Droplet Sliding on an Inclined Substrate with a Topographical Defect

Pinning and depinning of droplets on heterogeneous substrates are widely seen in nature and need to be carefully controlled in industrial processes such as substrate cleaning and spray coating. In this work, a two-dimensional droplet sliding on an inclined substrate with a topographical defect is studied with a thin-film evolution equation. Using results from time-dependent finite-difference calculations, we focus our discussion on the dynamic interactions between the sliding droplet and the topographical defect. For a Gaussian defect shape, we find that droplet pinning is primarily determined by the advancing contact line pinning at the defect surface where the topography slope is minimum. We demonstrate that with certain combinations of defect heights and widths, residual droplets can form on the defect as a result of geometric constraints involving the receding droplet meniscus and the defect shape. We show that the delay in sliding caused by the defect is mainly due to the pinning and depinning of the receding contact line, and less affected by the dynamic behavior of the advancing contact line. This topography-induced delay in sliding of an individual droplet may have important implications for controlling the collective sliding behavior of multiple droplets.