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

TL;DR

This paper introduces a thought experiment that redefines surface tension as a force per unit area using fluid mechanics principles, enabling new analysis methods for surface phenomena.

Contribution

It proposes a novel approach to analyze surface tension through equivalent force per unit area, offering alternative equations based on force equilibrium.

Findings

Reformulation of surface tension as force per unit area

Application of new equations to capillary and drop phenomena

Enhanced understanding of surface stress gradients

Abstract

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.