A reaction-diffusion model for the hydration of calciumsulphate (gypsum) and microstructure percolation

TL;DR

This paper models the hydration process of gypsum using a reaction-diffusion approach, revealing microstructural features, reaction dynamics, and percolation thresholds in 2D and 3D systems.

Contribution

It introduces a novel reaction-diffusion model for gypsum hydration that captures microstructure development and identifies dual percolation thresholds in different dimensions.

Findings

Hydration rate peaks early and then declines, approaching equilibrium solubility.

Microstructures show inner/outer hydrate features, induction, and bridging.

Two percolation thresholds are identified for 2D and 3D systems.

Abstract

We have numerically investigated a reaction-diffusion model for the hydration of calciumsulphate (gypsum). The simulations were conducted for two and three dimensional systems. While the dissolution of anhydrous gypsum is considered irreversible at a finite rate the precipitation/dissolution reaction for the calciumdihydrate is considered reversible. The latter reaction is assumed to be controlled by the dihydrate's equilibrium solubility {\em and} the abillity of the system to react on supersaturation only at a certain velocity described by the reaction rate constant of precipitation. For $d=2$ we find at early times an accelerated hydration period followed by a maximum and a decreasing hydration rate. For large times the ionic product of involved species assumes closely the value of the di-hydrate equilibrium solubility. Calculated model micro-structures exhibit typical features such as inner and outer hydrate products, induction and dormant period as well as bridging. Furthermore we find that the overall chemical reactivity as a function of initial anhydrous (volume) concentration $p$ exhibits a maximum close to the percolation point of the underlying lattice. Employing a rescaling procedure we find {\em two} percolation thresholds in $d=2$, $p_c^{min}=0.44\pm 0.015$ and $p_c^{max}=0.77\pm 0.02$, for the initial anhydrous gypsum concentration {\em between} which percolating dihydrate structures can be attained. For $d=3$ we find $p_c^{min}=0.10\pm 0.02$ and $p_c^{max}=0.95 \pm 0.02$.