On the lack of structure of Defay-Prigogine 2D-continua

International audienceIn this paper it is proved that the bidimensional continua modelling the interfaces between fluid phases have to be endowed with a shell-like structure. Indeed (generalizing the result due to Tolman [1]) the Gibbs-Tolman formula is proved to be universally valid for the class of fluid interfaces introduced by Defay and Prigogine in [3]. The starting assumption is that (following dell'Isola and Romano [2]) yhe interface between different phases can be modelled by nonmaterial bidimensional (2D-continua), whose independent constitutive variables are the temperature and the interfacial mass density. Moreover, for this class of 2D-continua (their introduction is suggested in [3]) we prove the Gibbs phase rule, Kelvin relation between interfacial curvature and vapour pressure, and propose a formula which could allow for experimental evaluation of the surface mass density for plane and curved interfaces. Unfortunately, as discussed in ADAMSON [4], the dependence of surface tension on the curvature which is experimentally measured is inconsistent with the Tolman formula. Our result implies that, in order to supply theoretical forecasting consistent with experimental data, it is useless to look for new constitutive equations for interfacial free energy: therefore, the conjecture formulated by DEFAY and PRIGOGINE in [3] seems to be not true. Instead, to account experimental evidence, it is necessary to construct 2D-continua endowed with a more complex structure. The minimal set of independent constitutive variables which seem to be necessary to this aim is determined in the epilogue