A hybrid model of sulphation reactions: stochastic particles in a random continuum environment

We present a hybrid stochastic-continuum model to study the sulphation of calcium carbonate and the consequent formation of gypsum, a key phenomenon driving marble deterioration. While calcium carbonate and gypsum are continuous random fields evolving according to random ordinary differential equations, the dynamics of sulfuric acid particles follow Itô-type stochastic differential equations. The particle evolution incorporates both strong repulsion between particles via the Lennard‒Jones potential and non-local interactions with the continuum environment. The particle–continuum coupling is also achieved through a chemical reaction, which is modelled as a Poisson counting process. We simulate the spatiotemporal evolution of this corrosion process using the Euler‒Maruyama algorithm with varying initial data combined with finite elements to address spatial discretization. Despite symmetric initial data, our simulations highlight an uneven progression of corrosion due to stochastic influences in the model.