Morphology of ice structures induced by a freezing rivulet

Abstract

We investigate the solidification of a water rivulet flowing over a cold inclined substrate and the resulting formation of three-dimensional ice structures. Using a controlled hydraulic and thermal setup, combined with spatiotemporal phase-shifting profilometry and infrared thermography, we characterize both the transient evolution and the final morphology of the ice. We show that a typical experiment proceeds through three stages: formation of a straight ice ridge that stabilizes the rivulet, destabilization and lateral excursions of the flow leading to rapid transverse spreading of the ice structure, and progressive thickening and smoothing of the ice block. Across a wide range of flow rates, inclinations and thermal conditions, the final morphology comprises an upstream triangular lateral envelope, followed by a downstream region of nearly constant width once the substrate edges are reached. Infrared measurements reveal that the rivulet residence time on the substrate follows a Gaussian distribution in the azimuthal angle, implying that the central region of the structure is visited far more frequently than its lateral edges. Focusing on the domain where the height has converged at the end of the experiments, we develop a two-dimensional theoretical model that couples a hydrodynamic model for the rivulet geometry with heat transport in both liquid and solid phases. In the large Péclet number limit, the model predicts an exponential increase of the stationary ice height along the flow direction and it shows an excellent agreement with the experimental height field. We further show how the combination of the stationary height profile and the non-uniform residence time distribution controls the angular convergence of the ice cross-sections.