Department of Energy and Process Technology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway and SINTEF Energy Research, NO-7465 Trondheim, Norway.
Department of Civil and Environmental Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway.
Phys Rev E. 2018 Jan;97(1-1):012126. doi: 10.1103/PhysRevE.97.012126.
Density gradient theory for fluids has played a key role in the study of interfacial phenomena for a century. In this work, we revisit its fundamentals by examining the vapor-liquid interface of argon, represented by the cut and shifted Lennard-Jones fluid. The starting point has traditionally been a Helmholtz energy functional using mass densities as arguments. By using rather the internal energy as starting point and including the entropy density as an additional argument, following thereby the phenomenological approach from classical thermodynamics, the extended theory suggests that the configurational part of the temperature has different contributions from the parallel and perpendicular directions at the interface, even at equilibrium. We find a similar anisotropy by examining the configurational temperature in molecular dynamics simulations and obtain a qualitative agreement between theory and simulations. The extended theory shows that the temperature anisotropy originates in nonlocal entropic contributions, which are currently missing from the classical theory. The nonlocal entropic contributions discussed in this work are likely to play a role in the description of both equilibrium and nonequilibrium properties of interfaces. At equilibrium, they influence the temperature- and curvature-dependence of the surface tension. Across the vapor-liquid interface of the Lennard Jones fluid, we find that the maximum in the temperature anisotropy coincides precisely with the maximum in the thermal resistivity relative to the equimolar surface, where the integral of the thermal resistivity gives the Kapitza resistance. This links the temperature anisotropy at equilibrium to the Kapitza resistance of the vapor-liquid interface at nonequilibrium.
一百年来，流体的密度梯度理论在界面现象的研究中发挥了关键作用。在这项工作中，我们通过研究氩的汽液界面来重新审视其基本原理，氩的汽液界面由切割和移动的 Lennard-Jones 流体表示。传统上，该理论的起点是一个使用质量密度作为变量的亥姆霍兹自由能泛函。通过使用内部能量作为起点，并将熵密度作为附加变量，遵循经典热力学的唯象方法，扩展理论表明，即使在平衡状态下，界面处的温度的构形部分也具有来自平行和垂直方向的不同贡献。我们通过分子动力学模拟检查构形温度，发现了类似的各向异性，并在理论和模拟之间获得了定性的一致性。扩展理论表明，温度各向异性源于非局部熵贡献，而这些贡献目前在经典理论中缺失。本文讨论的非局部熵贡献可能在界面的平衡和非平衡性质的描述中发挥作用。在平衡状态下，它们影响表面张力的温度和曲率依赖性。在 Lennard-Jones 流体的汽液界面上，我们发现温度各向异性的最大值与相对于等摩尔表面的热阻的最大值完全吻合，其中热阻的积分给出了 Kapitza 电阻。这将平衡时的温度各向异性与非平衡时汽液界面的 Kapitza 电阻联系起来。
