论文标题
液滴在润湿条纹上的高度
Height of a liquid drop on a wetting stripe
论文作者
论文摘要
考虑了液体在平面壁上的吸附，该平面墙壁被宽度$ l $装饰。在这种情况下，壁只是部分湿（或干），而条带倾向于完全湿润，在条纹上方形成液滴。下降的最大高度$ \ ell_m（δμ）$取决于条纹宽度$ l $和化学势从饱和$Δμ$中偏离，在该$δμ$中采用$ \ ell_0 = \ ell_m（0）$。 Assuming a long-range potential of van der Waals type exerted by the stripe, the interfacial Hamiltonian model is used to show that $\ell_0$ is approached linearly with $δμ$ with a slope which scales as $L^2$ over the region satisfying $L\lesssim ξ_\parallel$, where $ξ_\parallel$ is the parallel correlation function pertinent to the stripe.这表明，在饱和度接近饱和的情况下，存在通用曲线$ \ ell_m（Δμ）$，当适当重新缩放时，与$ l $不同值相对应的吸附等温线对应于不同的值。尽管可以通过考虑较高术语来形成基于界面的哈密顿模型的串联扩展，但提出了基于缩放参数的理性函数形式更适当的近似。近似值基于精确的渐近结果，即$ \ ell_m \simδμ^{ - 1/3} $对于$ l \ to \ to \ infty $，而$ \ ell_m $ obe of符合属于Interfacial Hamilton模型的结果的正确$Δμ\ to 0 $。所有预测都通过与微观密度函数理论（DFT）的比较来验证，尤其是理性函数近似（即使是最简单的形式）也被证明与DFT符合DFT非常合理的一致性，即$Δμ$和$ L $。
Adsorption of liquid on a planar wall decorated by a hydrophilic stripe of width $L$ is considered. Under the condition, that the wall is only partially wet (or dry) while the stripe tends to be wet completely, a liquid drop is formed above the stripe. The maximum height $\ell_m(δμ)$ of the drop depends on the stripe width $L$ and the chemical potential departure from saturation $δμ$ where it adopts the value $\ell_0=\ell_m(0)$. Assuming a long-range potential of van der Waals type exerted by the stripe, the interfacial Hamiltonian model is used to show that $\ell_0$ is approached linearly with $δμ$ with a slope which scales as $L^2$ over the region satisfying $L\lesssim ξ_\parallel$, where $ξ_\parallel$ is the parallel correlation function pertinent to the stripe. This suggests that near the saturation there exists a universal curve $\ell_m(δμ)$ to which the adsorption isotherms corresponding to different values of $L$ all collapse when appropriately rescaled. Although the series expansion based on the interfacial Hamiltonian model can be formed by considering higher order terms, a more appropriate approximation in the form of a rational function based on scaling arguments is proposed. The approximation is based on exact asymptotic results, namely that $\ell_m\simδμ^{-1/3}$ for $L\to\infty$ and that $\ell_m$ obeys the correct $δμ\to0$ behaviour in line with the results of the interfacial Hamiltonian model. All the predictions are verified by the comparison with a microscopic density functional theory (DFT) and, in particular, the rational function approximation -- even in its simplest form -- is shown to be in a very reasonable agreement with DFT for a broad range of both $δμ$ and $L$.
