Modeling of Thin Film Lubrication

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Abstract
A rheological model is proposed which can be applied to boundary lubrication. The model satisfies the formal continuum mechanics considerations of material objectivity, i.e., it is indifferent to changes in coordinate system and reference frame. The model is applicable to thin films in which the molecular length scale is the same order as the film thickness, due to the use of ensemble, rather than spatial, averaging. The microstructure is described through the use of a director, a unit vector aligned with the molecular orientation. The model contains three material parameters, i.e., the conventional viscosity, a director viscosity which describes varying flow resistance depending on the director orientation, and an elastic modulus relating to moments required to change the director orientation. Typically, the directors are anchored to the boundary surfaces in a favored direction. Calculations are performed for mass velocity, director orientation, and stress in a contact. The lubricant exhibits nearly solid-like behavior near the surfaces, and nearly all sliding takes place across a thin shear layer. Predictions of friction and load are made.