SETTLING AND ASYMPTOTIC MOTION OF AEROSOL-PARTICLES IN A CELLULAR-FLOW FIELD

This paper presents a proof that given a dilute concentration of aeros ol particles in an infinite, periodic, cellular flow field, arbitraril y small inertial effects are sufficient to induce almost all particles to settle. It is shown that when inertia is taken as a small paramete r, the equations of particle motion admit a slow manifold that is glob ally attracting. The proof proceeds by analyzing the motion on this sl ow manifold, wherein the flow is a small perturbation of the equation governing the motion of fluid particles. The perturbation is supplied by the inertia, which here occurs as a regular parameter. Further, it is shown that settling particles approach a finite number of attractin g periodic paths. The structure of the set of attracting paths, includ ing the nature of possible bifurcations of these paths and the resulti ng stability changes, is examined via a symmetric one-dimensional map derived from the flow.