A Damköhler number criterion for reaction-driven cracking in hydration experiments

The authors present a theoretical criterion linking the onset of reaction-driven cracking in periclase-hydration experiments to the Damköhler number $Da$ – the ratio of hydraulic to reaction time scales. The approach combines a chemohydraulic model, which predicts the evolution of periclase concentration during hydration and the associated eigenstrain gradient, with an elastic solution for tensile stresses in a cylinder subjected to eigenstrain loading. The analysis shows that the maximum eigenstrain gradient increases with $Da$ and that cracking occurs only when the zone undergoing active hydration remains thin compared to the core radius. These conditions yield a critical Damköhler number of order unity, broadly consistent with experimental observations. This work provides the mechanistic link between reaction kinetics, fluid transport, and fracture initiation in reactive porous media, leading to a framework to assess the conditions under which self-sustaining cracking can be generated in mineral hydration experiments.