Incremental viscosity by non-equilibrium molecular dynamics and the Eyring model.

Area of Science:

• Rheology
• Computational Fluid Dynamics
• Statistical Mechanics

Background:

• Sheared fluids exhibit complex viscoelastic behavior.
• Conventional viscosity definitions may not fully capture the physical state of sheared fluids.

Purpose of the Study:

• To introduce and validate "incremental viscosity" (IV) as a more accurate measure of fluid viscoelasticity.
• To derive analytic solutions for a time-dependent extension of the Eyring model (EM) for shear thinning.
• To explore the relationship between IV, shear stress fluctuations, and the Eyring model.

Main Methods:

• Non-Equilibrium Molecular Dynamics (NEMD) simulations to calculate viscoelastic behavior.
• Derivation of analytic solutions for an extended Eyring model.
• Comparison of IV with conventional viscosity and the Carreau formula.

Main Results:

• Incremental viscosity (IV) is proposed as a better physical measure than conventional shear rate-dependent viscosity.
• The IV of the Eyring model is a special case of the Carreau formula.
• An extended Eyring model incorporating Gaussian stress fluctuations retains the original analytic form.

Conclusions:

• Incremental viscosity provides a more accurate representation of the physical state of sheared fluids.
• The Eyring model, particularly its extension, effectively models shear thinning and stress fluctuations.
• The Eyring model's success is partly explained by its approximate satisfaction of the Fluctuation Theorem.