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Most of the lattice Boltzmann methods simulate an approximation of the sharpinterface problem of dissolution and precipitation. In such studies thecurvature-driven motion of interface is neglected in the Gibbs-Thomsoncondition. In order to simulate those phenomena with or withoutcurvature-driven motion, we propose a phase-field model which is derived from athermodynamic functional of grand-potential. Compared to the free energy, themain advantage of the grand-potential is to provide a theoretical frameworkwhich is consistent with the equilibrium properties such as the equality ofchemical potentials. The model is composed of one equation for the phase-field{\phi} coupled with one equation for the chemical potential {\mu}. In thephase-field method, the curvature-driven motion is always contained in thephase-field equation. For canceling it, a counter term must be added in the{\phi}-equation. For reason of mass conservation, the {\mu}-equation is writtenwith a mixed formulation which involves the composition c and the chemicalpotential. The closure relationship between c and {\mu} is derived by assumingquadratic free energies of bulk phases. The anti-trapping current is alsoconsidered in the composition equation for simulations with null soliddiffusion. The lattice Boltzmann schemes are implemented in LBM_saclay, anumerical code running on various High Performance Computing architectures.Validations are carried out with analytical solutions representative ofdissolution and precipitation. Simulations with or without counter term arecompared on the shape of porous medium characterized by microtomography. Thecomputations have run on a single GPU-V100.

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