Homogenization of soft interfaces in time-dependent hydrodynamic lubrication

The difficulty behind the unsteady lubrication problem is the oscillation of the film thickness in both position and time. The present study aims to extend the multiscale analysis of lubricated interfaces to the unsteady hydrodynamic lubrication case with deformable random microrough surfaces. For that purpose, the homogenization framework for the time-dependent problem is first presented in a setting that unifies all hydrodynamic lubrication cases. The differences between the periodic commensurate and incommensurate as well as random microrough surfaces are highlighted with numerical investigations. A time averaging method is proposed in order to deliver the effective macroscopic response and its efficacy is discussed for different types of microrough surfaces. Finally, the deformation is implemented through the numerically efficient Taylor assumption at the microscale and the ability of the proposed method to reflect the deformation effects is discussed.