Grand-potential-based phase-field model of dissolution/precipitation: lattice Boltzmann simulations of counter term effect on porous medium

Most of the lattice Boltzmann methods simulate an approximation of the sharp interface problem of dissolution and precipitation. In such studies the curvature-driven motion of interface is neglected in the Gibbs-Thomson condition. In order to simulate those phenomena with or without curvature-driven motion, we propose a phase-field model which is derived from a thermodynamic functional of grand-potential. Compared to the well-known free energy, the main advantage of the grand-potential is to provide a theoretical framework which is consistent with the equilibrium properties such as the equality of chemical potentials. The model is composed of one equation for the phase-field {\phi} coupled with one equation for the chemical potential {\mu}. In the phase-field method, the curvature-driven motion is always contained in the phase-field equation. For canceling it, a counter term must be added in the {\phi}-equation. For reason of mass conservation, the {\mu}-equation is written with a mixed formulation which involves the composition c and the chemical potential. The closure relationship between c and {\mu} is derived by assuming quadratic free energies of bulk phases. The anti-trapping current is also considered in the composition equation for simulations with null diffusion in solid. The lattice Boltzmann schemes are implemented in LBM_saclay, a numerical code running on various High Performance Computing architectures. Validations are carried out with several analytical solutions representative of dissolution and precipitation. Simulations with or without counter term are compared on the shape of porous medium characterized by microtomography. The computations have run on a single GPU-V100.