Theoretical analysis of contact angle hysteresis of suspended drops on micropillared superhydrophobic surfaces

The contact angle hysteresis of superhydrophobic surfaces is very important for many industrial applications, but related mechanisms of the motion of the contact line induced by varying drop volumes are not fully understood. In this work, a thermodynamic model was established to analyze contact angle hysteresis, and a relationship between the varying drop volume and free energy barriers is presented. The calculation results showed the advancing/receding free energy barriers changing markedly with addition of liquid to a drop as well as its removal from the drop, ultimately leading to pinning/depinning of three-phase contact lines and varying apparent contact angles. The advancing contact line tends to pin to the upper surface of micropillars, and the receding contact line shows a stick-slip motion on this surface. Regarding contact angle hysteresis, the theoretical value of the advancing contact angle was indicated to be independent of geometric parameters of micropillars, and to reach a value of 180 degrees. In contrast, the receding contact angle was strongly affected by micropillar structures, and specifically decreased with the increasing pillar width and decreasing pillar spacing. Moreover, the efficacy of the model was verified by a comparison with experimental observations for superhydrophobic surfaces with different geometric parameters. This work has offered insights into the stickiness of a suspended drop on a micropillared superhydrophobic surface.