  Lubrication problems at lengthscales for which the traditional Navier-Stokes
description fails can be solved using a modified Reynolds lubrication equation
that is based on the following two observations: first, classical Reynolds
equation failure at small lengthscales is a result of the failure of the
Poiseuille flowrate closure (the Reynolds equation is derived from a statement
of mass conservation, which is valid at all scales); second, averaging across
the film thickness eliminates the need for a constitutive relation providing
spatial resolution of flow profiles in this direction. In other words, the
constitutive information required to extend the classical Reynolds lubrication
equation to small lengthscales is limited to knowledge of the flowrate as a
function of the gap height, which is significantly less complex than a general
constitutive relation, and can be obtained by experiments and/or offline
molecular simulations of pressure driven flow under fully developed conditions.
The proposed methodology, which is an extension of the Generalized Lubrication
Equation of Fukui & Kaneko to dense fluids, is demonstrated and validated via
comparison to Molecular Dynamics simulations of a model lubrication problem.
