Theory and simulations of squeeze-out dynamics in boundary lubrication

Abstract

The dynamics of expulsion of the last liquidlike monolayer of molecules confined between two surfaces ͑measured recently for the first time ͓J. Chem. Phys. 114, 1831 ͑2001͔͒͒ has been analyzed by solving the two-dimensional Navier-Stokes equation combined with kinetic Monte Carlo simulations. Instabilities in the boundary line of the expelled film produce a rough boundary for all length scales above a critical value. The squeeze-out of liquid is shown to result from the 2D-pressure gradient in the lubrication film in the contact area. The Monte Carlo simulations agrees well with experiments, reproducing most qualitative and quantitative features. In particular it shows the formation of small islands, which ͑in the absence of pinning mechanism͒ drift slowly to the periphery of the contact area. We calculate the drift velocity analytically as a function of the distance of the island to the periphery of the contact area. Experiments indicate that some kind of pinning mechanism prevails, trapping fluid pockets for very long times. When including such pinning areas in the simulations, three distinct squeeze phases and time scales were observed: ͑1͒ initial fast squeeze of most of the fluid; ͑2͒ slower squeeze of unpinned fluid pockets; ͑3͒ long term pinning of fluid pockets. We also show that a distribution of small pinning areas may produce a synergistic effect, slowing down the second phase of the squeeze, compared to a small number of big pinning areas. The paper presents a new stochastic numerical approach to problems of moving boundaries which naturally accounts for thermal fluctuations and their effect in unstable dynamics.

Dynamics of squeeze-out: Theory and experiments

“…It is easy to qualitatively understand why the squeeze time is prolonged when the symmetry is broken: the flow lines no longer point only in the radial direction but a more complex flow pattern occurs in the 2D fluid such that the net flow out of the boundaries of the contact region is slower. Similar effects were observed in previous publications 23,24 where different time scales in the squeeze-out process were reported. In particular, we have shown there that the squeeze rate decreases as the boundary line becomes more complex.…”

“…In Ref. 24 we have already shown under slightly different conditions that trapped fluid pockets are squeezed out on a much longer time scale than the initial bulk of the fluid.…”

“…It has been shown experimentally and theoretically 19,20,23,24 that instabilities in the boundary line between the squeezed and nonsqueezed areas leads to a lower bound on the typical roughness wavelength c of the interfacial line. Another interesting experimental observation were trapped fluid pockets left behind long after the bulk of the squeeze is done.…”

Phenomenology of squeezing and sliding of molecularly thin Xe, CH4 and C16H34 lubrication films between smooth and rough curved solid surfaces with long-range elasticity

“…The elimination of each layer starts with the nucleation of a 2D void, which progressively grows by ejecting atoms into the low pressure regions. 7,[9][10][11]12 We have shown earlier that the void formation is a thermally activated process, which, for 2D liquid-like layers, can be described by concepts borrowed from classical nucleation theory. 9 In many practical situations the nucleation of the layering transition may occur at some ''weak'' point between the surfaces where imperfections, e.g., foreign adsorbates ͑like water or some organic contamination͒, may locally reduce the spreading pressure.…”

Friction laws for lubricated nanocontacts

“…1 Full understanding of this phenomenon demands for a comprehensive characterization of junctions' properties down to their nanoscale features; this emerges especially through surface force apparatus experiments, 2-7 analytical theories, 8,9 and molecular dynamics ͑MD͒ simulations, [10][11][12][13] attesting a significant dependence of lubricant thinning and shear dynamics on intermolecular forces, atomic-scale roughness, and contaminants. Such complexity seriously affects our predictive capabilities and often limits reproducibility of experimental results.…”