# Design and Evaluation of Face Mask Filtration: Mechanisms, Formulas, and Fluid Dynamics Simulations
## 3 Results and Discussions
### CFD Simulation Results  
Computational fluid dynamics simulations have been carried out using COMSOL Multiphysics (v. 5.6, COMSOL AB, Stockholm, Sweden) in order to give a 3D visualisation of the air flow velocity profile distribution within the air duct (see Figure 2) based on Equation (10). The air flow profile was obtained by creating a cut plane at the desired location in the model. Then, a surface plot was added to the 2D plot group. Finally, a height expression sub-node was added to the surface plot. To perform the simulation, an entry velocity of 38 m/s was chosen based on our previous measurements [9], and the top of the duct was selected as the inlet point. Figure 2a shows a 3D laminar air flow distribution that peaks at 38 m/s on the central access and falls to zero as the air contacts the inner surfaces. It is also assumed that, within the color legend, the velocity partitions into layered stacks with increasing velocity. Figure 2b shows the velocity profile obtained from using the 2D plot feature in COMSOL in combination with Equation (10) when applied to the y-direction. Subsequently, COMSOL Multiphysics was used to perform CFD simulations to give a flow visualisation of a laminar (see Figure 3a) and turbulent (see Figure 3b) velocity profile contour and to show the respective particle transmission patterns during these two air flow models (see Figure 3c,d). All CFD velocity simulations exclude the presence of the mannequin (see Figure 3a-d). The physical domain comprised the mannequin head, while the external computational domain was reduced to decrease the processing time. The particles were tacked on to trace the air flow trajectory. For the simulations, as a boundary condition, an inlet velocity flow was set to 38 m/s based on our previous study; the ambient temperature was set to 23 \({}^{\circ}\)C, while the temperature at the face of the mannequin was set to 32.1 \({}^{\circ}\)C, according to the average data obtained from the 12 volunteers [9]. The physical domain is described by the mannequin head, while the external computational domain was reduced to reduce the processing time. This study showed the exhalation phase (t = 3 s) of the breathing cycle to model and visualize the air velocity distribution using the mathematical model developed in this study. From the simulations, it emerges that for a turbulent air flow model, some particles travel longer distances with a higher velocity compared to particles in laminar air flow. Also, in the turbulent model, the particles tend to disperse into the surrounding environment, as shown in other studies [28; 29]. In the laminar flow from the mouth, velocity falls with distance progressively, as the simulation shows and is consistent with Figure 2. But, in the turbulent flow, the velocity distribution is ill-defined, with an island of maximum velocity surrounded by various slower motions with a greater diffusion rate. However, environmental factors such as temperature, relative humidity, and wind affect particle  
Figure 2: (**a**) The 3D and (**b**) 2D air flow velocity profiles based on laminar flow model. propagation. For instance, [PERSON] et al. [30] showed that particles travel further in low-temperature, high-humidity environments, while hot, dry environments facilitate particle accumulation. Another study investigated the survival and transmissibility of viruses under different environmental conditions [31]. An additional potential benefit for wearers of masks is that the humidity created within the mask may help combat respiratory diseases such as COVID-19. The results showed that the survival and transmissibility of viruses are high in a low-humidity environment. On the other hand, the transmissibility is low in a highly humid environment. [PERSON] et al. showed [32] that a high level of humidity could limit the spread of viruses to the lungs by stimulating mucociliary clearance (MCC), which is the primary innate defense mechanism of the lung in removing mucus and harmful particles.