An analysis of non-Newtonian effects on lubrication flows is presented based on the upper-convected Maxwell constitutive equation, which is the simplest viscoelastic model having a constant viscosity and relaxation time. By employing characteristic lubricant relaxation times in all order of magnitude analysis, a perturbation method is developed to analyze the flow of a non-Newtonian lubricant between two surfaces. The effect of viscoelasticity on the lubricant velocity and pressure fields is examined, and the influence of minimum film thickness on lubrication characteristics is investigated. Numerical simulations show a significant enhancement in the pressure field when the minimum film thickness is sufficiently small. This mechanism suggests that viscoelasticity does indeed produce a beneficial effect on lubrication performance, which is consistent with experimental observations.

true2016-03-16T16:38:26

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SUMMARYA new algorithm, which combines the spectral element method with elastic viscous splitting stress (EVSS) method, has been developed for viscoelastic uid ows in a planar contraction channel. The system of spectral element approximations to the velocity, pressure, extra stress and the rate of deformation variables is solved by a preconditioned conjugate gradient method based on the Uzawa iteration procedure. The numerical approach is implemented on a planar four-to-one contraction channel for a uid governed by an Oldroyd-B constitutive equation. The behaviour of the Oldroyd-B uids in the contraction channel is investigated with various Weissenberg numbers. It is shown that numerical solutions obtained here agree well with experimental measurements and other numerical predictions.