When filtering a non-clogging liquid through the membrane (such as pure water), the permeation flux, J, is proportional to the transmembrane pressure, TMP.
From laws such as Darcy's Law (Lucie and Lisa are discussing this over coffee and can explain), it's possible to write a relationship that defines the membrane's permeability:
\(J=\frac{L_p}{\mu}PTM\)
where \(L_p\) is the membrane pereability in m et \(\mu\) is the viscosity in Pa.s or in kg.m-1.s-1. Membrane permeability is a property intrinsic to the material (pore size and number, membrane thickness, etc.).
It is also possible to characterize the membrane by a hydraulic resistance with :
\(J=\frac{PTM}{\mu R_m}\)
where \(R_m\) is the hydraulic resistance of the membrane in m-1.
It is also possible to characterize the membrane by a hydraulic resistance with : \(L_p\) or \(R_m\) by measuring permeation flux as a function of pressure (5 measurements for 5 different pressures to get a good measurement). The next step is to check the linearity of permeation flux as a function of trans-membrane pressure, and then perform a linear regression to find the value. Different tools can be used: there's currently a meeting on the subject to find out whether it's better to use Python or a spreadsheet. You can go and attend it before doing the quiz where you'll have to determine permeability.
The purpose of this standard is to avoid defining permeability by the simple equation \(J=L_p^{*} \, PTM\) which can lead to bad practices. With this equation, you could sell a membrane with a water permeability of \(L_p^{*}\) of 250 L/(h.m2.bar) and the buyer could then only measure a permeability of 115 L/(h.m2.bar). The difference was that the permeability measurements had been taken with water at 60°C, whereas you then took the measurements at 20°C.
Writing in viscosity, closer to the physical mechanism of filtration in a porous medium (Darcy's Law), avoids these problems. Permeability \(L_p\) is then a property that depends only on the membrane material.
If flow is not linear with transmembrane pressure, a few questions need to be asked:
Doesn't the water I'm using clog the membrane? For example, if you use tap water on an ultrafiltration membrane, you may get clogged by small particles still present in the tap water, which will cause the high-pressure linear part to deviate. Test with ultrapure water.
When a membrane is used for the first time, the material may compact under the effect of pressure. Hydraulic resistance then increases. It is advisable to perform an initial filtration with pure water at high pressure for at least an hour to compact the material. After this stage, the material should have a stationary permeability.