The shape and dynamics of an axisymmetric pendant drop within uniform flow

Droplet shape and dynamics pose not only a canonical problem of multiphase phenomena, but also hold significant importance in various industrial applications. The theory of pendant drops is essential in engineering systems such as inkjet printing, surface cleaning, and optical tensiometry, as well as experimental techniques involving droplet-particle interactions. Despite extensive research on the hydrostatics of pendant drops under gravity, the influence of outer flow disturbances remains poorly understood. This study aims to incorporate aerodynamic effects in the description of pendant drop behavior. As a simplistic approach, irrotational flow parallel to the axis of a symmetric drop is obtained by means of a distribution of singularity elements within the drop. The equilibrium shape of the drop is subsequently determined from a numerical model, wherein the flow field is coupled with the Young-Laplace equation. The model is compared with droplet images acquired from high-speed shadowgraph in a vertical wind tunnel. Results are analyzed based on relevant dimensionless numbers, and dynamic behavior including droplet deformation, instability, and oscillation are also discussed.