ORIENTATION DYNAMICS AND STRETCHING OF PARTICLES IN UNSTEADY, 3-DIMENSIONAL FLUID-FLOWS - UNSTEADY ATTRACTORS

Recent studies of the nonlinear dynamics of deformable particles suspe nded in fluid flows have revealed a rich geometric structure. However, an analytic expression of the flow characteristic of principal intere st in the dynamics of polymer solutions, namely the stretching power o f the flow over deformable particles, has remained elusive when the hi story of particle orientations is complicated. This is the case, for e xample, when the orientation dynamics of particles is characterized by an unsteady attractor. This dynamical behavior is considered in some detail, both in steady and in time-periodic external flows. Strong flo w criteria are developed by consideration of the statistical distribut ion of orientations in time on the relevant unsteady attractor.