Perturbation theory for large Stokes number particles in random velocity fields

TL;DR

This paper develops a perturbative method to analyze the behavior of large Stokes number particles in random velocity fields, focusing on concentration fluctuations and collision statistics in the inertial limit.

Contribution

It introduces a novel perturbation expansion in inverse Stokes number to study particle dynamics and clustering in incompressible random flows.

Findings

Derived a perturbative framework for large Stokes number particles.

Quantified residual concentration fluctuations and clustering effects.

Compared results with compressible flow cases.

Abstract

We derive a perturbative approach to study, in the large inertia limit, the dynamics of solid particles in a smooth, incompressible and finite-time correlated random velocity field. We carry on an expansion in powers of the inverse square root of the Stokes number, defined as the ratio of the relaxation time for the particle velocities and the correlation time of the velocity field. We describe in this limit the residual concentration fluctuations of the particle suspension, and determine the contribution to the collision statistics produced by clustering. For both concentration fluctuations and collision velocities, we analyze the differences with the compressible one-dimensional case.