The goal of the proposed research is to investigate the behavior of drops that partially wet surfaces under the effect of a cross-wind. The surfaces are imperfect, more like realistic surfaces. Every day applications include the motion of drops on windows, the de-icing of airplanes, chemical process equipment (e.g., in condensers), ink jet printing, and the environment (where rain drops or spray drops move on leave surfaces).
Water droplets that adhere to surfaces then run under wind or gravity are ubiquitous in nature. Prediction of droplet depinning thresholds is a problem of fundamental importance in fluid mechanics and is relevant to many other engineering problems. While theories exist in the low Reynolds number regime, the problem becomes more complex in the high-Reynolds-number regime of engineering interest due to the unsteadiness associated with boundary layer separation. The overall objective of this proposal is to gain fundamental understanding of the stability limits of a partially-wetting droplet in the high Reynolds number regime, through reduced modeling and state-of-art experimental measurement techniques. The proposed work focuses on the development of a theoretical model that captures the droplet dynamics in the presence of the separated boundary layer flow. The newly developed droplet model incorporates the effects of the external wind in a time-averaged sense to circumvent the difficulties arising from inherent unsteadiness of the flow and droplet surface oscillations. Preliminary results show that the model effectively matches the stability limits of a single droplet on a rough surface in terms of macroscopic properties and is extended to include the effect of solid protuberance. In parallel, additional development of the measurement instrument will be conducted to visualize the unsteady air flow around the droplet and to improve the performance for contact-angle measurements necessary for theoretical validation. The broader impacts of the project include outreach activities for high school science programs in Texas. The droplet problem is an attractive one for science outreach because droplet depinning is simultaneously familiar yet difficult to understand. This project will use droplets as an example that illustrates how abstractions introduced in high school math and physics can explain phenomena seen in the physical world. The PIs will invite high-school science teachers to work in the lab and to develop curriculum based on the experiment. These teachers will deliver this content to their classes and report on their experiences at a teachers' summit hosted annually at Texas A&M.
