Unsettling Behavior: Diffusion's Role in a Sphere Settling Through Sharply Stratified Fluids

How do particles behave when settling in stratified fluids over extended periods? We delve into the long-term settling dynamics of spheres in such fluids, emphasizing the pivotal role of diffusivity in viscous-dominated regimes. Our study delineates three distinct regimes: Stokes, entrainment, and diffusion. In the Stokes regime, the predominant force results in delayed settling, while the entrainment regime is marked by an added buoyancy force that prolongs residence times at the density transition. Our key finding reveals that diffusivity is a crucial factor causing deviations from the non-diffusive model. Through the use of potassium iodide (KI), a less diffusive salt that aligns well with our model, and sodium chloride (NaCl), a more diffusive salt that exhibits significant discrepancies, we underscore the critical impact of diffusion. Theoretical and experimental comparisons highlight the essential role of diffusivity in understanding prolonged residence times.