Nonempirical Free Volume Viscosity Model for Alkane Lubricants under Severe Pressures

Abstract

Viscosities η and diffusion coefficients Ds of linear and branched alkanes at high pressures P <0.7 GPa and temperatures T =500-600 K are calculated by equilibrium molecular dynamics (EMD). Combining Stokes-Einstein, free volume and random walk concepts results in an accurate viscosity model η(Ds(P, T )) for the considered P and T. All model parameters (hydrodynamic radius, random walk step size and attempt frequency) are defined as microscopic ensemble averages and extracted from EMD simulations rendering η(Ds(P, T )) a parameter-free predictor for lubrication simulations.

Molecular origin of driving-dependent friction in fluids

“…The hydrocarbon C 40 H 82 represents a model lubricant with a well-established shear-velocity dependence [8]. To probe the friction and its dependence on velocity, we pull two tagged C 40 H 82 molecules apart along their centers of mass.…”

“…Since the arms of the two pulled alkane molecules can be in contact even for a center-ofmass distance of 2.0 nm, this velocity dependence at long distances may either be attributed to remaining direct interactions or to near-ordering effects as found for the other two systems. In fact, nonequilibrium MD simulations of similar systems revealed an overall alignment of the lubricants along the shearing direction, which also results in a decreased radius of gyration [7,8]. Unlike to the simpler systems, C 40 H 82 moreover exhibits a generic velocity dependence [Eq.…”

“…The latter is of great practical importance, e.g., for the design of lubricants which aim to minimize friction and wear [5]. Non-Newtonian behavior is believed to result from structural changes within the liquid, such as the alignment of polymers along the shearing direction [6][7][8][9] or from the formation of molecule clusters [10][11][12].…”

“…as a function of the pulling velocity v, using the cumulant approximation [Eq. (4)] and the full exponential estimator [Eq (8)…”

Microscopic origins of the viscosity of a Lennard-Jones liquid

“…Another line of thought, embodied in the free volume model, describes the dynamics of atoms as a succession of hard-sphere-like collisions that seldomly cause local mass transport. While the free volume model has enabled to describe the transport properties of many liquids [11][12][13][14], it builds on a microscopic concept -the free volume -which is difficult to relate to local atomistic parameters. Also, being derived at constant density, this model does not offer a direct explanation of the experimentally observed Arrhenius law.…”