Hydrodynamics Of Droplets In High-Reynolds-Number Flow Regimes

Abstract

Partially wetting water droplets that run on a surface under wind are ubiquitous in nature. Despite its ubiquity, predicting a droplet's response to a high speed wind flow is a complex problem of fundamental importance in fluid mechanics. From the practical standpoint, predicting droplet's behavior in this flow regime is relevant to aircraft icing, coating processes, etc. To that end, we perform laboratory experiments to investigate the dynamics of partially-wetting water droplets subject to different types of air flow in the high-Reynolds-number flow regime: a droplet in the wake of a solid hemisphere, a droplet in a stagnation-point flow, and a droplet subject to combined effects of wind and gravity. In all three problems, we implement lubrication equation to develop mathematical models In the first problem, we aim to gain fundamental understanding about a droplet's interaction with the wake of a solid object on a rough surface by conducting experiments and developing a mathematical model. Our experimental observations reveal that a droplet exhibit different behaviors in the wake of a solid hemisphere depending on its position with respect to the solid and its volume. Such behaviors include downstream depinning, upstream depinning, and splitting. We develop a simplified two-dimensional mathematical model to rationalize the limits of the upstream depinning behavior observed in the experiments. Motivated by the splitting behavior in the wake experiments, we investigate drops under a stagnation-point flow both experimentally and numerically. We find that the critical jet velocity for splitting depends on drop's volume and the jet's position with respect to the drop's centerline. We then develop a mathematical model that incorporates Prandtl boundary layer theory to find the drop's two-dimensional profile and compare it with the experiments. Finally, we develop a mathematical model to rationalize the experimental observations of Schmucker and White (2012) about a droplet under uniform wind on an inclined rough surface. We find that by applying a simple model for the separation of the airflow over the drop, we can partially explain the critical velocity for depinning. In addition, we show that by rescaling the experimental results with two modified dimensionless numbers, all experimental results collapse into a single curve.