An approximate analysis of fluid inertia effects in axisymmetric laminar squeeze film flow at arbitrary Reynolds number

Abstract

An approximate analytical solution is developed for the squeezing flow of a film of fluid between parallel disks, including fluid inertia effects. Earlier studies have sought either low or high Reynolds number (Re) asymptotic solutions to the Navier-Stokes equations, for various assumed plate motions. The curious fact has evolved that low Reynolds number first perturbation corrections to lubrication theory, strictly valid for Re≪1, are very accurate up to Re≈10. In the present paper, a solution has been developed based on ‘slug flow linearization’ of the convective inertia terms, i.e., an Oseen-type approximation. The approximate solution is thus valid for any Reynolds number in laminar flow although the results are limited to cases where the disk acceleration is small. The present solution also shows the remarkable linearity (with Reynolds number) of the inertia correction factor continuing to very high Re. In fact, the high Reynolds number asymptote is only slightly different than the low. The solution for reverse squeezing (plates separating) exhibits highly anomalous behavior at moderate to high Reynolds number (flow reversals, sign reversals of the load) similar to that obtained by other workers. Some of these conclusions are arguably false due to boundary layer considerations but more theoretical and experimental research is needed.