Reacting particles in open chaotic flows

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.