Dynamics of a partially wetting droplet under wind and gravity

Partially wetting drops are ubiquitous in nature and industry and are often subject to a combined forcing by wind and gravity. In particular, the stability of water drops under the combination of wind and other external forces is relevant in numerous applications that include aircraft de-icing, heat exchangers, and fuel cells. In this paper, we investigate the onset of droplet depinning from a solid substrate when a partially wetting water droplet is simultaneously exposed to high-Reynolds-number airflow and to gravity. We first develop simple scaling arguments which explain that the critical flow velocity for depinning, Ucr, and the droplet volume, V, scale as Ucr∼V-1/6 in the absence of gravitational effects, in good agreement with the existing experimental data. We then develop a two-dimensional model for a unidirectional flow over a slender drop under two scenarios: aligned with (downwind) or opposing the gravitational body force (upwind). Our results show a clear deviation in Ucr between the upwind and downwind cases as the droplet size is increased. The differences between these two regimes are further manifested in the distinct droplet shapes at the critical onset of depinning. Finally, we investigate the role of flow separation from the leeward side of the drop by systematically increasing the slope of the droplet surface at the separation point. Our results point to more pronounced effects of the flow separation in the upwind regime.