Eur. Phys. J. E (2019) 42: 10
https://doi.org/10.1140/epje/i2019-11771-5

Regular Article

Point-source dispersion of quasi-neutrally-buoyant inertial particles

Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal

^* e-mail: marcomartinsafonso@hotmail.it

Received: 31 March 2018
Accepted: 4 January 2019
Published online: 29 January 2019

Abstract

We analyze the evolution of the distribution, both in the phase space and in the physical space, of inertial particles released by a spatially-localized (punctual) source and advected by an incompressible flow. The difference in mass density between fluid and particles is assumed to be small, and represents the basic parameter for a regular perturbative expansion. By means of analytical techniques such as Hermitianization, we derive a chain of equations of the advection-diffusion-reaction type, easily solvable at least numerically. Our procedure provides results also for finite particle inertia, away from the over-damped limit of quasi-tracer dynamics.