  Inertial particles are often observed to be trapped, temporarily or
permanently, by recirculation cells which are ubiquitous in natural or
industrial flows. In the limit of small particle inertia, determining the
conditions of trapping is a challenging task, as it requires a large number of
numerical simulations or experiments to test various particle sizes or
densities. Here, we investigate this phenomenon analytically and numerically in
the case of heavy particles (e.g. aerosols) at low Reynolds number, to derive a
trapping criterion that can be used both in analytical and numerical velocity
fields. The resulting criterion allows to predict the characteristics of
trapped particles as soon as single-phase simulations of the flow are
performed. Our analysis is valid for two-dimensional particle-laden flows in
the vertical plane, in the limit where the particle inertia, the free-fall
terminal velocity, and the flow unsteadiness can be treated as perturbations.
The weak unsteadiness of the flow generally induces a chaotic tangle near
heteroclinic or homoclinic cycles if any, leading to the apparent diffusion of
fluid elements through the boundary of the cell. The critical particle Stokes
number Stc below which aerosols also enter and exit the cell in a complex
manner has been derived analytically, in terms of the flow characteristics. It
involves the non-dimensional curvature-weighted integral of the squared
velocity of the steady fluid flow along the dividing streamline of the
recirculation cell. When the flow is unsteady and St > Stc, a regular motion
takes place due to gravity and centrifugal effects, like in the steady case.
Particles driven towards the interior of the cell are trapped permanently. In
contrast, when the flow is unsteady and St < Stc, particles wander in a chaotic
manner in the vicinity of the border of the cell, and can escape the cell.
