Stability analysis of solid particle motion in rotational flows

A two-dimensional model of a rotational flow field is used to perform the s tability analysis of solid particle motion. It results that the stagnation points are equilibrium points for the motion of particles and the stability analysis allows to estimate their role in the general features of particle motion and to identify different regimes of motion. Furthermore, the effec ts of Basset history force on the motion of particles lighter than the flui d (bubbles) are evaluated by means of a comparison with the analytical resu lts found in the case of Stokes drag. Specifically, in the case of bubbles, the vortex centres are stable (attractive) points, so the motion is domina ted by the stability properties of these points. A typical convergence time scale towards the vortex centre is defined and studied as a function of th e Stokes number St and the density ratio gamma. The convergence time scale shows a minimum (nearly, in the range 0.1 < St < 1), in the case either wit h or without the Basset term. In the considered range of parameters, the Ba sset force modifies the convergence time scale without altering the qualita tive features of the particle trajectory. In particular, a systematic shift of the minimum convergence time scale toward the inviscid region is noted. For particles denser than the fluid, there are no stable points. In this c ase, the stability analysis is extended to the vortex vertices. It results that the qualitative features of motion depend on the stability of both the centres and the vertices of the vortices. In particular, the different reg imes of motion (diffusive or ballistic) are related to the stability proper ties of the vortex vertices. The criterion found in this way is in agreemen t with the results of previous authors (see, e.g., Wang et al. (Phys. Fluid s, 4 (1992) 1789)).