Hydrodynamic coupling and retention time of inertial spheres crossing and bouncing at density interfaces

Inertial spheres settling through sharp density interfaces can arrest, reverse direction, and resume descent, a phenomenon known as bouncing. Using synchronized particle image velocimetry and tracking in water-salt and water-glycerol stratifications, we demonstrate that bouncing is the dynamic response of a coupled sphere-fluid composite. As the sphere crosses the interface, it entrains a boundary layer of lighter fluid, creating a transient buoyant wake. We formalize this mechanism into a phenomenological dynamic model that couples the momentum of the sphere with the entrainment and detachment of the wake. Evaluating the stationary points of this system yields a criterion that classifies trajectory archetypes (smooth crossing, deep minima, and bouncing) across different fluid regimes. We identify a dual role of viscosity, which is often overlooked by density-only models: it acts kinematically to thicken the boundary layer and increase the entrained wake volume, and dynamically to alter the drag-to-weight balance. Furthermore, we describe the spatial dynamics of the crossing: inertia-dominated spheres penetrate further into the lower fluid before arresting due to a longer wake-detachment length, whereas buoyancy-dominated spheres arrest closer to the interface. Finally, we show that the retention time is governed by the buoyancy-driven detachment of the entrained film. By normalizing the measured retention times with a characteristic detachment timescale, we collapse the data from different viscosity regimes onto a single curve. These physical insights allow the prediction of trajectory archetype, deceleration depth, and retention time from bulk properties.