Sphere falling through stratified fluid at low Reynolds number

Advisors: Roberto Camassa and Richard M. McLaughlin

Laboratory Assistants: Claudia Falcon and Nicholas Mykins

Description of the problem
Solid body moving at low Reynolds number through a sharp, stable stratification of miscible fluids. We study the hydrodynamics of the forces in the system, including the fluid flow and the resultant behavior of the sphere.

As the sphere passes through the interface, the importance of the entrained fluid is enhanced by the buoyancy. We find that the sphere will slow down dramatically as it passes through the density transition. We develop a model from first principles of the highly coupled system to capture this effect.


Results
Our model, with no adjustable parameters, can predict the velocity field of the fluid, as well as the shape of the interface between the stratified fluids. The velocity profile, which shows this non-monotonic transition between terminal velocities of the upper layer and lower layer, can also be compared with the experimental data.