Engineering Contact Line Dynamics: Predicting Pinning beyond the Point-Defect Approximation

Contact line pinning on heterogeneous surfaces governs wetting dynamics across scales. While classical theory treats defects as point-like forces, this assumption breaks down at the nanoscale, where the finite physical width of a defect becomes significant. We hypothesize that this finite width determines both the pinning strength and the resulting contact line dynamics, enabling the determination of key mechanical parameters from the defect geometry and system dimensions within the framework of the present model. Simulations: We perform large-scale molecular dynamics (MD) simulations of a liquid bridge confined between two parallel solid plates. The plates move at a constant velocity in opposite directions along the x-axis. A single, well-defined nanoscale defect with finite width is introduced on the top plate. By systematically varying the defect size and the system length, we measure the full two-dimensional contact line morphology, effective contact line stiffness, maximum pinning force, and the complete time-resolved trajectory of the contact line apex xp(t) during the pinning and depinning processes.

A theoretical model is derived based on a Gaussian pinning potential, which yields an analytical contact line morphology that bridges a parabolic near-field and a logarithmic far-field. The present framework yields an effective global stiffness K and a closed-form expression for the position-dependent pinning force Fpinn(xp). These results enable a reduced Langevin equation for the apex dynamics, whose predictions are validated quantitatively by MD simulations without adjustable parameters. Furthermore, by inverting this relationship, we demonstrate that temporal wetting dynamics can be programmed through spatially engineered defect patterns.