Droplets on Microdecorated Surfaces: Evolution of the Polygonal Contact Line

Interaction of liquids with surfaces is ubiquitous in our physical environment as well as many engineering applications. Recent advances on this topic have not only provided us with valuable insight into nature's design, but also enabled improved fluidic manipulation for liquid-based printing applications such as biomicroarrays for protein and DNA sequencing, multicolor polymer-based LED displays, inkjet printing, and solder droplet printing, among others. For example, droplet contact lines, which are typically circular on a smooth and homogeneous surface, when deposited on a microdecorated surface may take various common polygonal shapes such as squares, rectangles, hexagons, octagons and dodecagons. These polygonal contact line shapes are highly stable due to the local energy barriers associated with the anisotropy in depinning contact angles. In addition to the knowledge of the eventual contact line shapes, liquid-based printing applications would require accurate prediction of temporal evolution of contact line on these surfaces. In this work, we model and validate the evolution of droplets on microdecorated surfaces with microgoniometry experiments reported in the literature. We show that various metastable contact line shapes are formed in-between the well-known stable polygonal contact line shapes usually observed in experiments. We elucidate that the movement of the contact line between adjacent micropillars can primarily be categorized as primary zipping and transition zipping. Primary zipping occurs when the contact line moves radially outward to the next row of pillars, often resulting in the formation of a metastable contact line shape. Conversely, metastable droplet attains stable polygonal contact line shape via transition zipping wherein the contact line advances sideways. We believe that the current simulation approach can be effectively utilized for designing optimized textured surfaces for applications where control over liquid supply via surface design is required.