J. Fluid Mech., page 1 of 25 c  Cambridge University Press 2009 doi:10.1017/S0022112009991534 1 Trapping and sedimentation of inertial particles in three-dimensional flows in a cylindrical container with exactly counter-rotating lids CRISTIAN ESCAURIAZA 1,2 AND FOTIS SOTIROPOULOS 1 † 1 St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55414, USA 2 Departamento de Ing. Hidr ´ aulica y Ambiental, Pontificia Universidad Cat´ olica de Chile, Av. Vicu˜ na Mackenna 4860, 7820436, Santiago, Chile (Received 16 January 2009; revised 5 August 2009; accepted 6 August 2009) Stirring and sedimentation of solid inertial particles in low-Reynolds-number flows has acquired great relevance in multiple environmental, industrial and microfluidic systems, but few detailed numerical studies have focused on chaotically advected experimentally realizable flows. We carry out one-way coupling simulations to study the dynamics of inertial particles in the steady three-dimensional flow in a cylindrical container with exactly counter-rotating lids, which was recently studied by Lackey & Sotiropoulos (Phys. Fluids , vol. 18, 2006, paper no. 053601). We elucidate the rich Lagrangian dynamics of the flow in the vicinity of toroidal invariant regions and show that depending on the Stokes number inertial particles could get trapped for long times in different equilibrium positions inside integrable islands. In the chaotically advected region of the flow the balance between inertia and gravity forces (represented by the settling velocity) can produce a striking fractal sedimentation regime, characterized by a sequence of discrete deposition events of seemingly random number of particles separated by hiatuses of random duration. The resulting staircase-like distribution of the time series of the number of particles in suspension is shown to be a devil’s staircase whose fractal dimension is equal to the 0.87 value found in multiple dissipative dynamical systems in nature. Our work sheds new light on the complex mechanisms governing the stirring and deposition of inertial particles and provides new information about the parameters that are relevant in the characterization of particle dynamics in different regions of chaotically advected flows. Key words: chaotic advection, particle/fluid flows, vortex flows 1. Introduction Transport and stirring processes in chaotically advected flows (Aref 1984) have been and continue to be the subject of intense research due to their profound role in determining scalar mixing in several engineering and geophysical flows. Recent experimental and computational studies have focused on two- and three-dimensional experimentally realizable flows, yielding new insights into the mechanisms via which flows that are simple from the Eulerian standpoint give rise to chaotic Lagrangian transport and efficient stirring of passive particles (e.g. King et al. 2001; Sotiropoulos, † Email address for correspondence: fotis@umn.edu