2008/08/10 by François Feuillebois, Martin Z. Bazant, Olga I. Vinogradova · 167 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Anisotropy #Composite material #Drag #Fluid Dynamics and Thin Films #Geometry #Isotropy #Lattice Boltzmann Simulation Studies #Materials science #Mathematics #Mechanics #Nanotechnology #Optics #Perpendicular #Physics #Slip (aerodynamics) #Surface Modification and Superhydrophobicity #Surface finish #Thermodynamics #Thin film #physics.flu-dyn
paper · pdf · doi:10.1103/physrevlett.102.026001
published in Physical Review Letters 102(2), 026001 (American Physical Society) · 4+ pages
arxiv created 2008/08/10 · openalex publication_date 2009/01/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Superhydrophobic surfaces reduce drag by combining hydrophobicity and roughness to trap gas bubbles in a microscopic texture. Recent work has focused on specific cases, such as arrays of pillars or grooves, with limited theoretical guidance. Here, we consider the experimentally relevant limit of thin channels and obtain rigorous bounds on the effective slip length for any two-component (e.g., low-slip and high-slip) texture with given area fractions. Among all anisotropic textures, parallel stripes attain the largest (or smallest) possible slip in a straight, thin channel for parallel (or perpendicular) orientation with respect to the mean flow. Tighter bounds for isotropic textures further constrain the effective slip. These results provide a framework for the rational design of superhydrophobic surfaces.