Partial wetting of water on ice

Is ice always covered by a thin layer of water? This question has been discussed for over 150 years. Here we show that the apparent contact angle of a droplet of water on ice increases steeply with decreasing ice temperature, from around 12 degrees near the melting point, to close to 160 degrees at <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>−</a:mo><a:msup><a:mn>100</a:mn><a:mo>∘</a:mo></a:msup><a:mi mathvariant="normal">C</a:mi></a:mrow></a:math>. This indicates that ice is never completely wetted. We quantitatively model the temperature dependence of the apparent contact angle by assuming the droplet's contact line gets pinned due to the crystallization of a thin layer of ice on the cold surface. However close to the melting temperature, where the formation of the ice layer is slowest, surface energy considerations need to be included to explain the nonzero contact angle observed in experiments.