In certain applications where the lubricant is subjected to rapidly changing conditions along its flowing path (such as an elastohydrodynamic contact), the inherently time dependent nature of the lubricant may be significant. The simplest type of model to correctly account for such time dependence is the second order fluid, which is a systematic small departure from Newtonian behavior, involving higher order rate-of-rate-of strain tensors. Using a regular perturbation in the Deborah number, with the conventional lubrication case as the leading term, a solution can be obtained. Viscoelasticity may raise or lower pressure depending on the nature of edge boundary conditions.

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