Plumes in kinetic transport: how the simple random walk can be too simple

TL;DR

This paper investigates a discrete particle model for kinetic transport on a 2D lattice, revealing unexpected phenomena with simple random walk dispersion and providing solutions for plume shape characterization.

Contribution

It identifies issues with simple random walk dispersion in kinetic transport models and offers explicit formulas for the plume shape, advancing understanding of particle dispersion behavior.

Findings

Strange phenomena occur with simple random walk dispersion.

Explicit expressions for plume shape are derived.

Resolution of issues with random walk dispersion in kinetic models.

Abstract

We consider a discrete time particle model for kinetic transport on the two dimensional integer lattice. The particle can move due to advection in the $x$-direction and due to dispersion. This happens when the particle is free, but it can also be adsorbed and then does not move. When the dispersion of the particle is modeled by simple random walk, strange phenomena occur. In the second half of the paper, we resolve these problems and give expressions for the shape of the plume consisting of many particles.