Time evolution of the reaction front in a subdiffusive system

TL;DR

This paper derives a formula describing how the reaction front in a subdiffusive system evolves over time, showing it follows a power law with an exponent related to the subdiffusion parameter, and confirms subdiffusion in tooth enamel through experimental data.

Contribution

It provides a theoretical formula for the time evolution of the reaction front in subdiffusive systems with different reactant diffusivities, including static cases.

Findings

Reaction front scales as t^{α/2} in subdiffusive systems.

Experimental data from tooth enamel matches the subdiffusive model.

Organic acid transport in enamel is confirmed to be subdiffusive.

Abstract

Using the quasistatic approximation, we show that in a subdiffusion--reaction system the reaction front $x_{f}$ evolves in time according to the formula $x_{f} \sim t^{\alpha/2}$, with $\alpha$ being the subdiffusion parameter. The result is derived for the system where the subdiffusion coefficients of reactants differ from each other. It includes the case of one static reactant. As an application of our results, we compare the time evolution of reaction front extracted from experimental data with the theoretical formula and we find that the transport process of organic acid particles in the tooth enamel is subdiffusive.