## 1 Introduction  
Wireless sensor networks are essential in our society, and are becoming an integral part of our environment [1, 2, 3, 4, 5, 6]. These sensors are the object of very active research because of the growing interest in them in many areas, such as environmental monitoring [1, 2], industrial control [3], information security [4], the Internet of vehicles [5] and network lifetime [6]. The goal of these studies is to develop sensitive, fast, and easy-to-use sensors. Microwave sensor technology may provide wireless passive sensors in addition to wireless sensor networks. Microwave sensors are the current technological framework that has most attracted the attention of researchers in recent years. These sensors offer many advantages, including low manufacturing costs, high sensitivity, and high durability; these advantages make them very attractive and preferred choices in a variety of research fields, including biomedicine [7, 8, 9, 10], chemistry [11, 12, 13], electronics, and industry [7, 14, 15]; they have even recently been used in food safety applications and mechanical systems [16, 17, 18]. In the field of microwave sensor technology, a new perspective has been developed using the concept of metamaterials [19, 20]. These are engineered materials first invented by [PERSON] [21], composed of subwavelength resonators, and have been experimentally validated in recent years. Metamaterials are of great interest, as they effectively contribute to the design of many new devices, ensuring unusual electromagnetic properties that may not be readily available in nature [22, 23], such as the realization of passive double-negative metamaterials (DNMs) for simultaneously negative permittivity (\(\varepsilon\)) and permeability (\(\upmu\)), and single-negative metamaterials (SNMs), where either (\(\varepsilon\)) or (\(\upmu\)) is negative, referred to as ENGs and MNGs, respectively [24, 25, 26, 27]. In the earlier literature, a variety of split-ring resonator (SRR) [28, 29, 30, 31] and complementary split-ring resonator (CSRR) [32, 33, 34, 35] sensors have been proposed and studied. SRRs and CSRRs are popular in the design of microwave components, meeting the highest standards of accuracy and sensitivity [36], and show great miniaturization capabilities as they allow a shift of the resonant frequency to lower values [28, 37, 38]. The disadvantage of SRR-based sensors is that they do not support high electric fields and are not suitable for the detection of large microwave signals. Efforts are constantly deployed to improve microwave sensor systems and overcome this problem. The CSRR-based microwave sensors are based on the electric coupling of CSRRs, which are generally etched in the ground plane and have large electric fields [39], and are the most widely used topology of metamaterials in the design of highly sensitive liquid concentration sensors, due to their low profile and adaptability for various practical applications [40]. In this simulation work, a symmetrical CSRR-based compact and highly sensitive bended microstrip sensor for liquid characterization is presented. This study is based on the flat sensor model studied by [PERSON] in [41], where the capillary tube placement was arranged to be normal to the surface of the sensor, crossing the patch, the substrate, and the ground plane. Modifications were made to the latter in order to improve its performance. First, the liquid test tube placement was readjusted to lie down on the sensor surface, helping to increase the interaction between the electric field and the examined liquid; this improved both the sensor sensitivity and the Q factor. Second, the flat thin structure was folded around a cylinder of radius R in order to further increase the contact area between the test tube and the sensor surface. The resulting bended shape strengthens the slow wave propagation within the structure. Thus, the slow wave effect leads to increased interaction time between the electric field and the liquid under test [27]. This phenomenon allows for higher sensitivity.