## 1 Introduction  
Characterization of the pore-size distribution (PSD) of porous/fiber materials has been widely studied among the scientific community and membrane manufacturers [1, 2]. Understanding the constitution, structure, and functional behavior of the membrane has improved in the last few years as the membrane properties and the membrane process has been scaled up, coupled with the economic large-scale manufacture of the membrane [3]. This knowledge needs to be acquired by using appropriate methods, because the studied membranes are put into a large number of different uses and application, even within a particular separation process, then a membrane will be characterized in terms of its pore size, molecular weight cut-off, (MWCO), porosity, thickness, symmetry, permeability, hydrophobicity and hydrophilicity, adsorption, crystallization, etc. In other words, we can see that a complete characterization should include both the functional aspects of the problem and the structural ones, which are no less important. The characterization of pore size includes [4] the determinationof (average) pore size diameter and the pore size distribution (PSD). The average pore size of the membrane filter can determine, in the first instance, the size of the molecules to be retained. However, more complete knowledge would be acquired if we supply not only the average or mean pore size, but also the complete PSD, for example, the amount or percentage for each pore size of those present in the membrane. Particle removal performance can be simply analyzed by using the PSD trends of a membrane [5]. There are two main classification groups for membrane pore size characterization methods, divided into direct and indirect methods, respectively. The direct methods include all the microscopic techniques (e.g., scanning electron microscopy (SEM), transmission electron microscopy (TEM), atomic force microscopy (AFM), scanning tunneling microscopy (STM), which are only able to directly measure the pores visible in the pictures) and spectroscopic techniques (e.g., electrical impedance spectroscopy, positron annihilation spectroscopy, raman spectroscopy, nuclear magnetic resonance, which are more useful to directly visualize the membrane material) [6; 7; 8; 9]. On the other hand, indirect methods are based on some more or less complicated modeling to convert the direct data obtained for each filter into the resulting PSD. In this group, we can include techniques such as capillary flow porometry/liquid intrusion-extrusion techniques (CFP/LIEP), gas adsorption-desorption (GAD), evaporation techniques such as thermoporometry (THP), permoporometry (PMP), or the newest evapoporometry (EP) and solute rejection test. All these techniques can be used to determine the PSD of the porous membrane. The novelty of this study is in the comparison of the use of CFP and LEP indirect methods to characterize pore size distributions and mean pore diameters in a fully automated commercial setup available for performing both techniques. In this way, a single device is able to cover most of the filtration range from ultrafiltration (UF; 10 to 100 nm), microfiltration (MF; 0.1 to 10 \(\upmu\)m) to particle filtration (PF; \(>\)10 \(\upmu\)m) [10], reliably analyzing membranes with porous/fiber structure and made of quite different materials.  
This work aimed to assess their respective benefits and drawbacks demonstrating the features, potential, and possible problems arising from the use of two quite simple, fast, and cheap techniques based on the use of the Young-Laplace equation for interpretation of the results.