Chemical reactions in the presence of surface modulation and stirring

TL;DR

This paper investigates how surface modulation and stirring influence chemical reaction dynamics, deriving a reaction-advection-diffusion model, and demonstrating that substrate modulation can control reaction rates, yields, and propagation speeds through numerical case studies.

Contribution

We derive a reaction-advection-diffusion model for reactions on modulated surfaces with stirring and show modulation effects are equivalent to simpler models up to second order.

Findings

Modulating the substrate alters reaction rates and yields.

Surface modulation affects front propagation speed.

Homogenization justifies using simpler reaction-diffusion models.

Abstract

We study the dynamics of simple reactions where the chemical species are confined on a general, time-modulated surface, and subjected to externally-imposed stirring. The study of these inhomogeneous effects requires a model based on a reaction-advection-diffusion equation, which we derive. We use homogenization methods to show that up to second order in a small scaling parameter, the modulation effects on the concentration field are asymptotically equivalent for systems with or without stirring. This justifies our consideration of the simpler reaction-diffusion model, where we find that by modulating the substrate, we can modify the reaction rate, the total yield from the reaction, and the speed of front propagation. These observations are confirmed in three numerical case studies involving the autocatalytic and bistable reactions on the torus and a sinusoidally-modulated substrate