Interpretation of Young's equation for a liquid droplet on a flat and smooth solid surface: Mechanical and thermodynamic routes with a simple Lennard-Jones liquid.
Interpretation of Young's equation for a liquid droplet on a flat and smooth solid surface: Mechanical and thermodynamic routes with a simple Lennard-Jones liquid.
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DOI：
10.1063/1.5053881
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
Y. Yamaguchi;Hiroki Kusudo;D. Surblys;Takeshi Omori;G. Kikugawa
中科院分区：
文献类型：
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作者：
Y. Yamaguchi;Hiroki Kusudo;D. Surblys;Takeshi Omori;G. Kikugawa
在这项研究中，我们对平坦光滑的固体表面上的圆柱形Lennard-Jones液滴进行了分子动力学模拟，结果表明，杨氏方程作为固-液、固-汽和液-汽界面张力γSL、γSV和γLV之间的关系，仅适用于非常有限的条件。使用流体应力张量分布，我们检查了施加在围绕接触线设置的矩形控制体积上的表面横向方向上的力平衡。作为力学途径，通过思想实验将巴克方程推广到固体相关界面，将沿固-液界面法向的两个控制面的流体应力积分与相对于固-真空界面张力γS0的γSL和γSV理论上联系起来，将固-液界面平面的位置定义在流体分子所能达到的极限处。另一方面，沿固液界面侧向控制面的流体应力积分通过Young-Laplace方程与γLV联系起来。通过这种联系，我们证明了杨氏方程对于固体表面施加在接触线周围流体分子上的净侧向力为零的系统是有效的。此外，我们将机械途径获得的γSL - γS0 和γSV - γS0 与作为热力学途径之一的干表面法获得的固-液和固-气粘附功进行了比较，结果表明两种途径具有良好的一致性。此外，通过杨氏方程与这些界面张力预测的接触角与使用先前定义的固液界面平面位置确定的表观液滴接触角非常一致。然而，我们的理论推导表明，这种对应关系是实现的，因为在具有平坦和光滑固体表面的本系统中满足零侧向力条件。这些结果表明，接触角不仅应该通过界面张力来预测，还应该通过接触线周围施加的钉扎力来预测。
In this study, we carried out molecular dynamics simulations of a cylindrical Lennard-Jones droplet on a flat and smooth solid surface and showed that Young's equation as the relation among solid-liquid, solid-vapor, and liquid-vapor interfacial tensions γSL, γSV, and γLV, respectively, was applicable only under a very restricted condition. Using the fluid stress-tensor distribution, we examined the force balance in the surface-lateral direction exerted on a rectangular control volume set around the contact line. As the mechanical route, the fluid stress integrals along the two control surfaces normal to the solid-fluid interface were theoretically connected with γSL and γSV relative to the solid-vacuum interfacial tension γS0 by Bakker's equation extended to solid-related interfaces via a thought experiment, for which the position of the solid-fluid interface plane was defined at the limit that the fluid molecules could reach. On the other hand, the fluid stress integral along the control surface lateral to the solid-fluid interface was connected with γLV by the Young-Laplace equation. Through this connection, we showed that Young's equation was valid for a system in which the net lateral force exerted on the fluid molecules from the solid surface was zero around the contact line. Furthermore, we compared γSL - γS0 and γSV - γS0 obtained by the mechanical route with the solid-liquid and solid-vapor works of adhesion obtained by the dry-surface method as one of the thermodynamic routes and showed that both routes resulted in a good agreement. In addition, the contact angle predicted by Young's equation with these interfacial tensions corresponded well to the apparent droplet contact angle determined by using the previously defined position of the solid-fluid interface plane; however, our theoretical derivation indicated that this correspondence was achieved because the zero-lateral force condition was satisfied in the present system with a flat and smooth solid surface. These results indicated that the contact angle should be predicted not only by the interfacial tensions but also by the pinning force exerted around the contact line.