A new microscopic paradigm for modeling the non-Newtonian behavior of simple liquids

What is it about?

The aim of this paper is to present a model for the rheological behavior of simple liquids as a function of the amplitude of the imposed shear stress or strain. The formalism thus obtained allows us to model the rheological behavior of liquids over a wide range of velocity gradients, including the intermediate narrow range corresponding to the Newtonian regime.

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Why is it important?

This new paradigm allowed us to describe in previously published papers quantitatively and simultaneously within the experimental accuracy, the dynamic viscosity, the self-diffusion coefficient as well as the shear elastic and viscous moduli of fluids. Indeed, we have shown the consistency and efficiency of our new approach on the water, potassium and thallium data set. It was shown that this microscopic model emerges from the introduction of fractional calculus in a traditional model of condensed matter physics based on an elastic energy functional, which allows, among other things, to integrate phase transitions directly into this modeling. In this new paper, we propose a generalization of the model presented in the above papers in order to describe quantitatively the variation of the dynamic viscosity according to the imposed velocity gradient. This generalized theory can be seen as a particular aspect of the general problem of perturbation by the measurement, associated with that of the coupling between fluctuation and dissipation. This generalization leads to a “finitary” character of the model. These rheological properties (i.e. shear-thinning, Newtonian plateau and shear-thickenning) have already been observed in several fluids but they have been little studied for low viscosity fluids and they remain largely unexplainable within the classical paradigm of molecular dynamics. In order to quantitatively test our model, we present and analyze new experimental results for liquid water at atmospheric pressure and room temperature. It is also shown that liquid n-octane exhibits the same qualitative behaviors as those of liquid water.

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