Dissolution and precipitation processes control fundamental properties of porous media in the subsurface such as porosity and permeability thus affecting ground water flow and solute transport. These processes occur at different time and length scales, and are often not easily captured by a single macroscopic continuum scale reactive transport model. Precipitation of even small amounts of solid phases along the major transport pathways may result in substantial change of rock permeability. A mechanistic description of these processes in the pore space is therefore a prerequisite. In order to bridge atomistic and macroscopic scales, it is necessary to understand the processes and subsequently to upscale the pore-scale results to macroscopic simulation codes. In this direction, we develop a methodology combining a sophisticated microfluidic experimental setup and multiscale modelling numerical diagnostics. This allows exploring the processes of mass transport coupled to nucleation, mineral precipitation and dissolution in confined space. For this purpose, a system with relatively few chemical species, but with well-defined kinetic parameters was chosen. As a result of the advective and diffusive mixing of solutions of Sr²⁺ and SO₄^2- ions, celestine precipitated inside the microfluidic chambers. The reactions inside the microfluidic experiment were marked by 4 stages: the induction period, the crystal growth, the clogging which prevented the mixing of the reactant solutions, and finally the dissolution of celestine crystals. The growth and dissolution rates of celestine inside the chambers were found to be in good agreement with literature data obtained in bulk experiments. The pore scale modelling of the processes inside the microfluidic reactor was based on the Lattice Boltzmann method and was used to spatially resolve the solution composition (not accessible experimentally), to predict the induction time, and to calculate the local saturation indices using full speciation. The information gained from the cross-scale pore-level model helped to gain insights into the underlying processes and to explain the preferential growth direction of the crystals during the experiment. The combination of microfluidic lab-on-chip experiments with complementary multiphysics numerical diagnostics is a promising methodology to provide insights into pore scale phenomena, to optimize the design of experiments and to parameterize appropriate constitutive equations for coupled processes in porous media.