# The Simulation of Dielectric Barrier Discharge for Breakdown Voltage in Starch Modification
## 3 Results and Discussion
### Effect of Starch Granule Shape  
The effect of the starch's granule shape on the breakdown voltage was the focus of our next study. The results of simulations employing mesh-plate electrodes and parallel plate electrodes with gap sizes between the electrodes varying from 0.2 to 1.0 cm at pressure 760 torr are shown in Table 4. The starch had a size of 150 microns, relative permittivity values of 3.1, and a shape that changed from sphere to ellipsoid and polyhedral, respectively.  
Using the data from Table 4, Figures 13 and 14 depict the Paschen curves of each granule shape and different electrode types.  
According to Figure 13, the mesh electrode can reduce the breakdown voltage of the sphere and ellipsoid shapes compared to a conventional electrode by approximately 5.6% at a small gap (\(pd=152\) torr cm) and by about 2.0% at a large gap (\(pd=760\) torr cm). Meanwhile, in polyhedral-shaped starch, the breakdown voltage of the mesh electrode was lower than that of parallel plate electrodes, roughly 1.5% and 1.2% for narrow and large gaps, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{\
\begin{tabular}{c} **Gap Distance** \\ **(cm)** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} _pd_ \\ **(torr cm)** \\ \end{tabular} } & \multicolumn{3}{c}{**Breakdown Voltage (V)**} & \multicolumn{3}{c}{**Polyhedral**} \\ \cline{3-8}  & & & **Sphere** & & **Ellipsoid** & & **Polyhedral** \\ \cline{3-8}  & & **Plate** & **Mesh** & **Plate** & **Mesh** & **Plate** & **Mesh** \\ \hline
0.2 & 152 & 6006 & 5659 & 6123 & 5795 & 5145 & 5055 \\
0.3 & 228 & 7307 & 7185 & 7448 & 7338 & 6818 & 6681 \\
0.4 & 304 & 8865 & 8701 & 8994 & 8871 & 8390 & 8286 \\
0.5 & 380 & 10,570 & 10,369 & 10,665 & 10,337 & 9969 & 9859 \\
0.6 & 456 & 11,968 & 11,749 & 12,048 & 11,827 & 11,498 & 11,371 \\
0.7 & 532 & 13,644 & 13,221 & 13,551 & 13,307 & 13,017 & 12,874 \\
0.8 & 608 & 14,947 & 14,662 & 15,029 & 14,742 & 14,511 & 14,354 \\
0.9 & 684 & 16,399 & 16,086 & 16,491 & 16,176 & 15,970 & 15,821 \\
1.0 & 760.0 & 17,839 & 17,473 & 17,937 & 17,560 & 17,408 & 17,202 \\ \hline \hline \end{tabular}  
* Plate means the parallel plate electrode. Mesh means mesh electrodes with mesh sizes of 1.5 cm\({}^{2}\).  
\end{table}
Table 4: The breakdown voltage of various starch granule shapes at pressure 760 torr.  
Figure 12: Schemes of the Paschen curves of different relative permittivity results using (**a**) parallel plate electrode and (**b**) mesh-plate electrode.  
Figure 14 presents the breakdown voltage for each electrode to initiate the discharge for various shapes. In two types of electrodes, a comparison of the results for starch with different shapes showed that the breakdown voltage weakly increased when changing the shape of starch from sphere to ellipsoid. However, the breakdown voltage was clearly lower in the polyhedral shape than in other shapes, especially for short gaps in sphere shapes of lower than 14.3% and 10.7% for plate and mesh electrodes, respectively.  
When starch is placed on the dielectric layer, the surface of the starch acts on the surface of discharge between electrodes. Because of the crucial characteristic of the polyhedral shape, each granule has a sharp-edged granule [51]. The effect causes the surface of the dielectric to become rough. As a result, the roughness causes the electric field within the electrode gap to increase [49; 52; 53]. This means that the initial discharge voltage for polyhedral shapes is lower than the breakdown voltage for sphere and ellipsoid shapes.