Contact angle hysteresis and meniscus corrugation on randomly heterogeneous surfaces with mesa-type defects

The results of a numerical study of the various characteristics of the static contact of a liquid meniscus with a flat but heterogeneous surface, consisting of two types of homogeneous materials, forming regularly and randomly distributed microscopic defects are presented. The solutions for the meniscus shape are obtained numerically using the full expression of the system free energy functional. The goal is to establish how the magnitude and the limits of the hysteresis interval of the equilibrium contact angle, the Cassie's angle, and the contact line (CL) roughness exponent are related to the parameters, characterizing the heterogeneous surface-the equilibrium contact angles on the two materials and their fractions. We compare the results of different ways of determining the averaged contact angle on heterogeneous surfaces. We study the spread of the CL corrugation along the liquid meniscus. We compare our results with the numerical results, obtained using linearized energy functional, and also with experimental results for the CL roughness exponent. The obtained results support the conclusion that some characteristics depends on the type (regular or random) of the heterogeneity pattern.