Capillary Waves Joint to Super-Hydrophobic Bars

Abstract

Super-hydrophobic coating reduces hydrodynamic drag of rigid surfaces due to separation of a part of the surface from the flow by air. The drag reduction ratio is proportional to the ratio of the surface area covered by air to the whole surface area. The maximum ratio may be achieved for coating with a regular spanwise super-hydrophobic bar. The air–water boundary over such bar would be a capillary wave with wavelength equal the distance between bar apexes. The numerical analysis of such waves was carried out by solving a two-dimensional nonlinear free-boundary problem of ideal fluid theory. Besides several wave shapes, the main computational results include dependencies of wavelengths and dimensionless pressure coefficient necessary for wave maintenance on Weber number. These dependencies make it possible to select the bar size and inflow speed allowing for existence of such waves and the highest drag reduction ratios.