Pattern formation in recirculating flows of suspensions of orientable particles

Abstract

The global, dynamical behaviour of suspensions of small, orientable, non-interacting particles is investigated. Owing to spatial inhomogeneity of the flow field, certain orientations of particles may be favoured in different regions of the flow. Favoured orientations may be deduced from an analysis of the history of flows experienced by a particle along its path. In flows that are time-periodic in the lagrangian frame of the suspended phase (e.g. steady, recirculating flows in the eulerian frame), the orientation dynamics may be characterized by periodic or quasi-periodic attractors. After the decay of initial transients, such attractors lead to the formation of patterns of orientation of the suspended particles that are temporally fixed but spatially varying in the eulerian frame of reference. In effect, these patterns constitute a new type of global ordering of the suspension that arises not from interaction effects among the particles, but rather from the smoothly varying influences of the flow. Examples of these flow-induced patterns are explored in two- and three-dimensional flows that may be produced in the laboratory. The arguments presented are purely kinematical; as such the conclusions regarding pattern formation pertain to steady, recirculating flows whether or not the particles have an effect on the flow field. As the phenomena described herein have not been previously reported as experimental observations, this work constitutes a theoretical prediction of a new physical phenomenon.