A novel approach for modeling the non-Newtonian behavior of simple liquids: application to liquid water viscosity from low to high shear rates

TL;DR

This paper introduces a generalized elastic-inertial mode theory to model the non-Newtonian rheological behavior of simple liquids like water across various shear rates, validated through experimental viscosity measurements.

Contribution

It develops a new theoretical framework combining elastic and inertial modes to accurately describe liquid viscosity from low to high shear rates, including the Newtonian regime.

Findings

Model accurately predicts water viscosity over a wide shear rate range.

Experimental data confirms the qualitative behavior of water and n-octane.

The theory connects rheology with quantum mechanics and turbulence phenomena.

Abstract

The aim of this paper is to present a modeling for the rheological behavior of simple liquids as a function of the amplitude of the imposed shear stress or strain. The elastic mode theory (Ref. 6) is first generalized to take into account the fact that during a flow experiment, mechanical energy is injected in a system initially at thermodynamic equilibrium. 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. It is then combined with the inertial mode theory (Ref. 7). The formalism thus obtained allows to model the rheological behavior of liquids over a wide range of velocity gradients, including the intermediate narrow range corresponding to the Newtonian regime. As experimental tests, viscosity measurements with two kinds of moving rotor rheometers were performed. Only data obtained with liquid water at room temperature are presented and quantitatively analyzed here. It is also shown that liquid n-octane exhibits the same qualitative behaviors as those of liquid water. In the appendices, connection of this theory with quantum mechanics and turbulence phenomena are discussed, and the notion of viscous mass is introduced.