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Microstructure suspended in three-dimensional flows

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

The dynamical behaviour of stretchable, orientable microstructure suspended in a general three-dimensional fluid flow is investigated. Model equations given by Olbricht, Rallison & Leal (1982) are examined in the case of microstructure travelling through arbitrarily complicated flows of the carrier fluid. As in the two-dimensional analysis of Szeri, Wiggins & Leal (1991), one must first treat the orientation dynamics problem; only then can the equation for stretch of the microstructure be analyzed rationally. In three-dimensional flows that are steady in the Lagrangian frame, attractors for the orientation dynamics are shown to be equilibria or limit cycles; this asymptotic behaviour was first deduced by Bretherton (1962). In three-dimensional flows that are time periodic in the Lagrangian frame (e.g. recirculating flows), the orientation dynamics may be characterized by periodic or quasi-periodic attractors. Thus, robust (generic) behaviour in these cases is always characterized by a single global attractor; there is no asymptotic dependence of orientation dynamics on the initial orientation. The type of asymptotic orientation dynamics – steady, periodic, or quasi-periodic - is signified by a simple criterion. Details of the relevant bifurcations, as well as history-dependent strong flow criteria are developed. Examples which illustrate the various types of behaviour are given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 250 , May 1993 , pp. 143 - 167
Copyright
© 1993 Cambridge University Press

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