LAUSR

Crystal dissolution and precipitation problems often originate in the fields of material sciences, chemical engineering, soil mechanics, hydrology, and other related fields. In this paper, we consider dissolution and precipitation of immobile species (minerals) on the surface of the solid parts and diffusion and reaction of mobile species in the pore space of a porous medium. The mathematical modeling of such processes leads to a system of semilinear parabolic partial differential equations coupled with a system of nonlinear ordinary differential equations, which involves multi-valued right-hand sides. The geometry under consideration here is evolving due to dissolution and precipitation on the interfaces. This moving interface problem is dealt with the help of a level set function. The pore (micro) scale model is upscaled to the macroscale by periodic homogenization and asymptotic expansion techniques.