical loading strain, critical wavelength, and critical coating thickness of the global wrinkling as a function of the initial substrate curvatures and loading conditions are revealed. Inspired by the resemblance between the hierarchical surface patterns and the surface riblets on sharks and dolphins, the potential application of utilizing the hierarchical wrinkling patterns to reduce fluid drag through computational fluid dynamics (CFD) studies is further investigated. Reduced drag resistance is observed on the hierarchical wrinkled surface with small wrinkles and large wrinkles perpendicular to each other.