滑冰理论
Theory of ice-skating
AI总结：
研究基于流体力学方程和Stefan定律建立冰刀融水膜厚度与接触长度的耦合理论，并通过边界层解揭示润滑层厚度及其参数依赖。
摘要：
冰面上几乎无摩擦的滑行依赖于一层薄薄的融水，该水层在机械上将冰刀与冰隔离开来。利用流体力学基本方程和Stefan定律，我们推导出一组关于薄膜厚度和接触长度的两个耦合方程，其中接触长度这一长度尺度不能取其静止时的值。对这些方程的解析研究使得可以定义一个依赖于纵向坐标的小型无量纲参数，该参数在除冰刀前端和末端接触点附近之外的所有位置均可忽略，而在这些接触点附近给出了边界层解。该解无需任何计算即可给出薄膜厚度的数量级，及其相对于滑行者速度、质量以及冰刀轮廓半径和咬入角等外部参数的依赖关系，并与数值研究结果吻合良好。此外，该解还表明，对于滑冰数据的标准值，始终存在宏观厚度的润滑水层，这与因热加热导致液滴空化的情况（Leidenfrost效应）相反。
英文摘要：
Almost frictionless skating on ice relies on a thin layer of melted water insulating mechanically the blade of the skate from ice. Using the basic equations of fluid mechanics and Stefan law, we derive a set of two coupled equations for the thickness of the film and the length of contact, a length scale which cannot be taken as its value at rest. The analytical study of these equations allows to define a small a-dimensional parameter depending on the longitudinal coordinate which can be neglected everywhere except close to the contact points at the front and the end of the blade, where a boundary layer solution is given. This solution provides without any calculation the order of magnitude of the film thickness, and its dependence with respect to external parameters like the velocity and mass of the skater and the radius of profile and bite angle of the blade, in good agreement with the numerical study. Moreover this solution also shows that a lubricating water layer of macroscopic thickness always exists for standard values of ice skating data, contrary to what happens in the case of cavitation of droplets due to thermal heating (Leidenfrost effect).
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