Contact angle hysteresis and pinning at periodic defects in statics

This article deals with the theoretical prediction of the wetting hysteresis on nonideal solid surfaces in terms of the surface heterogeneity parameters. The spatially periodical chemical heterogeneity is considered. We propose precise definitions for both the advancing and the receding contact angles for the Wilhelmy plate geometry. It is well known that in such a system, a multitude of metastable states of the liquid meniscus occurs for each different relative position of the defect pattern on the plate with respect to the liquid level. As usual, the static advancing and receding angles are assumed to be a consequence of the preceding contact line motion in the respective direction. It is shown how to select the appropriate states among all metastable states. Their selection is discussed. The proposed definitions are applicable to both the static and the dynamic contact angles on heterogeneous surfaces. The static advancing and receding angles are calculated for two examples of periodic heterogeneity patterns with sharp borders: the horizontal alternating stripes of a different wettability (studied analytically) and the doubly periodic pattern of circular defects on a homogeneous base (studied numerically). The wetting hysteresis is determined as a function of the defect density and the spatial period. A comparison with the existing results is carried out.