Reacting particles in open chaotic flows

TL;DR

This paper investigates how collision probabilities and reaction rates of particles in open chaotic flows scale with particle size, revealing a fractal dimension dependence validated by simulations.

Contribution

It introduces a power-law scaling law for collision probability and reaction rate based on fractal dimensions of invariant sets in chaotic advection.

Findings

Collision probability scales as a power law with particle size.

Reaction rates in low-density regimes follow the same scaling law.

Numerical simulations agree well with theoretical predictions.

Abstract

We study the collision probability $p$ of particles advected by open flows displaying chaotic advection. We show that $p$ scales with the particle size $\delta$ as a power law whose coefficient is determined by the fractal dimensions of the invariant sets defined by the advection dynamics. We also argue that this same scaling also holds for the reaction rate of active particles in the low-density regime. These analytical results are compared to numerical simulations, and we find very good agreement with the theoretical predictions.