Lubrication pressure model in a non-negligible gap for fluid permeation through a membrane with finite permeability

The membrane permeation of a pure fluid driven by lubrication pressure is studied in the range of wall-membrane gap widths that cannot be treated by the Reynolds lubrication equation. This lubrication effect is modeled by including a higher-order pressure component described by the wall-tangential derivative of the local Couette-Poiseuille velocity. A permeate flux model is developed by renormalizing the Couette component, which shows divergent behavior, into the lowest order pressure component, and successfully predicts the permeate flux from infinitesimal to finite permeability.