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Suspension properties at finite Reynolds number from simulated shear flow
This work examines the role of particle-scale inertia in a monodisperse suspension of non-Brownian and neutrally buoyant spherical particles subjected to simple-shear flow. The dimensionless parameter...

A weakly nonlocal anisotropic fluid model for inhomogeneous Stokesian suspensions

Phys. Fluids 20, 040601 (2008); doi:10.1063/1.2911011

Published 30 April 2008

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J. D. Goddard
Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0411, USA
A continuum model is proposed for a weakly inhomogeneous Stokesian suspensions, as an extension with minor amendments of a previous work on homogeneous suspensions [J. D. Goddard, J. Fluid Mech. 568, 1 (2006)]. In the present model, stress and particle flux are given as invariant tensor functions of particle volume fraction phi, deformation rate E, and second-rank anisotropy tensor A, in a form that is also linear in E and the gradients of phi, E, and A. In contrast to models without history dependence, all nonlinear dependence of particle flux on E arises from the evolution of A. Detailed attention is paid to unsteady viscometric flow, where a contribution of streamline curvature to particle migration emerges as a natural consequence of tensorial gradients. The model predicts equal curvature-induced fluxes in gradient and vorticity directions but there is an unexplained disagreement with recent experiments on Couette and torsional flows. A previously proposed corotational evolution equation for A, with a two-mode exponential relaxation, is employed to investigate the transient response following the reversal of shearing in sinusoidal and in steady shear. The model predicts roughly equal response for the two flows if sinusoidal strains are of order unity, which is consistent with some but not all experiments. The model for particle flux admits an asymmetric diffusion tensor which, owing to Stokesian reversibility, can become nonpositive upon abrupt reversal of shearing. This effect is diminished by non-Stokesian response on short strain scales, which, although poorly understood, appears essential to elementary models without dependence on shear history. A synthesis is given of multipolar Stokesian resistance and the associated Stokesian dynamics, showing how these follow from a single grand resistance kernel. In addition to unifying and extending large literature on Stokesian resistance formulae, this provides some justification for the proposed continuum model and possible multipolar extensions. ©2008 American Institute of Physics
History: Received 17 August 2007; accepted 16 December 2007; published 30 April 2008
Permalink: http://link.aip.org/link/?PHFLE6/20/040601/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.57.eb
    Diffusion and aggregation in suspensions (fluid dynamics)
  • 47.11.-j
    Computational methods in fluid dynamics
  • 47.20.Ft
    Instability of shear flows
  • 47.15.Fe
    Stability of laminar flows
  • 47.20.Qr
    Centrifugal flow instabilities
  • 83.50.Ax
    Steady shear flows, viscometric flow
  • YEAR: 2008

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PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
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REFERENCES (40)
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