Explicit formulas for reaction probability in reaction-diffusion experiments

TL;DR

This paper develops explicit formulas for reaction probability in reaction-diffusion experiments, applying them to metric graphs and 3D systems, and analyzes optimal arrangements of catalytic particles based on activity levels.

Contribution

It introduces a computational method for calculating conversion probabilities and derives explicit formulas for systems modeled by metric graphs.

Findings

Explicit formulas for conversion in metric graph systems.

Numerical validation for 3D system approximations.

Optimal particle arrangements depend on catalytic activity level.

Abstract

A computational procedure is developed for determining the conversion probability for reaction-diffusion systems in which a first-order catalytic reaction is performed over active particles. We apply this general method to systems on metric graphs, which may be viewed as 1-dimensional approximations of 3-dimensional systems, and obtain explicit formulas for conversion. We then study numerically a class of 3-dimensional systems and test how accurately they are described by model formulas obtained for metric graphs. The optimal arrangement of active particles in a 1-dimensional multiparticle system is found, which is shown to depend on the level of catalytic activity: conversion is maximized for low catalytic activity when all particles are bunched together close to the point of gas injection, and for high catalytic activity when the particles are evenly spaced.