Multilayer Modelling of Lubricated Contacts: A New Approach Based on a Potential Field Description

Abstract

A first integral approach, derived in an analogous fashion to Maxwell’s use of potential fields, is employed to investigate the flow characteristics, with a view to minimising friction, of shear-driven fluid motion between rigid surfaces in parallel alignment as a model for a lubricated joint, whether naturally occurring or engineered replacement. For a viscous bilayer arrangement comprised of immiscible liquids, it is shown how the flow and the shear stress along the separating interface is influenced by the mean thickness of the layers and the ratio of their respective viscosities. Considered in addition, is how the method can be extended for application to the more challenging problem of when one, or both, of the layers is a viscoelastic material.

Bilayer Couette flow over a profiled plate

“…\end{equation}$$The integration functions $$F_{1}(x_1),\ldots ,F_{4}(x_1)$$ are obtained by inserting the above solution into the boundary and interface conditions. This procedure is explained in detail in the literature [12] for a monolayer film flow and applied to bilayer Couette flow in the literature [13].…”

“…For validation and comparison purposes, a standard Galerkin finite element (FE) discretisation of the classical Navier–Stokes equations was undertaken and, as above, implemented within Python; further details are available in the literature [13, 15].…”