Mechanical approach to surface tension and capillary phenomena

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-Dupre 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).

Automated summary

The paper argues that using a mechanical approach to describe surface tension phenomena is feasible as long as the system on which the forces act is properly defined. After reviewing the microscopic origin of tangential tensile force at the interface, the correct interpretation of the Young-Dupre equation is emphasized. By defining a control volume that does not embed any contact line on its surface, it is possible to reliably identify the acting forces.