# Development and Testing of Copper Filters for Efficient Application in Half-Face Masks
## 3 Results and Discussion
The permeability, \(k^{\prime}\!_{f}\), and the resistance coefficient, \(\beta^{\prime}\), were determined from each pair of the measured pressure drop values. Based on this, the correlations between the pressure drop and the velocity of an air flow through the filter are shown (Figure 7a-d). The P-Cu-AW-315 filter (Figure 7d), made of water-atomized particles, contained relatively large grains of irregular shapes, which facilitated the formation of permeable channels with a larger hydraulic diameter; this was reflected by a lower coefficient of resistance. With the P-Cu-AW-75 filter (Figure 7c), this advantage was eliminated by a low permeability value, as it increases the linear member of the [PERSON]'s equation. According to EN 149, the maximum permissible value of the pressure drop in respirator filters is 300 Pa. The total required air flow during inhalation is 95 L-min\({}^{-1}\) and 160 L-min\({}^{-1}\) during exhalation. The required total cross-sectional area of the respirator filter for inhalation (S\({}_{\text{n}}\)) and exhalation (S\({}_{\text{v}}\)) is determined with respect to the maximum pressure loss, as described by the following equation:  
\[\text{S}=\frac{\text{Q}_{\text{v}}}{\text{V}}\left[\text{dm}^{2}\right] \tag{6}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Filters**} & \multirow{2}{*}{**Permeability**} & \multirow{2}{*}{**Resistance**} & **Required Filter** & **Required Filter** \\  & & **Resistance** & **Area for** & **Area for** \\  & & **Coefficient** & **Inhalation, S\({}_{\text{n}}\)** & **Exhalation, S\({}_{\text{v}}\)** \\  & & & **[dm\({}^{2}\)]** & **[dm\({}^{2}\)]** \\ \hline P-Cu-A-75 & \(5.23\times 10^{-9}\) & \(6.51\times 10^{3}\) & 2.03 & 3.42 \\ P-Cu-A-315 & \(6.29\times 10^{-9}\) & \(5.83\times 10^{3}\) & 1.67 & 2.80 \\ P-Cu-AW-75 & \(3.16\times 10^{-9}\) & \(9.54\times 10^{3}\) & 3.17 & 5.33 \\ P-Cu-AW-315 & \(4.30\times 10^{-9}\) & \(1.98\times 10^{3}\) & 0.264 & 0.445 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculated values corresponding to the total cross-sectional area of the leak in the filters. Figure 7: Correlation between the pressure losses and the velocity of the air flow. The measured and calculated values showed that the filter made of P-Cu-AW-315 powder by atomization in water met the requirements laid out in European standards and exhibited a pressure drop value that is convenient for use of this filter in half-face masks. Respecting the maximum pressure loss, the required total cross-sectional area of the respirator filter for inspiration was 0.264 dm\({}^{2}\), while for expiration it was 0.445 dm\({}^{2}\). Out of all the tested filters, this particular filter exhibited the lowest value of the resistance coefficient and an acceptable permeability value. A reproduction of the results of measurement of a pressure drop was carried out using three samples of a Cu filter, of P-Cu-AW-315 type, while all of them were manufactured by applying the identical method. The curves representing the changes in pressure drops observed in the analyzed samples are shown in Figure 8.  
A pressure drop deviation at a velocity of 0.6 m\(\cdot\)s\({}^{-1}\), which corresponds to a pressure drop of 300 Pa, amounted to 7.5%. An X-ray tomography measurement was carried out with the P-Cu-AW-315 filter. Figure 9 shows a reconstructed 3D image of the specimen together with selected xz projections after performing segmentation based on the threshold settings. Figure 9 demonstrates inhomogeneity in particle sizes (from a few tens of microns up to a few hundreds of microns) and their distribution in the specimen volume. The smallest particles (20-30 microns) were only present on one side of the specimen in a layer about 50-60 microns thick. Further on along the specimen's thickness, (\(y\)-axis in Figure 9), distant from the surface with small particles, the particle dimensions become significantly larger (about 200 microns).