Abstract
We elucidate the origin of the critical Stokes number
$\mathrm{St}_\mathrm{c}$ for inertial particle capture by obstacles in flow
fields, and explain the empirical observation made by Araujo et al. [Phys. Rev.
Lett. 97, 138001 (2006)] that the capture efficiency grows as
$(\mathrm{St}-\mathrm{St}_\mathrm{c})^\beta$ with $\beta=1/2$ for some critical
Stokes number. This behaviour, which is inaccessible to classic perturbation
theory, derives from the global structure of the phase space of particle
trajectories from which viewpoint it is both generic and inevitable except in
the limit of highly singular stagnation point flows which we example. In the
context of airborne disease transmission, the phenomenon underlies the sharp
decline in filtration efficiency of face coverings for micron-sized aerosol
droplets.