Mechanical criteria and analytical modeling of mixed-state wetting on multiscale surfaces: Of the importance of nanoscale topography for water-repellency

Abstract

Multiple natural surfaces exhibit excellent water-repellent properties. Such surfaces systematically demonstrate multiscale surface topographies. However, current mechanical criteria for composite-wetting equilibrium can only be applied on model micrometric pillars. This paper suggests a theoretical basis on the foundation of which we introduce multiscale mechanical criteria for mixed-state equilibrium on real surfaces. A method for the analytical modeling of mixed-state wetting on real textured surfaces and the retrieval of critical wetting parameters such as the total solid-liquid contact area and the total triple line perimeter at the effective anchorage depth is introduced. This method is applied to the case of the sacred Lotus leaf on which we predict the effective anchorage depth of the triple lines. Results show that the nanoscale topography of these leaves leads to the minimization of the effective anchorage depth of the droplet on the sides of the micrometric asperities, a determining parameter with regards to its effect on the total solid-liquid contact area and the total triple line perimeter, unveiling a little more the role of nanoscale wax crystals in nature’s strategies for water-repellency.