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Inertial particles are often observed to be trapped, temporarily orpermanently, by recirculation cells which are ubiquitous in natural orindustrial flows. In the limit of small particle inertia, determining theconditions of trapping is a challenging task, as it requires a large number ofnumerical simulations or experiments to test various particle sizes ordensities. Here, we investigate this phenomenon analytically and numerically inthe case of heavy particles (e.g. aerosols) at low Reynolds number, to derive atrapping criterion that can be used both in analytical and numerical velocityfields. The resulting criterion allows to predict the characteristics oftrapped particles as soon as single-phase simulations of the flow areperformed. Our analysis is valid for two-dimensional particle-laden flows inthe vertical plane, in the limit where the particle inertia, the free-fallterminal velocity, and the flow unsteadiness can be treated as perturbations.The weak unsteadiness of the flow generally induces a chaotic tangle nearheteroclinic or homoclinic cycles if any, leading to the apparent diffusion offluid elements through the boundary of the cell. The critical particle Stokesnumber Stc below which aerosols also enter and exit the cell in a complexmanner has been derived analytically, in terms of the flow characteristics. Itinvolves the non-dimensional curvature-weighted integral of the squaredvelocity of the steady fluid flow along the dividing streamline of therecirculation cell. When the flow is unsteady and St > Stc, a regular motiontakes place due to gravity and centrifugal effects, like in the steady case.Particles driven towards the interior of the cell are trapped permanently. Incontrast, when the flow is unsteady and St < Stc, particles wander in a chaoticmanner in the vicinity of the border of the cell, and can escape the cell.

Critical Stokes number for the capture of inertial particles by recirculation cells in 2D quasi-steady flows