## 2 Materials and Methods  
Four different brands, among the most widespread in the markets of all of the Italian regions, were considered for the characterization and, for each brand, samples of whole (WM) and semi-skimmed (SSM) types of milk were considered. For three out of the four brands, lactose-free (LFM) milk samples were also considered (because they were available in the markets), and, for two brands, fat-free (FF) milk (one of which also lactose-free) was also considered. The main nutritional values of the samples are reported in Table 1.  
The different types of milk in Table 1 with the same numerical digit are produced by the same brand. The milk of the brands 2, 3, and 4 is available in Tetra Pak, while the milk of brand 1 is available in plastic bottles. The impedance measurements were performed employing a benchtop LCR meter, the Agilent 4284A (Agilent, Santa Clara, CA, USA). The LCR Meter was interfaced with a personal computer by a dedicated software developed in Lab Windows CVI, in order to allow an easier visualization of the measured admittances and for data storage for postprocessing, performed by OriginPro 2021b (Origin Lab Inc., Northampton, MA, USA). The calibration corrections were performed before the measurements, in order to eliminate errors due to cables' impedance. The measurements were performed in the frequency range 20-100 kHz. The milk samples were in cylindrical containers with a diameter of 35 mm and a height of 30 mm. The containers were filled up to the height of 20 mm (clearly marked). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**MILK SAMPLE** & **Fat** & **Saturated** & **Carbohydrates** & **Proteins** & **Salt** & **Calcium** \\ \hline WM1 & 3.6 & 2.4 & 4.8 & 3.2 & 0.13 & 0.12 \\ WM2 & 3.6 & 2.5 & 5.0 & 3.2 & 0.10 & 0.12 \\ WM3 & 3.6 & 2.5 & 5.0 & 3.3 & 0.10 & 0.12 \\ WM4 & 3.6 & 2.4 & 4.8 & 3.2 & 0.14 & 0.12 \\ SSM1 & 1.6 & 1 & 4.9 & 3.3 & 0.13 & 0.12 \\ SSM2 & 1.6 & 1.1 & 5.0 & 3.2 & 0.10 & 0.12 \\ SSM3 & 1.6 & 1.1 & 5.0 & 3.3 & 0.10 & 0.12 \\ SSM4 & 1.6 & 1.1 & 4.9 & 3.3 & 0.14 & 0.12 \\ LEFM1 & 0.1 & 0.07 & 4.9 & 3.3 & 0.13 & 0.12 \\ FFM2 & 0.1 & 0.07 & 5.0 & 3.2 & 0.10 & 0.12 \\ LFM1 & 1 & 0.7 & 4.9 & 3.2 & 0.13 & 0.12 \\ LFM2 & 1.1 & 0.8 & 5 & 3.3 & 0.10 & 0.12 \\ LFM3 & 1 & 0.8 & 4.9 & 3.1 & 0.10 & 0.12 \\ \hline \hline \end{tabular}  
* all the values are expressed in g/100 mL of milk.  
\end{table} 
Table 1: Main nutritional values * of milk samples. Planar technology was selected to realize the compact and lightweight sensing probes. In detail, the RO3010 substrate was employed. Manufactured by Rogers Corporation (Chandler, AZ, USA) [40], it is a ceramic-filled Polytetrafluoroethylene (PTFE) composite (er = 10.2 \(\pm\) 0.3, t = 640 mm), with 17.5 mm-thick copper metallization. The probes, gold plated, were realized in a cost-effective way by employing an in-laboratory prototyping system, a high precision mechanical plotter S103 Protomat by LPKF Laser & Electronics (Garbsen, Germany). The geometry was optimized to reduce parasitic effects. The layout and a picture of the electrode are shown in Figure 1, whereas the values of the lengths in Figure 1 are reported in Table 2.  
Figure 2 shows the assembly of the electrodes and their positioning inside the sample holder. The measurements were performed with the samples at a temperature of 23 \({}^{\circ}\)C. The samples from six different packs were characterized for each type of milk. All of the compared samples had the same expiration period, except for the expired ones. The characteristics of all of the types of milk by category (whole, semi-skimmed) were compared; the different types of milk belonging to the same brand were compared, highlighting the differences between the whole, semi-skimmed, fat-free and lactose-free milk; the variation in the characteristics of the stored milk, once opened, at room temperature or in the refrigerator was studied; the change in the characteristics of the expired milk was highlighted.