The dynamics of the expulsion of the last liquid monolayer of molecules confined between two surfaces (measured recently for the first time) 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 were observed. We show that the instabilities produce a rough boundary for all length scales above a critical value and a smooth boundary for shorter lengths. The squeezing out of all but a few trapped islands of liquid is shown to be the result of the pressure gradient in the contact area.

The properties of Xe, CH 4 and C 16 H 34 lubricant confined between two approaching solids are investigated by a model that accounts for the curvature and elastic properties of the solid surfaces. We consider both smooth surfaces, and surfaces with short-scale roughness. In most cases we observe well defined molecular layers develop in the lubricant film when the width of the film is of the order of a few atomic diameters, but in some cases atomic scale roughness inhibit the formation of these layers, and the lubricant exhibit liquid-like properties. An external squeezing-pressure induces discontinuous, thermally activated changes in the number n of lubricant layers. We observe that the layering transition tends to nucleate in disordered or imperfect regions in the lubrication film. We also present and discuss results of sliding dynamics for Xe and C 16 H 34 lubrication films.

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We present a simple model which illustrates the nature of the contact between an elastic solid and a hard surface with cosine-corrugation profile. In the continuum limit, the contact mechanics depends only on two dimensionless parameters, namely the ratio between the height and wavelength of the substrate corrugation, and the ratio between a surface energy and an elastic energy. The theory shows that the complete contact state is always a local energy minima ͑in the zero temperature limit͒, but for large enough surface roughness the global minima correspond to a partial contact state. We show that at nonzero temperature, the contribution to the free energy from the vibrational entropy is very important, and favors the detached state. Computer simulations results are also presented where we study more complicated roughness geometries and the influence of temperature on the adhesion. Simulation results agrees well with the analytical predictions.

We used a surface forces apparatus to investigate layering transitions and frictional properties of chain alcohol films. All but the last two monolayers, strongly bound to each mica surface can be removed by squeezing. Unlike other systems however, chain alcohol films of undecanol and octanol were found to retain their bulk-like lubrication properties down to a thickness of only one (bi)layer. The transition where this last molecularly thin liquid layer is expelled from the gap proceeds in less than one second. From two-dimensional snapshots of the contact area during the expulsion process, we find that the boundary line between the areas of initial and final film thickness bends and roughens as it moves across the contact area. In the final state, we frequently find pockets of trapped liquid. Both the bending and roughening of the boundary line and the trapped pockets are due to a dynamic instability that we describe with a two-dimensional hydrodynamic model. The length scale of the roughening is determined by an elastic line tension.

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.

Articles you may be interested inA model of transluminal flow of an anti-HIV microbicide vehicle: Combined elastic squeezing and gravitational sliding Phys. Fluids 20, 083101 (2008); 10.1063/1.2973188Phenomenology of squeezing and sliding of molecularly thin Xe, CH 4 and C 16 H 34 lubrication films between smooth and rough curved solid surfaces with long-range elasticity Squeezing lubrication films: Layering transition for curved solid surfaces with long-range elasticityWe consider the dynamics of squeeze-out of a molecularly thin confined two-dimensional ͑2D͒ liquidlike layer. The squeeze-out is described by a generalized 2D Navier-Stokes equation which is solved exactly for the limiting case where the squeeze-out nucleates at the center of the contact area, and where the ͑perpendicular͒ three-dimensional pressure profile is Hertzian. We also present numerical results for the case where the nucleation is off-center. The theoretical results are in good agreement with recent experimental data by two of us for octamethylcyclotetrasiloxane. In light of our theoretical model calculations, we also discuss the spatially resolved diffusion experiments of Mukhopadhyay et al. ͓Phys. Rev. Lett. 89, 136103 ͑2002͔͒. Here, we obtain a puzzling disagreement between theory and experiment which requires more investigation.

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