Non-Newtonian lubrication with the Phan-Thien-Tanner model

We readdress a classical and practical problem as to whether viscoelasticity can have a measurable and beneficial effect on lubrication performance in thin film flows. In this paper, the viscoelasticity of the fluid is described by general Maxwell-Oldroyd type models. More specifically, it is modeled by the Phan-Thien-Tanner constitutive equations. A perturbation analysis for all the primary variables is carried out with the Deborah number as the perturbation parameter. The sequence of governing equations that results from the perturbation procedure is solved analytically up to first order in the Deborah number. Despite the inherent limitations of the perturbation method, the approach presented here demonstrates a reasonable way to determine the viscoelastic effects on lubrication performance in thin film flows. Numerical solutions indicate that there is a significant enhancement of the viscoelastic pressure when the minimum film thickness is sufficiently small. This mechanism suggests that viscoelasticity does indeed enhance the lubricant pressure field and produce a beneficial effect on lubrication performance, which is consistent with experimental observations.