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Motion of an arbitrarily shaped particle in a density stratified fluid

Published online by Cambridge University Press:  13 March 2020

Rajat Dandekar ,
Vaseem A. Shaik  and
Arezoo M. Ardekani Open the ORCID record for Arezoo M. Ardekani [Opens in a new window]
Rajat Dandekar
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 49707, USA
Vaseem A. Shaik
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 49707, USA
Arezoo M. Ardekani*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 49707, USA
*
†Email address for correspondence: [email protected]
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Abstract

In this work, we theoretically investigate the motion of an arbitrarily shaped particle in a linear density stratified fluid with weak stratification and negligible inertia. We calculate the hydrodynamic force and torque experienced by the particle using the method of matched asymptotic expansions. We analyse our results for two classes of particles (non-skew and skew) depending on whether the particle possesses a centre of hydrodynamic stress. For both classes, we derive general expressions for the modified resistance tensors in the presence of stratification. We demonstrate the application of our results by considering some specific examples of particles settling in a direction parallel to the density gradient by considering both the limits of high ($Pe\gg 1$) and low ($Pe\ll 1$) Péclet numbers. We find that presence of stratification causes a slender body to rotate and settle along the broader side due to the contribution of the hydrostatic torque. Our work sheds light on the impact of stratification on the transport of arbitrarily shaped particles in density stratified environments in low-Reynolds-number regimes.

JFM classification

Geophysical and Geological Flows: Stratified flows Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 890 , 10 May 2020 , A16
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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