The Flow Structure and Dynamics of Unsteady Particle Sedimentation*

Particles in fluid flows, such as plankton in the ocean, droplets in clouds, and suspended particulate matter in the atmosphere, are ubiquitous. Understanding their behavior is crucial for understanding large-scale geophysical processes. Both theoretical analyses and experimental studies underscore the significance of the history forces in the sedimentation of spherical particles within the unsteady Stokes flow regime. In this work, we focus on the unsteady flow structures generated by these particles. We employ particle image velocimetry to investigate these flow structures through a series of controlled experiments. During the initial sedimentation stages, a vortex emerges near the particle, representing a cross-sectional view of a three-dimensional vortex ring. As sedimentation progresses, the vortex core shifts away from the particle. Increasing the particle diameter induces larger inertial effects, altering the flow structure. We model these experimental observations using newly derived theoretical unsteady stream functions. Furthermore, we experiment with the simultaneous sedimentation of two spheres, varying their separation distance and characterizing the interactions between the particles within the flow field.