Crystal Precipitation and Dissolution in a Thin Strip∗

A two-dimensional micro-scale model for crystal dissolution and precipitation in a porous medium is presented. The local geometry of the pore is represented as a thin strip. The model allows for changes in the pore volume. A formal limiting argument leads to a system of 1D effective upscaled equations. The effective equations allow for travelling wave solutions. Existence and uniqueness of these travelling wave solutions are proven. Numerical solutions of the effective equations are compared with numerical solutions of the original equations on the thin strip and with analytical results. Also a comparison is made with a model from the literature that does not allow changes in the pore volume.