Contact angle hysteresis on random self-affine rough surfaces in Wenzel's wetting regime: Numerical study

We present a numerical study of the advancing and receding apparent contact angles for a liquid meniscus in contact with random self-affine rough surfaces in Wenzel's wetting regime. Within the framework of the Wilhelmy plate geometry, we use the full capillary model to obtain these global angles for a wide range of local equilibrium contact angles and for different parameters that determine the self-affine solid surfaces: Hurst exponent, wave vector domain, and root-mean-square roughness. We find that the advancing and receding contact angles are single-valued functions that depend only on the roughness factor determined by the set of values of the parameters of the self-affine solid surface. Moreover, the cosines of these angles are found to depend linearly on the surface roughness factor. The relations between the advancing, the receding, and Wenzel's equilibrium contact angles are investigated. It is shown that for materials with self-affine surface structure, the hysteresis force is the same for different liquids and it depends only on the surface roughness factor. A comparison with existing numerical and experimental results is carried out.