# Development and Testing of Copper Filters for Efficient Application in Half-Face Masks
## 2 Experimental Materials and Methods
The controlling software of the prototype device also contained an additionally programmed section of the controlling code which facilitated using the obtained values \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Materials**} & \multirow{2}{*}{**Production**} & **Grain Size,** & **Apparent** & **Top Density,** \\  & & **[um]** & **Density,** & **[g\(\cdot\)cm\({}^{-3}\)]** \\ \hline P-Cu-A-75 & Atomized with air & \(5\leq 75\) & 4.674 & 5.563 \\ P-Cu-A-315 & Atomized with air & \(10\leq 315\) & 5.252 & 5.924 \\ P-Cu-AW-75 & Atomized with water & \(20\leq 75\) & 3.962 & 5.099 \\ P-Cu-AW-315 & Atomized with water & \(20\leq 315\) & 3.543 & 4.232 \\ \hline \hline \end{tabular} \(\mathbb{P}\)–powder, Cu—copper, A—atomization with air, and AW—atomization with water; 75 or 315 maximum particle size.  
\end{table} 
Table 1: Technical parameters of powders. of physical parameters to calculate the coefficient of resistance and filter permeability. Figure 1a shows a functional prototype device intended for the identification of pressure drops in filters with automatic measurement of permeability and coefficient of resistance [18]. The device determined two pressure loss values at different air velocities (average values of 100 measurements over about 12 s), from which the permeability and the resistance coefficient of the filter were calculated. The pressure drop in the filter can be described by a differential equation derived from the [PERSON]'s equation for a laminar flow by adding a member for a turbulent flow:  
\[\frac{\mathrm{d}p}{\mathrm{d}x}=\frac{\eta}{k_{f}}\cdot v+\beta\cdot\rho\cdot \frac{v^{2}}{2} \tag{1}\]  
\[\Delta p=\frac{\eta}{k_{f}}\cdot v\cdot\delta+\beta\cdot\rho\cdot\frac{v^{2}}{ 2}\cdot\delta \tag{2}\]  
For a filter with an average thickness of \(\delta\), it is possible to make the following substitution:  
\[k^{\prime}_{f}=\frac{k_{f}}{\delta} \tag{3}\]  
\[\beta^{\prime}=\beta\cdot\delta \tag{4}\]  
Then, Equation (2) takes the following form:  
\[\Delta p=\frac{\eta}{k^{\prime}_{f}}\cdot v+\beta^{\prime}\cdot\rho\cdot\frac {v^{2}}{2} \tag{5}\]  
After permeability, \(k^{\prime}_{f}\), and resistance coefficient, \(\beta^{\prime}\), were calculated, Equation (5) was used to show the analytically obtained pressure drop. The measurements were repeated several times to obtain a possible pressure losses variance. Figure 1a shows a measuring stand for determining a pressure loss, permeability, and resistance coefficient of filters; Figure 1b shows the location of the filter in the measuring stand. An X-ray tomography measurement was carried out using the I12-JEEP beamline [19]. A small piece of a CU filter, approximately 5 \(\times\) 12 \(\times\) 1 mm\({}^{3}\) (h \(\times\) 1 \(\times\) w) in size, was mounted and aligned on the beamline rotation stage. Each projection was collected at an exposure time of 0.075 s with the monochromatic X-ray beam, with the energy level of 52.8 keV. Projections were acquired using the PCO.edge camera at a sample-to-detector distance of 700 mm and an optical module 3 corresponding to a resolution of 3.24 \(\upmu\)m\({}^{2}\) per  
Figure 1: (**a**) Measuring stand for determining pressure losses, permeability, and resistance coefficient; (**b**) the location of the filter in the measuring stand. pixel, in a 1600 \(\times\) 1800 pixels\({}^{2}\) field of view (5.2 \(\times\) 5.8 mm\({}^{2}\)). In total, 1800 projections were collected with a step of 0.1 deg per tomogram. The collected images were processed using the SAVU system [20]; DarkFlatFieldCorrection plugin and DezingerSinogramDeprecated plugin [21] to reduce zinger artifacts; RemoveAllRings plugin [22] to reduce ring artifacts; VoCentering plugin [23] for an automatic determination of the center of rotation; and AstraReconGpu plugin [24] to perform the final reconstruction. The reconstructed 32-bit slices were downscaled to 8-bit tiff format images to reduce requirements on the processing memory.