Point-source inertial particle dispersion

TL;DR

This paper analytically investigates the dispersion of inertial particles emitted from a point source in the small inertia limit, deriving simplified equations for their probability density function from first principles.

Contribution

It introduces a reduced model for inertial particle dispersion by decoupling position and velocity variables in the small inertia limit, simplifying the analysis.

Findings

Derived coupled PDEs for particle dispersion in the small inertia limit.

Reduced the problem to solving two forced advection-diffusion equations.

Provided a first-principles derivation of the simplified equations.

Abstract

The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,v,t), x and v being the particle position and velocity, respectively. For finite inertia, position and velocity variables are coupled, with the result that p(x,v,t) can be determined by solving a partial differential equation in a 2d-dimensional space, d being the physical-space dimensionality. For small inertia, (x,v)-variables decouple and the determination of p(x,v,t) is reduced to solve a system of two standard forced advection-diffusion equations in the space variable x. The latter equations are derived here from first principles, i.e. from the well-known Lagrangian evolution equations for position and particle velocity.