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On the rotation of porous ellipsoids in simple shear flows

Published online by Cambridge University Press:  26 September 2013

Hassan Masoud ,
Howard A. Stone  and
Michael J. Shelley
Hassan Masoud*
Affiliation:
Applied Mathematics Laboratory, Courant Institute of Mathematical Sciences, New York University, NY 10012, USA Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Howard A. Stone
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Michael J. Shelley
Affiliation:
Applied Mathematics Laboratory, Courant Institute of Mathematical Sciences, New York University, NY 10012, USA
*
†Email address for correspondence: hmasoud@princeton.edu
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Abstract

We study theoretically the dynamics of porous ellipsoids rotating in simple shear flows. We use the Brinkman–Debye–Bueche (BDB) model to simulate flow within and through particles and solve the coupled Stokes–BDB equations to calculate the overall flow field and the rotation rate of porous ellipsoids. Our results show that the permeability has little effect on the rotational behaviour of particles, and that Jeffery’s prediction of the angular velocity of impermeable ellipsoids in simple shear flows (Proc. R. Soc. Lond. A, vol. 102, 1922, pp. 161–179) remains an excellent approximation, if not an exact one, for porous ellipsoids. Employing an appropriate scaling, we also present approximate expressions for the torque exerted on ellipses and spheroids rotating in a quiescent fluid. Our findings can serve as the basis for developing a suspension theory for non-spherical porous particles, or for understanding the orientational diffusion of permeable ellipses and spheroids.

JFM classification

Low-Reynolds-number flows: Porous media Non-Newtonian Flows: Rheology Complex Fluids: Suspensions
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 733 , 25 October 2013 , R6
Copyright
©2013 Cambridge University Press 

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