## 1. Introduction  
Milk is an essential nonurishment for human body, both for its development and the maintenance of good health [1; 2; 3]. Nowadays, there is a great variety of milk on the market classified according to different factors such as, for example, the thermal processing method (raw, pasteurized, ultra-pasteurized), the percentage of fat (whole, skimmed, semi-skimmed, fat-free), the nutrient concentration (with vitamins added, fortified), the absence of lactose. In Europe, the Ultra-High Temperature (UHT) pasteurized milk is the most variety of milk [4]. The UHT processing consists of sterizing milk by heating it above 135 \({}^{\circ}\)C, that is the temperature required to kill many bacteria and spores, for about 2 to 5 s, which gives the milk a shelf life of several months [5]. Indeed, UHT milk can sit out unrefrigerated for about three months (this can vary by brand), and once the container is opened, the milk should be refrigerated and has the same shelf life as other milk (about seven to ten days).  
As milk is subjected to degradation or adulteration, careful testing methods are needed. For example, considering the importance of milk in our daily diet and the increased environmental pollutants, methods to assess the heavy metals in milk have been developed [6]. In [7], a liquid chromatography-tandem mass spectrometry (UHPLC-MS/MS) method for lactose determination in commercial UHT milk samples was developed and validated. However, due to the cost and the complexity of the standard analyses, the efforts are focused on the development and optimization of alternative techniques. Electrical Impedance Spectroscopy (EIS) has proven to be a valid study method in the field of food safety [8; 9; 10; 11; 12; 13; 14; 15]. EIS has also been applied to the study of the quality of milk [16; 17; 18], to the detection of aflat (one of the most hazardous compounds in foodstuffs) [19; 20], to quantify the content of bacteria in raw cows' milk [21; 22], to study milk composition and classification [23; 24; 25; 26; 27; 28; 29; 30], to detect milk adulteration [31; 32] and mastitis [33; 34; 35; 36; 37; 38; 39], one of the most important factors that affects the quality of the milk and reduces the milk yield and the well-being of the cows, also causing relevant economic damages. In these studies, however, the EIS technique is either associated with other characterization techniques or requires special sample preparation or the use of specially designed and manufactured sensors and hardware. Moreover, in many of these works, it is not the actual impedance that is used, but rather the study of electrical quantities, such as conductivity or dielectric permittivity. In this paper we want to propose a study based on the analysis of commercial milk samples, as purchased on the market, without any initial preparation, by means of a conventional impedance meter and through the circuital interpretation of the obtained results. This work is a preliminary study that aims to demonstrate the potential of the method, which makes it possible to distinguish between the different types of milk (whole, partially skimmed, fat-free, lactose-free) and between the milk stored correctly in the refrigerator or left at room temperature once opened. Obviously, validation with a large-scale work would be needed to make the impedance measurements on a par with the officially recognized techniques for studying milk quality.  
The paper is organized as follows: Section 2 illustrates the samples and tools used for the investigation; Section 3, divided into three sub-sections, illustrates the results of the measurements from a qualitative and quantitative point of view on the classification of the different types of milk and, in the last subsection, the effects of the methods of storage and expiration is studied; in Section 4, some considerations are made on the results obtained and on possible future developments; in Section 5, the conclusions are drawn.