Equilibrium shapes and dynamics of pendant drops within a uniform vertical flow

Pendant drops appear in many engineering applications, such as inkjet printing and optical tensiometry, and they have also been the subject of studies of droplet–particle interaction. While the hydrostatics of pendant drops has been studied extensively, the influence of external flow disturbances has received limited attention. This research aims to incorporate aerodynamic factors into the understanding of pendant drop behaviour. Employing a simplified model, an irrotational flow aligned with the drop’s axis is derived from a distribution of singularity elements within the drop. The drop’s equilibrium shape is then determined using a numerical model that couples the flow field with the Young–Laplace equation. The model’s predictions are compared to droplet images captured via high-speed shadowgraph in a vertical wind tunnel, showing good agreement with the experimentally observed shapes. Additionally, under certain flow conditions, the drop exhibits instability in the form of periodic pendulum-like motion. This instability was linked to two distinct critical drop heights, and the corresponding stability criterion was mathematically derived from the numerical model. Our theoretical and experimental findings provide the first quantitative description of the equilibrium shape and stability criterion of pendant drops under the influence of external flow.