Strong Flows of Dilute Suspensions of Microstructure Andrew J

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Strong flows of dilute suspensions of microstructure Andrew J. Szeri* Department of MechanicaI and Environmentat Engineering, University of California, Santa Barbara, Calljrrnia 93 IO6 Stephen Wiggins Applied Mechanics, California Institute of Technology, Pasadena, Cal@rnia 91125 and Center for Nonlinear Studies, Los Alamos National Laboratory, Las Alamos, New Mexico 87545 L. Gary Lea1 Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, California 93106 (Received 28 August 1990) We consider dilute suspensions that have a microstructure that may be characterized by an axial state vector. Examples include axisymmetric particles, line elements of the fluid itself, or, as an approximation, droplets of fluid or polymer molecules. Past studies, in which sufficient conditions for stretch or coherent orientation of the microstructure are obtained for steady flows with homogeneous velocity gradient. tensors are shown not to apply to the general situation. Instead, a careful analysis of the microdynamical equations reveals that stretching and orientation of the microstructure by the flow must be analyzed over a time interval. Using techniques from the theory of dynamical systems, a quantitative measure is developed to determine orientations and/or stretched lengths of the microstructure, that are robust and attractive to nearby states. This leads to a strongJlow criterion for unsteady flows with inhomogeneous velocity gradient tensors in which the effects of history dependence are apparent. A particular model system is treated in the case of general two-dimensional flow. The sensitivity of the results to changes in the modeling assumptions is investigated. 1438 Phys. Fluids A 3 (5), May 1991 0899-8213/91/051438-01$02.00 @ 1991 American Institute of Physics 1438 Downloaded 02 Apr 2006 to 131.215.240.9. Redistribution subject to AIP license or copyright, see http://pof.aip.org/pof/copyright.jsp.

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