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Enhanced drag of a sphere settling in a stratified fluid at small Reynolds numbers

Published online by Cambridge University Press:  27 July 2009

KING YEUNG YICK ,
CARLOS R. TORRES ,
THOMAS PEACOCK  and
ROMAN STOCKER
KING YEUNG YICK
Affiliation:
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
CARLOS R. TORRES
Affiliation:
Universidad Autónoma de Baja California, Km 107 Carretera Tijuana-Ensenada, Ensenada 22830, Baja California, México
THOMAS PEACOCK
Affiliation:
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
ROMAN STOCKER*
Affiliation:
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
*
†Email address for correspondence: romans@mit.edu
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Abstract

We present a combined experimental and numerical investigation of a sphere settling in a linearly stratified fluid at small Reynolds numbers. Using time-lapse photography and numerical modelling, we observed and quantified an increase in drag due to stratification. For a salt stratification, the normalized added drag coefficient scales as Ri0.51, where Ri = a3N2/(νU) is the viscous Richardson number, a the particle radius, U its speed, ν the kinematic fluid viscosity and N the buoyancy frequency. Microscale synthetic schlieren revealed that a settling sphere draws lighter fluid downwards, resulting in a density wake extending tens of particle radii. Analysis of the flow and density fields shows that the added drag results from the buoyancy of the fluid in a region of size (ν/N)1/2 surrounding the sphere, while the bulk of the wake does not influence drag. A scaling argument is provided to rationalize the observations. The enhanced drag can increase settling times in natural aquatic environments, affecting retention of particles at density interfaces and vertical fluxes of organic matter.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 632 , 10 August 2009 , pp. 49 - 68
Copyright
Copyright © Cambridge University Press 2009

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