To understand lubrication-induced membrane permeation, the effects of permeability and membrane geometry on lubrication pressure and permeate flux are studied in a range of a wall-membrane gap width wherein the effect of lubrication cannot be resolved using the Reynolds lubrication equation. The unresolvable lubrication effect (referred to as the non-Reynolds lubrication effect) is modelled by including a higher-order effect as the wall-tangential variation of the local Couette–Poiseuille velocity. Analytical prediction of the permeate flux is then validated with the fully validated numerical simulation. The result shows that, while the traditional Reynolds lubrication model underestimates the permeate flux, the permeation with the effect of the non-Reynolds lubrication is effectively improved in a small permeability range. Furthermore, the non-Reynolds lubrication model also enables reproduction of the characteristic variation in the permeate flux along the membrane. The effective range of the permeability for the non-Reynolds permeate model is discussed through the order analysis of the pressure terms in the Reynolds and non-Reynolds lubrication regimes.

为了理解润滑引起的膜渗透，在壁-膜间隙宽度范围内研究渗透率和膜几何形状对润滑压力和渗透通量的影响，其中使用雷诺润滑方程无法解决润滑的影响。不可解决的润滑效应（称为非雷诺润滑效应）通过将高阶效应作为局部 Couette-Poiseuille 速度的壁切向变化来建模。然后通过完全验证的数值模拟验证渗透通量的分析预测。结果表明，虽然传统的雷诺润滑模型低估了渗透通量，但在较小的渗透率范围内，非雷诺润滑作用下的渗透得到了有效改善。此外，非雷诺润滑模型还可以再现沿膜渗透通量的特征变化。通过对雷诺和非雷诺润滑状态中压力项的阶次分析，讨论了非雷诺渗透模型的渗透率的有效范围。