Inertial-particle dispersion and diffusion

Abstract

We analytically investigate the dynamics of inertial particles in incompressible flows in the limit of small but finite inertia, focusing on two specific instances. First, we study the concentration of particles continuously emitted from a point source with a given exit velocity distribution. The anisotropy of the latter turns out to be a necessary factor for the presence of a correction (with respect to the corresponding tracer case) at order square root of the Stokes number. Secondly, by means of a multiple-scale expansion, we analyse the particle effective diffusivity, and in particular its dependence on Brownian diffusivity, gravity effects and particle-to-fluid density ratio. In both cases, we obtain forced advection-diffusion equations for auxiliary quantities in the physical space, thus simplifying the problem from the full phase space to a system which can easily be solved numerically.