Analysis of Wetting and Contact Angle Hysteresis on Chemically Patterned Surfaces

The wetting and contact angle hysteresis on chemically patterned surfaces in two dimensions are analyzed from a stationary phase-field model for immiscible two phase fluid. We first study the sharp interface limit of the model by the method of matched asymptotic expansions. We then justify the results rigorously by the Γ-convergence theory for the related variational problem and study the properties of the limiting minimizers. The results also provide a clear geometric picture of the equilibrium configuration of the interface. This enables us to explicitly calculate the total surface energy for the two phase systems on chemically patterned surfaces with simple geometries, namely the two phase flow in a channel and the drop spreading. By considering the quasi-static motion of the interface described by the change of volume (or volume fraction), we can follow the change of energy landscape which also reveals the mechanism for the stick-slip motion of the interface and contact angle hysteresis on the chemically patterned surfaces. As the interface passes through patterned surfaces, we observe not only stick-slip of the interface and switching of the contact angles but also the hysteresis of contact point and contact angle. Furthermore, as the size of the pattern decreases to zero, the stick-slip becomes weaker but the hysteresis becomes stronger in the sense that one observes either the advancing contact angle or the receding contact angle (when the interface is moving in the opposite direction) without the switching in between.