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

TL;DR

This paper develops an analytical framework to study the dispersion of inertial particles from a point source in incompressible flows, accounting for small density differences and finite inertia, extending beyond the tracer limit.

Contribution

It introduces a perturbative method to analyze inertial particle dispersion, deriving solvable advection-diffusion-reaction equations that include finite inertia effects.

Findings

Provides a chain of equations for particle distribution evolution

Enables numerical solutions for finite inertia cases

Extends analysis beyond the quasi-tracer limit

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 as 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.