Chemical and biological activity in three-dimensional flows

Reacting particles in open chaotic flows

We study the collision probability p of particles advected by open flows with chaotic advection. We show that p scales with the particle size (or, alternatively, reaction distance) δ 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 they are found to agree very well.

Are the fractal skeletons the explanation for the narrowing of arteries due to cell trapping in a disturbed blood flow?

We show that common circulatory diseases, such as stenoses and aneurysms, generate chaotic advection of blood particles. This phenomenon has major consequences on the way the biochemical particles behave. Chaotic advection leads to a peculiar filamentary particle distribution, which in turn creates a favorable environment for particle reactions. Furthermore, we argue that the enhanced stretching dynamics induced by chaos can lead to the activation of platelets, particles involved in the thrombus formation. In particular, we vary the size of both stenoses and aneurysms, and model them under resting and exercising conditions. We show that the filamentary particle distribution, governed by the fractal skeleton, depends on the size of the vessel wall irregularity, and investigate how it varies under resting or exercising conditions.