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A new computational method for the solution of flow problems of microstructured fluids. Part 2. Inhomogeneous shear flow of a suspension

Published online by Cambridge University Press:  26 April 2006

Andrew J. Szeri  and
L. Gary Leal
Andrew J. Szeri
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92717-3975, USA
L. Gary Leal
Affiliation:
Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106, USA
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Abstract

A numerical investigation is conducted into the flow of a dilute suspension of rigid rod-like particles between parallel flat plates, driven by a uniform pressure gradient. The particles are assumed to be small relative to lengthscales of the flow with the effect that particle orientations evolve according to the local velocity gradient; the particles are also assumed to be small in an absolute sense, with the consequence that Brownian motions are of consequence. The calculations are performed using a novel approach, with a theoretical basis that has been developed previously in a companion paper (Szeri & Leal 1992). The new approach permits one to solve flow problems of microstructured fluids (such as suspensions, liquid crystals, polymer solutions and melts) without ‘pre-averaging’ or closure approximations. In the present work, the new approach is used to expose previously unknown pathological, non-physical predictions in various constitutive models derived using closure approximations. This appears to have passed unnoticed in prior work. In addition, the new approach is shown to possess several computational advantages. The determination of the orientation distribution of particles is self-adaptive; this leads, in effect, to a very efficient solution of the associated Smoluchowski (or Fokker–Planck) equation. Moreover, the new approach is highly suited to parallel (and vector) implementation on modern computers. These issues are explored in detail in the context of the example flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 262 , 3 October 1994 , pp. 171 - 204
Copyright
© 1994 Cambridge University Press

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