Directional self-migration of droplets on an inclined surface driven by wettability gradient

In the current study, the anti-gravity directional self-migration of droplets on an inclined surface driven by wettability gradient ( ω) was investigated using a front-tracking method. A unified mechanical model of droplet motion on an inclined wettability gradient wall was derived, considering the driving force generated by ω ( Fd), gravity ( G), and flow resistance ( Ff). The model demonstrates that ω, G, and inclination angle ( α) are key parameters affecting droplet motion. By varying ω, Bond number ( Bo), and α, the droplet dynamic characteristics were analyzed, and a real-time Capillary number ( Ca) was introduced to measure the droplet migration speed. The results indicate that a larger ω generates a greater Fd, leading to faster migration and more pronounced spreading. When the ratio of the channel width to the droplet diameter is 0.7, the droplet can cross three regions, obtaining double Fd, and Ca curve exhibits a bimodal structure. When the ratio of the channel width to the droplet diameter is 1.2, the droplet slides and spreads in the middle region without ω, resulting in a trimodal Ca curve. A larger Bo implies a stronger gravity effect, reducing the net driving force for upward migration and slowing the migration speed. At α=30° and ω=0.54, Bo reaches its critical value at 0.5, where G exceeds Fd, causing the droplet to slide downward along the wall. α affects droplet motion by controlling the gravitational component along the wall ( Gx). A larger α results in a smaller net driving force for upward migration, reducing the migration speed.