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Inertial drag on a sphere settling in a stratified fluid

Published online by Cambridge University Press:  24 September 2018

R. Mehaddi ,
F. Candelier  and
B. Mehlig Open the ORCID record for B. Mehlig [Opens in a new window]
R. Mehaddi
Affiliation:
Université de Lorraine, UMR CNRS 7563, LEMTA (Laboratoire d’Énergétique et Mécanique Théorique et Appliqué), F-54500 Vandoeuvre-Les-Nancy, France
F. Candelier
Affiliation:
Université d’Aix-Marseille, UMR CNRS 7343, IUSTI (Institut Universitaire des Systèmes Thermiques et Industriels), F-13013 Marseille, France
B. Mehlig*
Affiliation:
Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden
*
†Email address for correspondence: Bernhard.Mehlig@physics.gu.se
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Abstract

We compute the drag force on a sphere settling slowly in a quiescent, linearly stratified fluid. Stratification can significantly enhance the drag experienced by the settling particle. The magnitude of this effect depends on whether fluid-density transport around the settling particle is due to diffusion, to advection by the disturbance flow caused by the particle or due to both. It therefore matters how efficiently the fluid disturbance is convected away from the particle by fluid-inertial terms. When these terms dominate, the Oseen drag force must be recovered. We compute by perturbation theory how the Oseen drag is modified by diffusion and stratification. Our results are in good agreement with recent direct numerical simulation studies of the problem.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Multiphase flow

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 1074 - 1087
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Copyright
© 2018 Cambridge University Press 

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