A two-dimensional model of a rotational flow field is used to perform the stability 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 effects of Basset history force on the motion of particles lighter than the fluid (bubbles) are evaluated by means of a comparison with
the analytical results found in the case of Stokes drag. Specifically, in the case of bubbles, the vortex centres are stable (attractive) points, so the motion is dominated
by the stability properties of these points. A typical convergence time scale towards the vortex centre is defined and studied as a function of the Stokes number St and the density ratio γ. The convergence time scale shows a minimum (nearly, in the range 0.1 < St < 1), in the case either with or without the Basset term. In the considered range of parameters, the Basset force modifies the convergence time scale without altering the qualitative 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 case, 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 regimes of motion (diffusive or
ballistic) are related to the stability properties of the vortex vertices. The criterion found in this way is in agreement with the results of previous authors (see, e.g.,
Wang et al. (Phys. Fluids, 4 (1992) 1789))
