Contact-angle hysteresis on periodic microtextured surfaces: Strongly corrugated liquid interfaces

We study numerically the shapes of a liquid meniscus in contact with ultrahydrophobic pillar surfaces in Cassie's wetting regime, when the surface is covered with identical and periodically distributed micropillars. Using the full capillary model we obtain the advancing and the receding equilibrium meniscus shapes when the cross-sections of the pillars are both of square and circular shapes, for a broad interval of pillar concentrations. The bending of the liquid interface in the area between the pillars is studied in the framework of the full capillary model and compared to the results of the heterogeneous approximation model. The contact angle hysteresis is obtained when the three-phase contact line is located on one row (block case) or several rows (kink case) of pillars. It is found that the contact angle hysteresis is proportional to the line fraction of the contact line on pillars tops in the block case and to the surface fraction for pillar concentrations 0.1-0.5 in the kink case. The contact angle hysteresis does not depend on the shape (circular or square) of the pillars cross-section. The expression for the proportionality of the receding contact angle to the line fraction [Raj et al., Langmuir 28, 15777 (2012)LANGD50743-746310.1021/la303070s] in the case of block depinning is theoretically substantiated through the capillary force, acting on the solid plate at the meniscus contact line.