论文标题
表面张力和毛细管现象的机械方法
Mechanical approach to surface tension and capillary phenomena
论文作者
论文摘要
许多涉及表面张力的教科书有利于热力学方法（一些热力学潜力，例如自由能），以描述毛细血管现象，表明后者是有缺陷和误导的。然而，机械方法对学生而言比自由能量最小化更为直观，并且不需要任何热力学知识。在本文中，我们表明，只要使用机械方法，毛细血管现象就可以明确地描述，只要对部队作用的系统正确定义。在提醒界面处切向拉伸力的显微镜起源之后，我们得出了Young-dupr {é}方程，强调该关系应解释为在接触线处的界面条件，而不是力量平衡方程。这种正确的解释避免了对给定系统作用的毛细作用力的错误识别。此外，我们表明，正确识别作用力的可靠方法是定义一个不会在其表面上嵌入任何接触线的控制量。最后，作为这种方法的例证，我们在一个经典的示例中以多种方式应用机械方法：毛细管升高的平衡高度的推导（Jurin的定律）。
Many textbooks dealing with surface tension favor the thermodynamic approach (minimization of some thermodynamic potential such as free energy) over the mechanical approach (balance of forces) to describe capillary phenomena, stating that the latter is flawed and misleading. Yet, mechanical approach is more intuitive for students than free energy minimization, and does not require any knowledge of thermodynamics. In this paper we show that capillary phenomena can be unmistakably described using the mechanical approach, as long as the system on which the forces act is properly defined. After reminding the microscopic origin of a tangential tensile force at the interface, we derive the Young-Dupr{é} equation, emphasizing that this relation should be interpreted as an interface condition at the contact line, rather than a force balance equation. This correct interpretation avoids misidentification of capillary forces acting on a given system. Moreover, we show that a reliable method to correctly identify the acting forces is to define a control volume that does not embed any contact line on its surface. Finally, as an illustration of this method, we apply the mechanical approach in a variety of ways on a classic example: the derivation of the equilibrium height of capillary rise (Jurin's law).
