NUMERICAL STUDY OF THE STATIC CONTACT ANGLE HYSTERESIS IN THE PRESENCE OF PERIODIC DEFECTS

Here we study numerically the static hysteresis interval of the observable contact angles (CAs) for the dipped plate geometry, where the immersed in a tank of liquid vertical smooth solid plate has doubly periodic heterogeneous surface. The two types of heterogeneity domains have sharp borders between them which is a case qualitatively different from the case when the surface tension of the plate varies smoothly. The hysteresis interval is obtained on the basis of exact solutions for the meniscus shape and position without any assumptions for small curvatures of the meniscus deformations caused by the heterogeneities on the plate. We use two definitions for the receding and advancing CAs. The first definition defines the minimal and the maximal possible averaged cosine of the CA among all possible positions of the plate with respect to the liquid level, while the second definition defines the averaged advancing and receding CAs over different realizations of the position of the defects on the plate relative to the liquid level. In the second definition the receding CAs can be considered as effective CAs for very small values of the plate velocity for immersing and withdrawing plate correspondingly. We find that the second hysteresis interval is contained in the first.