# Design and Evaluation of Face Mask Filtration: Mechanisms, Formulas, and Fluid Dynamics Simulations
## 3 Results and Discussions
### Prediction from Fluid Flow Mechanics
The air flow velocity distribution outside the face mask wearer during the exhalation is shown in Figure 5.  
The air flow velocity is evenly distributed inside the _FFP3_ and _FFP2_ (Figure 5a,b) due to their similar pore sizes (1000 \(\upmu\)m and 1600 \(\upmu\)m) and fiber diameters (14 \(\upmu\)m and 12 \(\upmu\)m), respectively. The contour lines showed the disturbance caused by the exhalation of  
Figure 5: Velocity profiles during the exhalation phase for _FFP3_**(a)**, _FFP2_**(b)**, _Surgical_**(c)**, _Reusable Cotton_**(d)**, _Silk_**(e)**, and _Antiviral_**(f)** masks. the surrounding air at room temperature into the external domain. The color key shows a range of velocities across the masks. A higher velocity value appears for the _Surgical_ mask (Figure 5c) due to the larger pore size and fiber diameter. The _Reusable Cotton_, _Silk_, and _Antiviral_ masks (Figure 5d,f) showed higher air flow velocity. The figure shows that during the exhalation phase, more air passes more quickly through the _Silk_ and _Antiviral_ masks (blue areas in Figure 5e,f). These results correlate with the high pore size and low filtration efficiencies measured for the _Silk_ and _Antiviral_ face masks [5]. Overall, the simulation results obtained using our newly developed model are compatible with the k-\(\epsilon\) turbulence model results [1; 2; 3]. This indicates that both models (k-\(\epsilon\) turbulence and quadrant-based average velocity) are suitable for simulating the mask air flow velocity distribution. Alternatively, our symmetrical ellipsoidal surface is sufficiently represented by its quadrant-based formula (Equation (10)). In this paper, we present a new model that is less complex than the k-\(\epsilon\) model but equally accurate in simulating the effects of different flow models on air velocity distribution. Our recently published paper [9] simulated the time-dependent temperature distribution for the above six different masks during the berthing cycle at inhalation (t = 3 s) and peak exhalation (t = 1 s). The temperature inside the masks increases during exhalation due to the high temperature of exhaled air, while it remains almost unchanged during inhalation. Different masks exhibit varying behaviors: _FFP3_ and _FFP2_ masks show low temperature fluctuations (29-32 \({}^{\circ}\)C) but higher temperatures near the nose and mouth (31-33 \({}^{\circ}\)C), indicating high resistance to airflow and high filtration efficiency. _Surgical_ and _Reusable Cotton_ masks also show temperature rises during exhalation, particularly around the nose and mouth, but lack high-temperature regions, indicating less airflow resistance. _Silk_ and _Antiviral_ masks show high-temperature areas throughout (30-33 \({}^{\circ}\)C), indicating low resistance to airflow. These simulation results align with the velocity profiles and data, confirming the high filtration efficiency of _FFP3_ and _FFP2_ masks according to the EN 149 standard [48]. Figure 6 presents a graph based on simulated experimental data obtained in our previous study [9]. The graph shows the temperature distribution inside the face mask while wearing it at the inhalation peak (t = 3 s) and the exhalation peak (t = 1 s) during the breathing cycle. As the temperature of the exhaled air is high, this can increase the temperature inside the mask, whereas during the inhalation phase, the temperature inside the mask remains almost the same. However, different face masks exhibit different behaviors. Figure 6: A line graph showing the temperature distribution during a breathing cycle, with the exhalation peak occurring at time t = 1 s and the inhalation peak at t = 3 s.  
Figure 6 indicates that _FFP3_ and _FFP2_ masks maintain a high temperature during the exhalation phase, followed by a drop during the inhalation phase. In contrast, _Surgical_ and _Reusable Cotton_ masks exhibit only a small temperature variation between the two phases (approximately 2.5 \({}^{\circ}\)C).