In certain applications where the lubricant is subjected to rapidly changing conditions along its flowing path (such as an elastohydrodynamic contact), the time dependent nature of the lubricant may be significant. One of the simplest types of models to account for such fluid time dependence is the Maxwell model. The time derivative used in such a model must be written with respect to coordinates which translate and rotate with the fluid, or coordinates which deform with the fluid. Unfortunately, such derivatives greatly complicate problems and are rarely used, due to nonlinear coupling of stresses. An admissible formulation of the Maxwell viscoelastic fluid model using the convected derivative has been applied to lubrication flow. Using a regular perturbation in the Deborah number, with the conventional lubrication solution as the leading term, a solution can be obtained. Viscoelasticity may raise or lower pressure depending on combinations of surface slope and curvature.

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