Contact angle hysteresis on nonwetting microstructured surfaces: Effect of randomly distributed pillars or holes

We present a numerical study of the advancing and receding apparent contact angles for a liquid meniscus in contact with an ultrahydrophobic surface with randomly distributed microsized pillars or holes in the Cassie's wetting regime. We study the Wilhelmy plate system in the framework of the full capillary model to obtain these angles using the heterogeneous surface approximation model for a broad interval of values of pillar or hole concentration and for both square and circular shapes of the pillars or holes cross-section. Three types of random placing of defects on the plate are investigated, i.e., two with restrictions: (1) with maximum and (2) with minimum distance between the defects (in these cases the defects are isolated), and (3) without restrictions (the defects can overlap). The results show that the type of defect distribution and also the type of the defects shape (circular or square) does not affect the magnitude of the two angles. The results of the numerical simulations showed that the retention force for a plate with randomly located defects is not greater, and for larger concentrations of pillars or holes, it is smaller than that for periodically spaced ones. Comparisons with experimental results for the receding contact angle on surfaces with pillars and with the advancing contact angle on surfaces with periodically arranged holes is carried out.