Droplet evaporation on mesas

Droplet evaporation on a mesa, a raised region with a flat top, occurs in spray coating, microreactors and printed-electronics fabrication. In printed-electronics fabrication, maintaining a pinned contact line is often desirable, and depositing droplets on wide and short mesas offers a simple and effective way to achieve this. We combine flow-visualisation experiments with mathematical modelling to systematically characterise contact-line motion on mesas having heights much smaller than their widths. Flow visualisation reveals that the contact line pins at the mesa edge for a significant amount of time, with lower heating temperatures or larger initial liquid volumes further prolonging this pinning. To interpret these trends, we construct a lubrication-theory-based model that employs a precursor-film/disjoining-pressure approach to account for contact-line motion and a one-sided framework to describe evaporation. Numerical solutions reveal that higher heating temperatures enhance evaporation near the droplet edge, leading to shorter pinning times, while larger initial liquid volumes induce more convex interfaces and stronger outward flows, which extend the pinning. Our model qualitatively explains the experimental trends and suggests strategies for controlling droplet pinning in printed-electronics fabrication.