Contact angle hysteresis and the shape of the three-phase line

Abstract

The effects on contact angle and capillary rise hysteresis of a specific pattern of mixed wettability are examined. The capillary rise of a liquid onto a vertical plate consisting of closely spaced alternating horizontal stripes characterized by two different contact angles is considered. For each value of the average rise height, the approximate shape of the liquid surface is determined by an energy minimization technique. An assumed straight horizontal contact line is shown to be unstable to small perturbations when the average rise height lies near those stripe boundaries where the material with smaller equilibrium contact angle lies above the other material. A second family of solutions, suggested by experiment, is shown to be less energetic in these regions. The calculated variation of total energy with mean rise height exhibits multiple energy minima; these metastable states can explain the hysteresis phenomenon. The energy barriers between adjacent minima are found to be significantly smaller than previous calculations suggest, the difference arising from the contact line deformation. This suggests a potential decrease in contact angle hysteresis. In addition, a virtual insensitivity of the energy barrier heights to the intensity of the wall wettability variation is revealed.