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

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 $p_c^{max}=0.95 \pm 0.02$.