Analysis of surface tension in terms of force gradient per unit area. Part II : Theoretical model of a statistical molecular reorganization gradient at interfaces

Abstract

Classically, surface tension is seen as a force per unit length or as energy per unit area. The surface energy is calculated thermodynamically on the surface of a mathematical layer with no thickness. The surface energy concept is certainly practical and elegant, but it doesn't seem entirely satisfactory to us. In an earlier article 1 , we proposed a thought experiment in which surface tension is replaced with an equivalent force per unit area according to the principles of fluid mechanics. This theoretical tool can be used to rewrite the classical static equations in terms of surface stress gradient and propose a new way of calculating known phenomena such as meniscus, capillary tube, water drops, etc. In this article, we propose a new thought experiment assuming that beyond the classical interaction forces acting at short distance, molecules at liquid interfaces statistically reorganize according to a stationary process of creation/destruction at long distance. The process is such that the degree of statistical molecular organization decreases with a gradient from the surface to the bulk, where the molecules recover the natural disorder of Brownian motion. Assuming that this reorganization process follows an Avrami-type law, we will reinterpret the effects of surface tension in terms of energy per unit volume, which will allow us to retrieve the previous equations of force gradient per unit area.