Sodium chloride crystallization induced by evaporation of aqueous solution is studied from visualization experiments in a circular capillary tube. In agreement with recent studies, the onset of crystallization is observed with a significant supersaturation. Detailed information on the precipitation kinetics and transport of ions is obtained from numerical computations of the ion mass fraction field during the evaporation process. It is shown that the precipitation kinetics is fast compared to transport so that the crystal growth is mostly controlled by the transport. This offers possibles implifications for analyzing more involved situations such as crystallization in porous media. The fact that the significant super- saturation does not lead to tube damage is explained.