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arXiv 2003.13550physics.flu-dyn
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表面张力和接触角对温度的依赖性，如扩散界面模型所述

Dependence of the surface tension and contact angle on the temperature, as described by the diffuse-interface model

E. S. Benilov

发表信息：
Phys. Rev. E 101, 042803 (2020)
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摘要：

本文报道了接触线扩散界面模型（DIM）的四个结果。首先，推导出一个边界条件，该边界条件表明，固体壁附近的流体必须具有一定的密度$ρ_{0}$，这取决于固体的属性。与以前的推导不同，这里提出的推导基于与DIM本身相同的物理学，并且不需要额外的假设。其次，渐近估计用于检查一个猜想躺在基础上的DIM，以及所有其他模型的接触线：液体-蒸汽界面几乎是等温的。事实证明，对于水，它们不是--尽管，对于更粘稠的流体，它们可以是。非等温性发生局部，界面附近，但仍然可以影响接触线动力学。第三，结合水的实际状态方程，用DIM方法计算了表面张力$σ$对温度$T$的依赖关系，与经验公式$σ(T)$吻合较好。第四，使用相同的框架来计算水蒸气界面的静态接触角。结果表明，随着温度的升高，接触角变为$180^{\circ}$（完全疏水性）或$0^{\circ}$（完全亲水性），这取决于$ρ_{0}$是否分别与饱和蒸气或液体的密度相匹配。这样的行为可能发生在所有的流体中，而不仅仅是水，并且对于所有足够强的参数变化，而不仅仅是温度变化-正如在可变电场下对液滴的现有观察所证实的那样。

英文摘要：

Four results associated with the diffuse-interface model (DIM) for contact lines are reported in this paper. First, a boundary condition is derived, which states that the fluid near a solid wall must have a certain density $ρ_{0}$ depending on the solid's properties. Unlike previous derivations, the one presented here is based on the same physics as the DIM itself and does not require additional assumptions. Second, asymptotic estimates are used to check a conjecture lying at the foundation of the DIM, as well as all other models of contact lines: that liquid-vapor interfaces are nearly isothermal. It turns out that, for water, they are not -- although, for a more viscous fluid, they can be. The non-isothermaility occurs locally, near the interface, but can still affect the contact-line dynamics. Third, the DIM coupled with a realistic equation of state for water is used to compute the dependence of the surface tension $σ$ on the temperature $T$, which agrees well with the empiric $σ(T)$. Fourth, the same framework is used to compute the static contact angle of a water-vapor interface. It is shown that, with increasing temperature, the contact angle becomes either $180^{\circ}$ (perfect hydrophobicity) or $0^{\circ}$ (perfect hydrophilicity), depending on whether $ρ_{0}$ matches the density of saturated vapor or liquid, respectively. Such behavior presumably occurs in all fluids, not just water, and for all sufficiently strong variations of parameters, not just that of the temperature -- as corroborated by existing observations of drops under variable electric field.

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