Analysis of surface tension in terms of force gradient per unit area -- Part I : a thought experiment using the principle of equivalence in fluid mechanics

Conventionally, surface tension is expressed as a force per unit length or as an energy per unit area. In this paper, we propose a thought experiment that consists of replacing the surface tension with an equivalent force per unit area according to the principles of fluid mechanics. Such a system of equivalent forces makes it possible to analyze the surface tension phenomenon in terms of surface stress gradient or in terms of energy per unit volume and allows us to rewrite the known equations by calculating the equilibrium of forces in the stationary state. These new equations will be applied to known phenomena such as meniscus, capillary tube, Wilhelmy blade and equilibrium of drops and semi-drops.