A new single equation of state to describe the dynamic viscosity and self-diffusion coefficient for all fluid phases of water from 200 to 1800 K based on a new original microscopic model

A microscopic model, which is able to simultaneously describe the dynamic viscosity and the self-diffusion coefficient of fluids, is presented. This model is shown to emerge from the introduction of fractional calculus in a usual model of condensed matter physics based on an elastic energy functional. The main feature of the model is that all measurable quantities are predicted, depending on external parameters in a non-trivial way (e.g., the experimental set-up geometry, in particular the sample size). On the basis of an unprecedented comparative analysis of a collection of published experimental data, the modeling is applied to the case of water in all its fluid phases, in particular in the supercooled phase. It is shown that the discrepancies in the literature data are only apparent and can be quantitatively explained by different experimental configurations (e.g., geometry, calibration). This approach makes it possible to reproduce the water viscosity with a better accuracy than the 2008 International Association for the Properties of Water and Steam (IAPWS) formulation and also with a more physically satisfying modeling of the isochors. Moreover, it also allows the modeling within experimental accuracy of the translational self-diffusion data available in the literature in all water fluid phases. Finally, the formalism of the model makes it possible to understand the "anomalies" observed on the dynamic viscosity and self-diffusion coefficient and their possible links.