Roughness optimization for biomimetic superhydrophobic surfaces

For non-wetting liquids the contact angle with a rough surface is greater than with a flat surface and may approach 180 degrees, as reported for leaves of water-repellent plants, such as lotus. Roughness affects the contact angle due to the increased area of solid-liquid interface and due to the effect of sharp edges of rough surfaces. High roughness may lead to composite solid-liquid-air interface, which may be either stable or unstable. A comprehensive analytical model is proposed to provide a relationship between local roughness and contact angle, which is used to develop roughness distribution and to create biomimetic superhydrophobic surfaces. Various roughness distributions are considered, including periodic and surfaces with rectangular, hemispherically topped cylindrical, conical and pyramidal asperities and the random Gaussian height distribution. Verification of the model is conducted using experimental data for the contact angle of water droplet on a lotus leaf surface. For two solid bodies in contact, for wetting liquids, wetting leads to the meniscus force, which affects friction. Dependence of the meniscus force on roughness, previously ignored, is considered in the paper and it is found that with increasing roughness meniscus force can grow due to scale effect.