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Inhomogeneous distribution of a rigid fibre undergoing rectilinear flow between parallel walls at high Péclet numbers

Published online by Cambridge University Press:  10 July 2009

JOONTAEK PARK  and
JASON E. BUTLER
JOONTAEK PARK
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
JASON E. BUTLER*
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
*
†Email address for correspondence: [email protected]
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Abstract

We use slender-body theory to simulate a rigid fibre within simple shear flow and parabolic flow at zero Reynolds number and high Péclet numbers (weak Brownian motion). Hydrodynamic interactions of bulk fibres with the bounding walls are included using previously developed methods (Harlen, Sundararajakumar & Koch, J. Fluid Mech., vol. 388, 1999, pp. 355–388; Butler & Shaqfeh, J. Fluid Mech., vol. 468, 2002, pp. 205–237). We also extend a previous analytic theory (Park, Bricker & Butler, Phys. Rev. E, vol. 76, 2007, 04081) predicting the centre-of-mass distribution of rigid fibre suspensions undergoing rectilinear flow near a wall to compare the steady and transient distributions. The distributions obtained by the simulation and theory are in good agreement at sufficiently high shear rates, validating approximations made in the theory which predicts a net migration of the rigid fibres away from the walls due to a hydrodynamic lift force. The effect of the inhomogeneous distribution on the effective stress is also investigated.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 630 , 10 July 2009 , pp. 267 - 298
Copyright
Copyright © Cambridge University Press 2009

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