When water flows over a cold surface or in a cold environment, a complex coupling arises between ice formation and the flow itself. 
At the millimeter scale, free-surface flows are particularly sensitive to what happens at the triple line (where the solid substrate, liquid, and gas phases coexist). The question of how this contact line behaves during solidification is therefore crucial to understanding the changes in flows subjected to phase change.
I will discuss the results we obtained when a thin stream of water flows over a very cold plate. A small wall of ice forms with a characteristic shape that we are able to predict quantitatively. After a certain amount of time, the flow becomes unstable and takes another path. This continues until, after 18 hours, a complex three-dimensional structure is formed. An in-depth study of this structure has enabled us to highlight the importance of heat exchange and identify a final stationary structure.
These results can serve as a basis for understanding the formation of ice structures through runoff in natural conditions (stalactites, ice falls) as well as artificial conditions (wing icing).