Veins are common in Earth's crust, and are formed by a wide range of processes, which lead to crystal growth in dilation sites. The first-order processes in vein formation have been identified, but it is much less clear how these can be diagnosed from field studies. In order to better understand the microstructural evolution during vein growth, we grew veins of analogue material [alum, KAl(SO4)2·12H2O] in a transmitted-light cell from an advecting supersaturated fluid. Real-time observation shows the effects of flow rate and supersaturation on the evolving microstructure: (1) along-vein trends in growth rate caused by decreasing supersaturation, and (2) growth competition between clear crystals in the absence of nucleation and primary fluid inclusions. Although the overall trends in growth rate are in agreement with previous work, the local effects at the scale of individual grains reported here are less well understood; these new data form a basis for better interpretation of natural microstructures. To explore the possible effects of experimentally observed processes during vein growth, we simulate the growth kinetics of a quartz vein at various conditions of advective flow in Earth's crust. Results show that in general the along-vein changes in growth rate occur at length scales much larger than a typical outcrop.