Reaction-diffusion on metric graphs and conversion probability

TL;DR

This paper models irreversible diffusion-reaction processes on metric graphs to predict fractional conversion based on diffusion and geometric properties, providing explicit formulas for thin-tube networks.

Contribution

It introduces a stochastic model for diffusion-reaction on metric graphs and derives explicit formulas for fractional conversion in thin-tube reactor networks.

Findings

Explicit formulas for fractional conversion in thin-tube networks

Stochastic model linking diffusion, geometry, and reaction

Application to heterogeneous catalysis scenarios

Abstract

Motivated by a problem in heterogeneous catalysis, we study a model for irreversible first-order reactions in which gas transport occurs only by diffusion, and reaction occurs only at a small number of well-localized sites. The main problem is to determine fractional conversion in terms of the diffusion coefficient and geometric properties of the reactor. We formulate an appropriate stochastic model for this problem, and then show that, when the domain is composed of a network of thin tubes, reasonably explicit formulas can be obtained.