Force balance model for spontaneous droplet motion on bio-inspired topographical surface tension gradients

Abstract

Passive gradient-driven droplet motion has been demonstrated in nature, inspiring coating-free surface tension gradient surfaces that can be fabricated via laser ablation. These surfaces can potentially enhance heat exchanger performance, promoting drop-wise over film-wise condensation, and be suitable for lab-on-a-chip applications, allowing the directional transport of microliter size droplets. In this work, a theoretical model and its application to variable-pitch hierarchical superhydrophobic gradients are discussed, and the method is experimentally validated against various gradient topographical designs. The proposed force balance model allows analysis of the impact of the topography on the forces acting on the droplet. The discrepancy between modeled and observed contact angles in most cases does not exceed 10%. The modeled droplet footprint fits the experimentally measured ones with an error of less than 10% for most cases. Though modeled motion distances were twice greater than experimentally observed ones, the comparison of the proposed model with the originally developed theory showed that the difference in the net force was less than 5%. Both observed and average velocities were within less than 30% difference. Like the traditional models, the new model overestimates droplet kinematics; however, it does not require knowledge a priori of all the contact angles across the gradient during droplet motion, relying only on the material's surface tension and the local surface area fraction. Therefore, the model presents a simplified and convenient means of designing a linear topographical gradient for spontaneous droplet motion.