Sphere falling through stratified fluid at low Reynolds number

Advisors: Roberto Camassa and Richard M. McLaughlin

Laboratory Assistants: Claudia Falcon, Anna Miller, and Nicholas Mykins

Description of the problem
Consider a 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 due to its buoyancy in the lower, denser fluid. 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, and thus 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.

For more information
1. Camassa, R., Falcon, C., Lin, J., McLaughlin, R. M. & Mykins, N., A first principle predictive theory for a sphere falling through sharply stratified fluid at low Reynolds number, J. Fluid Mech. doi: 10.1017/S0022112010003800, Published online by Cambridge University Press 12 October 2010.
2. Camassa, R., Falcon, C., Lin, J., McLaughlin, R. M. & Parker, R., Prolonged residence times for particles settling through stratified miscible fluids in the Stokes regime, Phys. Fluids 21(2009), 031702-1–4.
3. American Physical Society Virtual Press Room
4. Falling sphere experiments
5. Marine Science and Applied Math Fluids Lab

On-going research
We are currently studying the extensions of our model to linear or continuous stratifications, multibody sedimentation, and infinite fluid medium.


Work was supported by NSF RTG DMS-0502266