Soft Wetting: An Analytical Model for Pillar Topography- and Softness-Dependent Droplet Depinning Force

The extent to which a droplet pins on a textured substrate is determined by the dynamics of the contact line and the liquid-vapor interface. However, the synergistic contribution of contact line sliding and interface distortion to the droplet depinning force remains unknown. More strikingly, current models fail to predict the depinning force per unit length of droplets on soft pillar arrays. Therefore, we fabricate soft pillar arrays with varying geometrical dimensions and mechanical properties and measure the depinning forces per unit length by allowing droplets to evaporate on such substrates. We then analyze the decrease in excess Gibbs free energy of the apparent droplet caused by the detachment of the droplet boundary from the previously pinned pillars. In contrast to prior notions, based on the measured decreases in excess Gibbs free energy, we find that the coefficient, that governs the ratio of interface distortion's contribution to the depinning force to that of the sliding contact line, increases with a decrease in pillar packing density. By considering the combined contribution from contact line sliding, liquid-vapor interface distortion, and pillar deflection, we introduce an analytical model to predict the droplet depinning force per unit length and corroborate the model using experimental data reported in this and prior studies.