Chaotic dynamics of inertial particles in three-dimensional rotating flows

Transport and mixing problems in non-turbulent flows have been studied with chaotic advection theory to understand and quantify the characteristics of the fluid particle dynamics in simple analytical flows, and new analyses have been recently extended to realistic and more complex, experimentally realizable flows. Many environmental and engineering flows have also two or more phases, but little progress has been made in understanding the properties of these flows when there are inertial particles within the fluid. The purpose of this research is to study numerically the dynamics of inertial particles in a three-dimensional flow inside a closed cylinder with exactly counter-rotating lids. The one-way coupling simulations are based on analytical models of the forces acting on the particles, and on a simple elastic collision scheme with the boundaries. The solutions show how the effect of gravity can suppress the chaotic motion observed in fluid particles due to sedimentation. Particle dynamics without gravity force is also analyzed through Lagrangian average maps and particle variance of concentration, confirming the effect of inertia that decreases mixing in the container. Additionally, from periodic orbit theory we evaluate a global average of the flow such as particle dispersion, based on the spectrum of the orbits obtained from the determinant calculated with few prime cycles of the system.