Caustics in turbulent aerosols

TL;DR

This paper investigates the formation and long-term behavior of caustic patterns in turbulent aerosols, linking their morphology to Lyapunov exponents and encounter rates, and develops a theory to predict these quantities from flow statistics.

Contribution

It introduces a theoretical framework to determine caustic encounter rates and Lyapunov exponents from gas flow properties in turbulent aerosols.

Findings

Caustic patterns influence particle coagulation in turbulent flows.

The morphology of caustics is governed by Lyapunov exponents and encounter rates.

A theory is developed to predict these quantities from flow statistics.

Abstract

Networks of caustics can occur in the distribution of particles suspended in a randomly moving gas. These can facilitate coagulation of particles by bringing them into close proximity, even in cases where the trajectories do not coalesce. We show that the long-time morphology of these caustic patterns is determined by the Lyapunov exponents lambda_1, lambda_2 of the suspended particles, as well as the rate J at which particles encounter caustics. We develop a theory determining the quantities J, lambda_1, lambda_2 from the statistical properties of the gas flow, in the limit of short correlation times.