Depinning force of a receding droplet on pillared superhydrophobic surfaces: Analytical models

It was experimentally shown that a depinning force of a receding droplet on a micropillared superhydrophobic surface has an apparently linear correlation with the maximal three-phase contact line attainable along an actual droplet boundary. However, the experimental observation has not yet been supported by any theoretical basis or analysis. This study establishes an analytical model that theoretically supports the experimental observation on the basis of the dynamics of a contact line. The depinning force of a receding droplet was experimentally measured in evaporation on micropillared superhydrophobic surfaces with varying structure pitches but a fixed size. The analytical model was established by considering the energy dissipated by the displacement of a microscopic contact line on pillar tops and the energy consumed for the distortion of a liquid-gas interface between pillar tops. The model shows that the depinning force can theoretically be estimated by the physical dimensions of pillars and the intrinsic hydrophobicity of the surface, showing excellent agreement with the experimental results. Especially, the model indicates that the depinning force is fundamentally determined and practically controllable by the normalized maximal contact line at the droplet boundary, which can effectively be represented as the ratio of the pillar top perimeter to pitch.