Direct numerical simulations of the Br⁻ diffusion through the silica-gel-filled capillaries described in Section 2.1 were conducted using the Lattice Boltzmann (LB) method, a computational fluid dynamics (CFD) technique that has become increasingly popular for simulating both single and multi-phase fluid transport in the past three decades . This method, stemming from the Boltzmann equation, models the fluid behavior based on kinetic theory of gases by considering particle velocity distribution functions . The multi-component LB model, integrating a primary fluid medium with several passive scalar particle populations, can effectively simulate ion diffusion. This approach approximates the Navier-Stokes (N-S) equations at the macroscopic level, providing a detailed understanding of fluid dynamics and diffusion processes . The selection of LBM is well-suited for this study, as it effectively handles diffusion processes and provides a robust framework for future studies of reactive transport, including crystal dissolution and precipitation. This adaptability supports the rationale for using LBM, allowing for a seamless transition to more chemically reactive systems. However, the physical solver is just one modular component of the proposed framework and can be replaced with other types of solvers as needed.