Derivation of porous squeeze-film Reynolds equations using the Brinkman model and its application

The derivation of general modified Reynolds equations for porous squeeze-film curved surfaces is of interest. On the basis of the Brinkman model (BM), considering the continuity of velocities, viscous shear stresses and pressures at the porous medium/fluid interface, two coupled Reynolds equations governing the porous squeeze-film pressure are derived. These general coupled equations can be applied to predict the porous squeeze-film characteristics. An example of one-dimensional porous parallel plates is illustrated to guide the application of these equations. To show the effects of viscous shear stresses of the BM, the results are compared to the slip-flow model (SFM) and the Darcy model (DM). On the whole, the BM predicts quite different squeeze-film characteristics to those derived by the SFM and DM.