Instabilities in the dynamics of neutrally buoyant particles

The asymptotic dynamics of finite-size particles is governed by a slow manifold that is globally attracting for sufficiently small Stokes numbers. For neutrally buoyant particles suspensions , the slow dynamics coincide with that of infinitesimally small particles, therefore the suspension dynamics should synchronize with Lagrangian particle motions. Paradoxically, recent studies observe a scattering of suspension dynamics along Lagrangian particle motions. Here we resolve this paradox by proving that despite its global attractivity, the slow manifold has domains that repel nearby passing trajectories. We derive an explicit analytic expression for these unstable domains; we also obtain a necessary condition for the global attractivity of the slow manifold. We illustrate our results on neutrally buoyant particle motion in a two-dimensional model of vortex shedding behind a cylinder in crossflow and on the three-dimensional steady Arnold–Beltrami–Childress flow. © 2008 American Institute of Physics. DOI: 10.1063/1.2830328