Pinning-Depinning Transition Behavior of Droplets on Geometric Edges

When a slowly sliding droplet encounters a sharp edge on an inclined plane, its contact line can become pinned. Literature indicates that the pinning behavior of a droplet is governed by the geometric factor of edge angle and the material property of contact angle. However, the quantitative effect of these parameters on the pinning-depinning transition is not yet well understood. To address this gap, we hypothesize that it is possible to quantitatively characterize the critical depinning condition based on a friction theory that incorporates these governing parameters. A friction-based theoretical model coupling droplet volume, edge geometry, and surface wettability is developed to investigate the depinning behavior of a droplet encountering a sharp edge, and is extended to scenarios with chemically heterogeneous edges. The critical tilt angle αmax is introduced as a quantifiable metric to characterize the pinning-depinning transition, which otherwise remains a qualitative description of contact line dynamics. The proposed model is employed to systematically examine how droplet volume, edge geometry, and surface wettability govern the depinning transition. Simulations validate the model against experimental measurements, and reveal that these parameters monotonically affect the critical tilt angle (αmax) by altering the force balance of the droplet at the edge. For a specific system, a droplet sliding across an edge without pinning has been observed when a defined relationship between the surface properties on both sides of the edge is satisfied.