Comparing the molecular and global rheology of a fluid under high pressures

The unresolved definition of the pressure-viscosity coefficient

In the classical approach to elastohydrodynamic lubrication (EHL) a single parameter, the pressure-viscosity coefficient, quantifies the isothermal pressure dependence of the viscosity for use in prediction of film thickness. Many definitions are in current use. Progress toward a successful definition of this property has been hampered by the refusal of those working in classical EHL to acknowledge the existence of accurate measurements of the piezoviscous effect that have existed for nearly a century. The Hamrock and Dowson pressure-viscosity coefficient at high temperature requires knowledge of the piezoviscous response at pressures which exceed the inlet pressure and may exceed the Hertz pressure. The definition of pressure-viscosity coefficient and the assumed equation of state must limit the use of the classical formulas, including Hamrock and Dowson, to liquids with high Newtonian limit and to low temperature. Given that this problem has existed for at least fifty years without resolution, it is reasonable to conclude that there is no definition of pressure-viscosity coefficient that will quantify the piezoviscous response for an analytical calculation of EHL film thickness at temperatures above ambient.

Transport coefficients of model lubricants up to 400 MPa from molecular dynamics

In this paper, the predictive power of molecular dynamics methods is demonstrated for the cases of model paraffinic and aromatic lubricant liquids at pressures up to 400 MPa. The shear viscosity and self-diffusion coefficients are calculated for 2,2,4-trimethylpentane (C₈H₁₈) at 298 K and 1,1-diphenylethane (C₁₄H₁₄) at 333 K. Three force fields with different levels of accuracy are compared by the ability to predict the experimental data. The Stokes-Einstein correlation between viscosity and self-diffusion is demonstrated for both compounds.

Shear Thinning in the Prandtl Model and Its Relation to Generalized Newtonian Fluids

The Prandtl model is certainly the simplest and most generic microscopic model describing solid friction. It consists of a single, thermalized atom attached to a spring, which is dragged past a sinusoidal potential representing the surface energy corrugation of a counterface. While it was primarily introduced to rationalize how Coulomb’s friction law can arise from small-scale instabilities, Prandtl argued that his model also describes the shear thinning of liquids. Given its success regarding the interpretation of atomic-force-microscopy experiments, surprisingly little attention has been paid to the question how the Prandtl model relates to fluid rheology. Analyzing its Langevin and Brownian dynamics, we show that the Prandtl model produces friction–velocity relationships, which, converted to a dependence of effective (excess) viscosity on shear rate η ( γ ˙ ) , is strikingly similar to the Carreau–Yasuda (CY) relation, which is obeyed by many non-Newtonian liquids. The two dimensionless parameters in the CY relation are found to span a broad range of values. When thermal energy is small compared to the corrugation of the sinusoidal potential, the leading-order γ ˙ 2 corrections to the equilibrium viscosity only matter in the initial part of the cross-over from Stokes friction to the regime, where η obeys approximately a sublinear power law of 1 / γ ˙ .

The prediction of high-pressure volumetric properties of compressed liquids using the two states model

In this work, we argue that the volumetric properties of liquids cannot be reproduced by a single isothermal equation of state derived by the compressibility route for the whole pressure region extended up to a GPa pressure but require the consideration of two states associated with qualitatively different molecular packing properties. This is confirmed by examples of polar and non-polar substances within the range of temperatures from 203.15 K to 491.48 K and pressures up to 1200 MPa. The proposed two states model is truly predictive for the high-pressure density and isothermal compressibility using several easily measurable physico-chemical quantities: the density, the isobaric heat capacity, and the speed of sound at atmospheric pressure only. The experimental data on the density for 15 different compressed liquids, given in the literature as a function of temperature and very high-pressures, were used for the comparison and its analysis. The relative absolute average deviation for 2138 experimental data points by a two states model is close to 0.17%.

Shear heating, flow, and friction of confined molecular fluids at high pressure

Understanding the molecular-scale behavior of fluids confined and sheared between solid surfaces is important for many applications, particularly tribology where this often governs the macroscopic frictional response. In this study, nonequilibrium molecular dynamics simulations are performed to investigate the effects of fluid and surface properties on the spatially resolved temperature and flow profiles, as well as friction. The severe pressure and shear rate conditions studied are representative of the elastohydrodynamic lubrication regime. In agreement with tribology experiments, flexible lubricant molecules give low friction, which increases linearly with logarithmic shear rate, while bulky traction fluids show higher friction, but a weaker shear rate dependence. Compared to lubricants, traction fluids show more significant shear heating and stronger shear localization. Models developed for macroscopic systems can be used to describe both the spatially resolved temperature profile shape and the mean film temperature rise. The thermal conductivity of the fluids increases with pressure and is significantly higher for lubricants compared to traction fluids, in agreement with experimental results. In a subset of simulations, the efficiency of the thermostat in one of the surfaces is reduced to represent surfaces with lower thermal conductivity. For these unsymmetrical systems, the flow and the temperature profiles become strongly asymmetric and some thermal slip can occur at the solid-fluid interface, despite the absence of velocity slip. The larger temperature rises and steeper velocity gradients in these cases lead to large reductions in friction, particularly at high pressure and shear rate.

Elastohydrodynamic lubricant flow with nanoparticle tracking

Lubricants operating in elastohydrodynamic (EHD) contacts exhibit local variations in rheological properties when the contact pressure rises.