In this work, a diffuse-interface lattice Boltzmann method (DI-LBM) is proposed for the dissolution through nonlinear heterogeneous reaction. In this method, the sharp boundary between the fluid and solid phases is replaced by a diffuse interface with the nonzero thickness. To describe the changes of physical variables from the fluid region to solid region, a smooth function φ is introduced, and simultaneously, the nonlinear Robin boundary condition imposed on the fluid-solid interface is reformulated as a source term into the modifed convection-diffusion equation. We then test the DI-LBM through several benchmark problems, and find that the numerical results are in agreement with the analytical solutions and available data. Finally, the present DI-LBM is adopted to study the dissolution in a two-dimensional porous medium, and the results show that with the decrease of reaction order, the reactant in the central region with a large fluid velocity reacts and faster forms a conical pathway.

Lattice Boltzmann simulation