## 4 Results and Discussion  
### Milk-Filled Pipe  
The simulation model is shown in Figure 1. Moreover, the material properties are provided in Table 1 for milk and the bacterial biofilm. For the simulations, the relative permittivity levels of milk and biofilms were assumed to be 67.5 and 4, respectively [17; 18]. For the milk tube model, the inner radius of the tube was 10.16 mm (Figure 1a), and the tube length was 1 m (Figure 1b). For the initial simulation, milk only was modeled; then, the simulation was repeated for a pipe wall biofilm thickness of 1 \(\upmu\)m, as shown in Figure 1c. Please note that these simulations were carried out using a CST high-frequency solver with two simple RF input and output ports, as can be seen in Figure 1c. A mesh optimization study was carried out, and mesh cells of \(\approx\)550,000 were used to achieve the converged result. Figure 2 shows the S11 for milk only and for milk and biofilm, where the black line shows the S11 without the biofilm and the red line shows the S11 with the biofilm. In Figure 2, the response of the S11 reflection coefficient to the presence of biofilms can be seen. The reflection coefficient changed substantially due to the presence of the biofilm on the pipe wall. The frequency for the minimum S11 shifted from 0.19 to 0.229 GHz, and the S11 amplitude decreased from \(-\)30 dB to \(-\)10 dB, which equates to a 100-fold change. This large change was due to the introduction of the biofilm, which changed the permittivity of the waveguide (in this case, the milk transportation tube). This result demonstrates the sensitivity of the reflection coefficient to biofilm formation. Further simulation work was also carried out, and the results demonstrated the sensitivity levels for different biofilm thicknesses. Figure 3 shows the S11 response for a biofilm thickness variation from 5 \(\upmu\)m to 10 \(\upmu\)m. From Figure 3, it can clearly be seen that the S11 frequency along with the amplitude change significantly with a variation from 0.82 GHz to 1.18 GHz in frequency and \(-\)78 dB to \(-\)105 dB in amplitude. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multicolumn{3}{c}{**Electrical Properties**} \\ \cline{2-4}  & **Conductivity (S/m)** & **Relative Permittivity (\(\varepsilon\)r)** & **Loss Tangent (tan \(\delta\))** \\ \hline Milk & 0.40–0.55 [19; 20] & 67.5 [17; 18] & 0.15–0.2 [21; 22] \\ \hline Biofilm & 0.09–0.1 [23] & 2–4 [24] & 0.1–0.15 [25] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Electrical property values of milk and biofilm used in the simulation. Figure 3: Reflection coefficient responses of the simulated pipe model for various biofilm thicknesses. Only milk and biofilm thickness variations of 5 \(\upmu\)m to 10 \(\upmu\)m (noted as (1) to (5)) with a step value of 1 \(\upmu\)m were simulated. A clearance difference in S11 was observed. Figure 2: Simulated reflection coefficient for a 0–1.5 GHz sweep frequency through a milk-filled pipe (black, bottom trace) or through a milk-filled pipe with a 1 \(\upmu\)m thick biofilm along the entire inner wall (red, top trace). dB = decibels. Furthermore, to produce a more practical model, two dielectric patch antennas were designed and used for the simulation. Figure 4 shows the pipe model with the antenna. Two dielectric patch antennas were placed on the surface of the pipe at the two ends of the tube. Please note that zirconia material was used as the dielectric material, with a dielectric constant (\(\varepsilon_{\mathrm{r}}\)) and loss tangent (tan \(\delta\)) of 37 and 0.035, respectively. Zirconia is known to have low interaction with bacterial biofilms [26, 27]. One patch antenna was used as a transmitter and the other as a receiver. The simulation results when using the antennas showed a similar sensitivity to biofilms as the simple model described previously.