Numerical evidence for the existence of a low-dimensional attractor and its implications in the rheology of dilute suspensions of periodically forcedslender bodies

We provide numerical evidence for the existence of a low-dimensional chaoti c attractor in the rheology of dilute suspensions of slender bodies in a si mple shear flow. The rheological parameters which characterize the stress d eformation behavior of the suspension are calculated based on appropriate a verages over the orientation vectors of the slender bodies. The system cons idered in this work, therefore, exhibits chaos in experimentally measurable averages over a large number of uncoupled chaotic oscillators. The numeric al demonstration that these parameters may evolve chaotically may thus have important consequences for both chaos theory and suspension rheology. We a lso provide plausible explanations for the existence of a low-dimensional c haotic attractor in the rheological parameters in terms of the expressions for the rheological parameters and the coupling between individually chaoti cally evolving orientations and the expressions for the rheological paramet ers. [S1063-651X(99)05712-8].