The generalized Clapeyron equation and its application to confined ice growth
The generalized Clapeyron equation and its application to confined ice growth
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DOI：
10.1017/jog.2023.28
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发表时间：
2023-01
影响因子：
3.4
通讯作者：
Robert W. Style;Dominic Gerber;A. Rempel;E. Dufresne
中科院分区：
文献类型：
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作者：
Robert W. Style;Dominic Gerber;A. Rempel;E. Dufresne
摘要 大多数由冻结引起的应力的理论描述都植根于（广义）克拉佩龙方程，该方程预测固体冷却到其熔化温度以下时可以施加的压力。该方程对于冰川学、地貌学、土木工程、食品储存和冷冻保存等主题都至关重要。然而，它具有固有的局限性，需要各向同性固体应力和接近体积平衡的条件。在这里，我们通过提供详细说明所有假设的严格推导来检查克拉佩龙方程何时适用。我们展示了各向异性应力状态的自然延伸，并且展示了有效性的温度和压力范围如何取决于明确定义的材料属性。最后，我们演示了如何通过添加高阶项来扩展（线性）克拉佩龙方程的适用范围，从而产生与冰压力融化的实验数据非常一致的结果。
Abstract Most theoretical descriptions of stresses induced by freezing are rooted in the (generalized) Clapeyron equation, which predicts the pressure that a solid can exert as it cools below its melting temperature. This equation is central for topics ranging beyond glaciology to geomorphology, civil engineering, food storage and cryopreservation. However, it has inherent limitations, requiring isotropic solid stresses and conditions near bulk equilibrium. Here, we examine when the Clapeyron equation is applicable by providing a rigorous derivation that details all assumptions. We demonstrate the natural extension for anisotropic stress states, and we show how the temperature and pressure ranges for validity depend on well-defined material properties. Finally, we demonstrate how the range of applicability of the (linear) Clapeyron equation can be extended by adding higher-order terms, yielding results that are in good agreement with experimental data for the pressure melting of ice.