On the Aggregation of Inertial Particles in Random Flows

TL;DR

This paper presents a criterion for particle aggregation in random flows based on the expectation of a stochastic variable, analyzed through Langevin equations in short correlation time limits.

Contribution

It introduces a new criterion for particle aggregation in turbulent flows and analyzes the stochastic differential equation governing particle behavior in the short correlation time regime.

Findings

Aggregation criterion based on negative expectation value

Analysis of stochastic differential equation in Langevin form

Conditions for particle clustering in random flows

Abstract

We describe a criterion for particles suspended in a randomly moving fluid to aggregate. Aggregation occurs when the expectation value of a random variable is negative. This random variable evolves under a stochastic differential equation. We analyse this equation in detail in the limit where the correlation time of the velocity field of the fluid is very short, such that the stochastic differential equation is a Langevin equation.