# Monitoring and Calibrating Building Materials Drying Kinetics with Capacitance Sensors
## 2 Materials and Methods  
### Capacitance Sensors  
In this work, sensors designed to create a fringing electric field are used to estimate the values for moisture content through capacitance measurements. The sensor used consists of a pair of flexible stainless-steel flattened conductors that can be easily inserted into a mortar joint or suitably adjusted for application to a brick or stone surface [27]. In Figure 1a, the twin tape capacitance sensor is presented. The advantage of this type of sensor is its length (25 cm), which can supply more reliable information when embedded inside masonry in comparison with most available sensors that measure at specific points or are limited in size. In Figure 2b, a characteristic specimen representing each of the three different categories of materials under investigation is presented, cement mortar, stone, and brick. In the mortar, the sensor is embedded within its mass, while in the case of stones and bricks, the sensors are inserted and held in place using tight straps. The sensors are then connected with wires to a datalogger that records the voltage variations. When examining samples from a historic building, special attention should be paid to the dimension of the samples. The samples should have at least a length greater than 25 cm, which is the length of the sensors, resulting in a configuration as shown in Figure 1b.  
The capacitance sensing tape connects to a 5 MHz sensing circuit via a coaxial cable connected to a datalogger where both the tape sensor and reference capacitor are measured.  
Figure 1: \(Cont.\)  
Figure 2 illustrates the coupling of the electrodes to the material through a fringing electric field. When an electric field is applied, the material within this coupled system functions as the dielectric medium of the capacitor. The upper surface of the two electrodes (\(D/S\)) interacts with the material with the dielectric constant \(\varepsilon_{m}\), while the downward surface material has a dielectric constant equal to \(\varepsilon_{s}\). The capacitance \(C(D/S)\) is then estimated by Equation (1) [27]:  
\[C(DS)=\frac{\varepsilon_{o}\bigg{(}\frac{\varepsilon_{m}+\varepsilon_{s}}{2} \bigg{)}k\bigg{(}\sqrt{1-\frac{a^{2}}{b^{2}}}\bigg{)}}{k\bigg{(}\frac{a}{b} \bigg{)}}+\varepsilon_{o}\varepsilon_{a}\frac{t}{a} \tag{1}\]  
where:  
\(\varepsilon_{o}\), electric constant (permittivity of free space);  
\(\varepsilon_{m}\), material dielectric constant;  
\(\varepsilon_{s}\), substrate dielectric constant;  
\(\varepsilon_{a}\), dielectric constant of material between two electrodes (air);  
\(k\), Coulomb constant;  
\(a\), inner distance between the two electrodes, 4.5 mm;  
\(b\), outer distance between the two electrodes, 14 mm.  
The system illustrated in Figure 3 operates at 5 MHz. The basic principle is based on the comparison of the charging duration between the sensor and reference \(RC\) circuit.  
Figure 1: (**a**) Tape capacitance sensor. (**b**) Three different samples, cement mortar, stone, and brick specimens, with sensors connected to a datalogger.  
Figure 2: Schematic of fringing electric field.  
The electric signal generated by this circuit exhibits different phases and amplitudes corresponding with variations in capacitance. \(Cr\) is a fixed capacitor, \(RCr\) is the reference, and \(RCs\) are the capacitance sensing side. An electric pulse is produced where its width correlates to the \(RC\) of the sensing circuit. After passing through a low pass filter, two output voltages, \(Va\) and \(Vb\), are generated. The voltage output \(Va\) is stable, while \(Vb\) alters according to the sensing capacitance, \(Cs\). The capacitance variation of the sensing capacitor (\(Cs\)) corresponds to the differential voltage between \(Va\) and \(Vb\). These two output values are transmitted to the datalogger, where the analog data are converted to digital data via an analog to digital converter.