## 2 Theory
### Liquid Intrusion/Extrusion Porometry (LIEP) Principles  
The intrusion/extrusion technique for pore size characterization on membrane media operates in similar way as the well-known mercury porometry (HgP) technique and, consequently, it is also among the characterization methods that are also based on the Young-Laplace equation [15; 16; 17; 18; 19]. The HgP technique relies on the fact that, in this case, it is mercury (i.e., a non-wetting liquid) that is forced to enter the pores measuring the intruded volume (more specifically, the differential increment of specific volume) versus applied pressure. These variables contain all the information needed to obtain the PSD of the sample. Normally, HgP runs include a complete intrusion-extrusion cycle. In the extrusion part of the cycle, the previously intruded mercury is ejected from the sample during the depressurization step.  
Similarly, LEIP, which can also be considered as a variation of the GLDP technique, consists of wetting the membrane to be analyzed with an appropriate wetting fluid and then placing the membrane onto a capillary barrier membrane. Then, pressure of a highly hydrophilic liquid (intrusion liquid) is applied in such a way that both the pores of the sample and capillary membrane are steeply filled [20] (Figure 3). Both media are immersed into the wetting fluid.  
To obtain a proper analysis, it must be assured that the capillary barrier membrane is such that its largest pore is smaller than the smallest pore of interest in the sample. Consequently, the gas pressure (i.e., non-wetting fluid) sufficient to extrude or drain the liquid from the pores of the sample is inadequate to empty the pores of the membrane acting as capillary barrier. Liquid extruded from the pores of the sample under gas pressure flows through the pores of the capillary barrier, while the pores of the membrane remain filled with the wetting liquid and prevent gas from passing through.  
Liquid extrusion/intrusion porosimetry is a method by which the capillary pressure (i.e., difference pressure of the non-wetting and wetting liquid in the sample) is changed by directly controlling the gas pressure applied to the sample. The wetting liquid mass coming out from the sample is tracked by measuring the amount of liquid uptake on an analytical balance. As the system reaches equilibrium at each capillary pressure, the volume (mass) of liquid drained and the differential pressure are recorded prior to further pressure increases, [21; 22; 23; 24; 25]. After completion of an intrusion run, a capillary pressure curve can be generated. Once the maximum pressure has expelled the intrusion liquid from all the pores of the sample (i.e., there is no more contribution of the liquid drained), the capillary pressure is slowly relieved and the wetting liquid flows back into the sample. Using these draining and flowing back data, the capillary pressure curves (frequently showing some hysteresis) can be generated [20], and using the Young-Laplace equation, converted into pore size information. Quite often, only the extrusion run is used, and is not followed by a new intrusion experience, and then the method can be simplified as liquid extrusion porometry (LEP).  
Figure 3: Principles of liquid extrusion porometry (LEP).