A sphere settling in a stratified fluid at small Reynolds number

We present a combined theoretical, experimental and numerical investigation of a sphere settling in a linearly stratified fluid at low Reynolds number (0.01 </= Re </= 2.1). We developed the microscale Synthetic Schlieren technique to study the wake of a microscale sphere settling through a density stratification. A video-microscope was used to magnify and image apparent displacements of a micron-sized random-dot pattern. Due to the nature of the wake, density gradient perturbations in the horizontal direction greatly exceed those in the vertical, requiring modification of a previously developed axisymmetric technique. We demonstrated that Schlieren could be extended to microscale (100 [mu]m) and obtained the first quantitative measurement of the density field in the wake of a sphere settling in a stratified fluid. As stratification breaks directional symmetry, the direction of motion strongly influences the dynamics, unlike in the homogeneous case. Previous work primarily focused on particles moving parallel to isopycnals. Here we investigate motion perpendicular to isopycnals. As the sphere settles, the particle draws lighter fluid downwards, generating buoyancy forces: this results in a long density wake, extending many particle diameters downstream. Using time-lapse photography, the drag on the sphere was measured and we have obtained the first experimental quantification of the added drag on a sphere due to stratification. We found that stratification increases the hydrodynamic drag, and that the added drag coefficient scales with the Richardson number Ri = a3N2/(vU) as Ri1/2, where a is the particle radius, U its speed, v the kinematic fluid viscosity and N the buoyancy frequency. These observations are confirmed by numerical simulations, and are in contrast with earlier results for higher Re.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2008

Author dc:creator

• Yick, King-Yeung, 1978-

Advisor dc:contributor.advisor

• Roman Stocker.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/45345

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/45345