## 2 Materials and Methods
### Mask Filter Model  
Fluid dynamics simulations were performed using _Solidworks Flow Simulation_ software, version SP0, 2022 (Dassault Systems, France) as a preliminary model study. The finite element analysis was also performed for a mesh study using Solidworks software, version SP0, 2022; we considered a standard fit of the mask to the mannequin's head. A small leaking gap around the chin area was taken into consideration. However, previous studies show that for particles greater than 100 nm, there is no strong relationship between leakage and particle size; on the other hand, particles below 100 nm were observed at low flow rates [18; 33]. Gravity was included in the study along the \(z\)-axis in the negative direction (\(-\)9.81 m/s\({}^{2}\)). Air and water were considered fluids for the analysis.  
During the simulation, no change in the water phase was assumed. Based on previous studies [34; 35], the ambient air composition was set to 0.03% CO\({}_{2}\), 20.71% O\({}_{2}\), 1.23% H\({}_{2}\)O, and 78.03% N\({}_{2}\); a turbulent flow type was selected. As a boundary condition, an inlet velocity flow was added based on the data provided in Table 1 in order to simulate someone without a mask breathing from a distance of 50 cm from the source. The engineering database within Solidworks was utilized to configure the porosity of the face masks. Porous material was selected from the drop-down menu, and the porosity was determined based on the data provided in Table 1 below. Goals were set to monitor the velocity on both the mask and on the face of the wearer. The computational domain was reduced in order to reduce the processing time.  
To study the air flow velocities and temperature distributions within six different face masks, computational fluid dynamics (CFD) simulations were carried out usingSolidworks_ software (SP2.0, 2022; Dassault Systems, Paris, France). The physical domain (mannequin head with face mask used for simulation) was designed before the simulations. Air was chosen as the working fluid for the simulations. Gravity was applied along the z-axis direction (\(-9.81\) m/s\({}^{2}\)). The RNG k-\(\epsilon\) turbulence model was used to simulate turbulent airflow. The k-epsilon turbulence model is a mathematical model used to simulate turbulence airflow conditions, while the sinusoidal breathing cycle has been defined by using a sinusoidal function. An inlet volume flux rate of 0.5 L/s was considered the boundary condition. The pore sizes of the six different masks were used to simulate air flow penetration. For this, the measured pore sizes have been added to reproduce the porosity of different face masks. As a result, the air passing through the mask will experience friction and, therefore, flow resistance due to the presence of pores in the mask. The different porosities were simulated using the engineering database available on _Solidworks_. A Quad/Tri mesh type was generated to ensure the accuracy of the results. Moreover, this mesh type generates a mesh density capable of analyzing the flow through the thickness of the mask. Controlled temperature and air flow velocity distributions were applied at the boundary. The transparent feature was applied to the face masks in order to analyze the air flow velocity and temperature distribution. The face velocity is defined as the ratio between the flow rate and the area of the filter. Since we considered the face mask as the final surface to conduct our analysis, the velocity obtained in our work from the simulations is the face velocity.