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

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.