Flow modeling of thin films from microscale to nanoscale

The Navier-Stokes equations can be employed to study fluid motion under ordinary conditions. However, to find solutions to these equations is far from elementary, and in applications we search for ways to simplify them Such simplification is made particularly easy for lubricant films, where we make use of thin film geometry to derive the Reynolds theory of lubrication. Though the Reynolds equation is employed extensively in numerous technical fields, there are two factors, one geometrical and the other material, that limit its applicability. In the case of sudden changes in film thickness the essentially two-dimensional flow approximation inherent in the Reynolds theory will not hold and the Stokes equation must be employed. Another circumstance limiting the validity of the lubrication approximation is the breakdown of the continuum assumption as the film is made progressively thinner. For gas flows the deviation from continuum flow is characterized by the Knudsen number, Kn, the ratio of the length of the mean free path to the thickness of the channel. In liquids it has been shown that down to 10 nm in film thickness the flow is well modeled by the Reynolds equation. However, for thinner films the behavior of the fluid is more solid-like than liquid-like.