Sphere Passing Through Corn Syrup

Roberto Camassa
Claudia Falcon
Richard M. McLaughlin
Nicholas Mykins
University of North Carolina

Roberto Camassa,
Applied Mathematics, University of North Carolina at Chapel Hill.

Claudia Falcon
University of North Carolina at Chapel Hill.

Joyce Lin (jtlin@email.unc.edu)
Applied Mathematics, University of North Carolina at Chapel Hill.

Richard M. McLaughlin,
Applied Mathematics, University of North Carolina at Chapel Hill,

Nicholas Mykins,
University of North Carolina at Chapel Hill

Overlaid images of a sphere entraining dyed corn syrup as it passes through the density transition in a strong, stable stratification of miscible fluids. At low Reynolds, the sphere can been seen to slow down beyond the terminal velocity of the bottom denser fluid and the stem of the entrainment persists to long lengths.

A montage at 10-second intervals of a sphere falling through a strongly stratified, two layer corn syrup medium. The top layer of the corn syrup is dyed green, and less dense than the bottom layer, which is a homogeneous mixture of corn syrup and salt. Notice the entrained fluid from the top layer that is dragged with the sphere into the bottom layer and the persistence of the green stem at long lengths. The positions of the sphere centers do not lie on a straight line, an indication of the departure of the sphere’s velocity from its terminal velocity value as it moves through the density jump and slows down.

Overlaid pictures at 10-second intervals of a sphere falling through a strongly stratified, two layer corn syrup medium. The top layer of the corn syrup is dyed green, and less dense than the bottom layer, which is a homogeneous mixture of corn syrup and salt. Notice the entrained fluid from the top layer that is dragged with the sphere into the bottom layer and the persistence of the stem at long lengths. Also notice that the distance between the spheres increases with time, an indication that the sphere slows down as it passes through the density jump.

This work was funded by NSF RTG DMS-0502266 and UNC College of Arts and Sciences

Publication: Camassa, R., Falcon, C., Lin, J., McLaughlin, R. M. & Parker, R. Prolonged residence times for particles settling through stratified fluids. [manuscript in preparation]