May 22, 2019 | Updated: 08:18 AM EDT

Mathematical Formula Explains Why Ice Is Slippery

Dec 10, 2015 09:23 PM EST

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It is still a scientific mystery why ice, with it being a solid material, is slippery. A new mathematical model might give the answer to this surprisingly enigmatic phenomenon.

Physicist Bo Persson of Forschungszentrum Jülich in Germany published in the "Journal of Chemical Physics" some hypotheses on why ice surface is slick when it is a solid form of matter. He provides a mathematical foundation pointing out the liquid-like form of water as the culprit.

Based on the study, ice by itself is not slippery by default. It just gets slippery when thin layer of water forms on the ice's surface. Water formation is due to several reasons, it may be heat in friction with the ice or it is just "pre-melting" (solid-liquid phase transition). He could describe this phenomenon after developing a mathematical model. His equation is simple, as it only relates to shear stress. These are the internal forces than object experiences in the directions parallel to the frictional force exerted by ice, on a frigid temperature.

"It is nice to see a solid physical justification of something that we always thought was happening," said Nicolas Spencer, editor of Tribology Letters, a journal focusing on studies of friction. "It all makes perfect sense to me." The result of this study should aid winter and sports gear manufacturers in designing their products increase or minimize sliding on ice.

"Persson's paper did a good job of providing possible models that can account for the sliding friction-velocity behavior of ice," Francis Kennedy, a retired engineering professor at Dartmouth College, wrote. Below is the excerpt of his mathematical model,

..this layer could be related to surface premelting of ice or just reflect increased mobilities of ice lattice defects. Using a phenomenological expression for the frictional shear stress,

τm=τ0m(1-TTc)β,

where β ≈ 0.15, I have shown that the calculated ice friction is in good agreement with experimental observations. I am not aware of any study of the rheological properties of confined premelted ice. For the ice-vapor interface, the thickness of the premelted layer is usually (theoretically) assumed to depend logarithmically on the temperature difference Tm - T between the ice (bulk) melting temperature Tm and the ice temperature T. However, the shear stress may depend on temperature in a different way if the premelted layer has rheological properties different from the bulk water, as indeed expected because of the underlying crystalline ice structure which is expected to induce some layering and ordering penetrating into the otherwise disordered fluid-like layer.