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, a 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 correctly described using the mechanical approach, as long as the system on which the forces act is properly defined. After reviewing the microscopic origin of a tangential tensile force at the interface, we derive the Young–Dupré 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).

中文翻译：

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机械方法处理表面张力和毛细现象

许多有关表面张力的教科书都倾向于使用热力学方法（最小化一些热力学势能，例如自由能），而不是用机械方法（力的平衡）来描述毛细现象，并指出毛细现象是有缺陷的并且具有误导性。但是，机械方法对学生来说比自由能最小化更为直观，并且不需要任何热力学知识。在本文中，我们表明，只要正确定义了作用力的系统，就可以使用机械方法正确描述毛细现象。在回顾了界面处切向拉伸力的微观起源之后，我们推导了Young-Dupré方程，强调应将此关系解释为接触线处的界面条件，而不是力平衡方程。这种正确的解释避免了错误识别作用在给定系统上的毛细作用力。而且，我们表明正确识别作用力的可靠方法是定义一个控制体积，该控制体积在其表面上不嵌入任何接触线。最后，作为对此方法的说明，我们在一个经典示例中以多种方式应用了机械方法：推导毛细管上升的平衡高度（Jurin定律）。