## 2 Materials and Methods
### Sensor Design  
To measure the change in the dielectric constant of soil mixtures, the method of impedance spectroscopy can be adapted, similar to the soil moisture measurement, which was described previously (Section 1.4) [2]. Since the sensor is used in the newly developed experimental set-up, it has to be designed in an appropriate manner. The following factors must be taken into account: the sensor should be able to detect a change in density over the entire cross-section of the motor mould, as it is not possible to predict at which point material transport will occur. However, the water flow must be affected as little as possible. Therefore, the sensor should cover as little of the flow area as possible. Vertical arrangements, such as rod-shaped electrodes, would form unwanted water lines on their surface, as the compaction of material in this area is impaired. It should also be considered that during compaction and during the test, large forces may affect the sensor and it must not be deformed or destroyed. For these reasons, a flat sensor arrangement was chosen for the first approach of detecting material transport. Two sensor geometries were investigated in advance: a flat coil and an interdigital capacitor (Figure 4). Both arrangements fulfil the previously described requirements regarding their suitability for use in the motor mould. To determine the influence of the conductivity and dielectric constant of the soil mixture on the impedance of the sensor, the method of finite element simulation (Comsol Multiphysics) was selected. For this purpose, a parameter study has been implemented that reveals the influence of the change in the dielectric constant (Section 2.1) and conductivity on the impedance of the sensor as a function of the percentage of water content. The change in conductivity is assumed to be nearly proportional to the change in volume fraction of the water [17]. The conductivity of freshwater of the Rhine River [18] was taken as the reference value for the conductivity of water. In Figure 5, the impedance spectrum of the flat coil for different water contents is presented. The results of the simulation show that the maximum impedance of the flat coil increases with decreasing water content and thus also with decreasing conductivity and dielectric constant. Besides the impedance, the eigenfrequency of the system also  
Figure 4: (**a**) Geometry of the flat coil; (**b**) geometry of the interdigital capacitor. increases. This process is caused by the parasite capacity of the coil, which decreases due to the reduced dielectric constant. In addition to the capacitance, the inductance also changes through the induction of eddy currents depending on the conductivity. When the conductivity decreases, the inductance increases as a result of lower eddy currents. The simulation results for the interdigital capacitor also show a change in impedance as a function of the changed dielectric properties of the mixture (Figure 6). With the decreasing volume of water, the impedance of the sensor increases. Since no resonance is observed with this arrangement, no shift of the curves on the frequency axis can be recognised. The simulations for both sensors show promising results for the ability to detect material transport. Due to the greater absolute change in impedance and the additional effect of a shifting resonance frequency, the flat coil has been implemented as a sensor in this first approach (Figure 7). Figure 5: Simulation results of the absolute value of flat coil impedance as a function of frequency at different volumes of water content. Figure 6: Simulation results of the absolute value of interdigital capacitor impedance as a function of frequency at different volumes of water content. In the next step, the measuring range of the coil has also been determined using finite element simulation in order to place the sensor in the experimental set-up in such a way that it allows the measuring range to cover the boundary layer of the materials where the material transport is expected to happen.