Work

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

Year: 2026

Type: article

Abstract: 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.

Source: Applied Mathematics in Science and Engineering

DOI: 10.1080/27690911.2026.2691359

Authors: Nicklas Jävergård, Daniela Morale, Adrian Muntean, Giulia Rui, Stefania Ugolini

Institutions: Karlstad University, University of Milan

Language: English

Topic: Building materials and conservation

Subfield: Earth-Surface Processes

Field: Earth and Planetary Sciences

Domain: Physical Sciences

Open Access status: diamond

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", National Science Council, Energimyndigheten

Awards: G2148247208, G5339074417, G5456286744