Validity of Laplace formula and dependence of surface tension on curvature in second gradient fluids

Francesco Dell'Isola (1, 2) , Giacomo Rotoli (3)

1 Dipartimento di Ingegneria Strutturale e Geotecnica
2 Laboratorio Strutture e Materiali Intelligenti - Fondazione Tullio Levi-Civita
3 Dipartimento di Ingegneria Meccanica, Energetica e Gestionale

Experiments on very small bubbles showed that classical Gibbs-Laplace theory on surface tension cannot be applied when the dimension of the interface becomes comparable with bubble radi[1]. On the other hand the pressure jump across the interface is from a experimental point of view the most suitable quantity to be measured in order to know surface tension and determine its dependence on curvature. Therefore Laplace formula needs to be generalized to the case of very small bubbles. The theory of second gradient fluids (Germain cf.[2]) accounts the effects of high density gradients (occurring in fluid interface) on fluid pressure. In [3] it is shown that second gradient theory allows the determination of the simplest consistent generalization of Laplace formula and an equivalent bubble theory in which surface tension and radius of a bubble are determined in terms of the density spatial field. This paper complements the quoted results analyzing them numerically. We find that our model: i) predicts the existence of a (minimal) nucleation radius, i.e. a radius which is a minimum possible for the equilibrium of a small bubble; ii) permits, through the new Laplace formula, to evaluate the dependence of surface tension on curvature with results very similar to actual experiments; iii) allows the determination of the range of validity of classical Laplace formula and a theoretical prediction on the departure of experimental data from it.

Domaines: Mécanique [physics.med-ph]

Francesco Dell'Isola, Giacomo Rotoli. Validity of Laplace formula and dependence of surface tension on curvature in second gradient fluids. Mechanics Research Communications, 1995, pp.6. ⟨hal-00498890⟩