The macroscopic contact angle of water on ice
Wettability quantifies the affinity of a liquid over a substrate, and determines whether the surface is repellent or not. When both the liquid and the solid phases are made of the same chemical substance and are at thermal equilibrium, complete wetting is expected in principle, as observed for instance with drops of molten metals spreading on their solid counterparts. However, this is not the case for water on ice. Although there is a growing consensus on the partial wetting of water on ice and several estimates available for the value of the associated contact angle, the question of whether these values correspond to the equilibrium angle without thermal effects is still open. In the present paper, we address this issue experimentally and demonstrate the existence of a macroscopic contact angle of water on ice using theoretical arguments. Indeed, when depositing water droplets on smooth ice layers with accurately controlled surface temperatures, we observe that spreading is unaffected by thermal effects and phase change close enough to the melting point. Whereas the short time \C{motion of the contact line} is driven by an inertial-capillary balance, the evolution towards equilibrium is described by a viscous-capillary dynamics and is therefore capillary - and not thermally - related. Moreover, we show that this contact angle remains constant for undercoolings below 1 K. This way, we show the existence of a non-zero equilibrium contact angle of water on ice, that it is very close to 12$^\circ$. We anticipate this key finding to significantly improve the understanding of capillary flows in the presence of phase change, which is especially useful in the context of ice morphogenesis and of glaciology, but also in the aim of developing numerical methods for resolving triple-line dynamics.