Hostname: page-component-7479d7b7d-pfhbr Total loading time: 0 Render date: 2024-07-15T20:29:16.487Z Has data issue: false hasContentIssue false
  • English
  • Français

Rigid particles suspended in time-dependent flows: irregular versus regular motion, disorder versus order

Published online by Cambridge University Press:  26 April 2006

Andrew J. Szeri ,
W. J. Milliken  and
L. Gary Leal
Andrew J. Szeri
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92717, USA
W. J. Milliken
Affiliation:
Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106. USA Present address: Chevron Oil Field Research, 1300 Beach Blvd., La Habra, CA 90631, USA.
L. Gary Leal
Affiliation:
Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106. USA
Get access Rights & Permissions [Opens in a new window]

Abstract

An experimental and analytical investigation is conducted into the dynamics of small, non-spherical, rigid particles suspended in a flow that is time-dependent from the point of view of the particle, which may be moving. The particles are unaffected by Brownian forces. Of special interest in this study are flows that are time-periodic in the Lagrangian frame; this allows for the use of mathematical tools that have been developed for periodically forced differential equations, and for precise and well-characterized experiments. For some classes of periodic flows, it is shown that there exists a global periodic attractor for the orientation dynamics of particles that follow a given particle path, i.e. there is 1:1 phase locking of the orientation dynamics with the forcing. This is an important situation because it leads to a strong ordering of an ensemble of particles that follow the same particle path as the flow; such order has significant ramifications for stress and birefringence. In other classes of periodic flows, no such attractor exists; therefore, an ensemble of random initial orientations of the particles on a particle path will not converge and disorder is maintained. Experiments are performed using a computer-controlled four-roll mill to create well-characterized flows in which these various types of dynamical behaviour are realized.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 237 , April 1992 , pp. 33 - 56
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aref, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1–21.Google Scholar
Arnold, V. I. 1988 Geometrical Methods in the Theory of Ordinary Differential Equations. Springer.
Bentley, B. J. & Leal, L. G. 1986 A computer-controlled four-roll mill for investigations of particle and drop dynamics in two-dimensional linear shear flows. J. Fluid Mech. 167, 219–240.Google Scholar
Bretherton, F. P. 1962 The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14, 284–304.Google Scholar
Cox, R. G. 1971 The motion of long slender bodies in a viscous fluid. Part 2. Shear flow. J. Fluid Mech. 45, 625–657.Google Scholar
Guckenheimer, J. & Holmes, P. 1990 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer.
Jeffrey, G. G. 1922 The motion of ellipsoidal particles immersed in a fluid. Proc. R. Soc. Lond. A 102, 161–179.Google Scholar
Nollert, M. U. & Olbricht, W. L. 1985 Macromolecular deformation in periodic extensional flows. Rheo. Acta 24, 3–14.Google Scholar
Szeri, A. J., Wiggins, S. & Leal, L. G. 1991 On the dynamics of suspended microstructure in unsteady, spatially inhomogeneous, two-dimensional fluid flows. J. Fluid Mech. 228, 207–241.Google Scholar
Wiggins, S. 1988 Global Bifurcations and Chaos - Analytical Methods. Springer.