Modelling hydrodynamic lubrication is crucial in the design of engineering
components as well as for a fundamental understanding of friction mechanisms.
The cornerstone of thin-film flow modelling is the Reynolds equation -- a
lower-dimensional representation of the Stokes equation. However, the
derivation of the Reynolds equation is based on assumptions and fixed form
constitutive relations, that may not generally be valid, especially when
studying systems under extreme conditions. Furthermore, these explicit
assumptions about the constitutive behaviour of the fluid prohibit applications
in a multiscale scenario based on measured or atomistically simulated data.
Here, we present a method that considers the full compressible Navier-Stokes
equation in a height-averaged sense for arbitrary constitutive relations. We
perform numerical tests by using a reformulation of the viscous stress tensor
for laminar flow to validate the presented method comparing to results from
conventional Reynolds solutions. The versatility of the method is shown by
incorporating models for mass-conserving cavitation, wall slip and
non-Newtonian fluids. This allows testing of new constitutive relations that
not necessarily need to take a fixed form, and may be obtained from
experimental or simulation data.Comment: 12 pages, 9 figure
