# Design and Evaluation of Face Mask Filtration: Mechanisms, Formulas, and Fluid Dynamics Simulations
## 1 Introduction  
In the past three years, the use of personal protective equipment (PPE) has increased rapidly due to the spread of the severe acute respiratory syndrome coronavirus (SARS-CoV-2, COVID-19). The use of face coverings has been found effective in preventing the transmission of infectious particles between individuals. In general, face masks are considered an effective shield to protect the respiratory system against harmful airborne particles. These particles can be biological organisms (e.g., viruses, bacteria) or man-made, such as industrial emissions [1, 2]. PPE is no longer mandatory, but its use is still encouraged in many countries around the world [3, 4]. One of the parameters used to determine the performance of a face mask is its filtration efficiency [5]. Filtration efficiency is defined as the ability of a face mask to protect the wearer from the passage of airborne particles [6]. Face masks have different filtration efficiency based on fiber size, morphology (random or ordered structure), pore size, and material weaire. Furthermore, air flow velocity and breathing have an impact on filtration efficiency [7, 8, 9, 10]. Therefore, researchers are investigating the fabrication of face masks with high filtration efficiency to decrease the spread of airborne diseases. For instance, [PERSON] et al. [11] have shown that flow rate and filtration efficacy are inversely proportional, i.e., as the flow rate increases, the filtration efficiency decreases. This behaviour was confirmed by [PERSON] et al. [12] and [PERSON] et al. [6], who analyzed the relationship between flow rate and particle penetration, showing that these are directly proportional. Therefore, as the flow rate increases, the particle penetration through the mask increases. This phenomenon may occur because high flow rates can enlarge the pore size in a single-layer material, allowing more particles to pass through. Fortunately, the porosity of overlaid face coverings can be restricted by multiplelayers of structural orientation and material folding. Previous studies by other scientists demonstrated that layering different filter materials enhanced the filtration efficiency of face masks [13; 14]. Typically, face masks have different layers, with each layer having a specific function [15]. In fact, certified masks can have up to six layers (e.g., _FFP3_) constructed in this manner. There are several established international standards for testing and certifying the filtration efficiency of face masks [16]. However, the advance of computational fluid dynamics (CFD) has made it possible to perform simulations to predict and improve the filtration efficiency of face coverings. Certain computational studies have been published by different researchers, and in most of these studies, the governing equations used were the mass conservation equation of Navier-Stokes coupled with [PERSON]'s friction law [17]. For instance, [PERSON] et al. [18] simulated air flow over the human face to predict the leakage between the head and the mask. Their research showed that leakage depends on air flow velocity and the viscous resistance coefficient of the filter. [PERSON] et al. [19] modelled the flow velocity, the carbon dioxide volume fraction, and the temperature distribution inside an N95 face mask using CFD simulation. They found that the temperature and CO\({}_{2}\) level within the mask were higher than the ambient level or room temperature. Furthermore, they demonstrated that the flow distribution inside the mask has a cup-shaped pattern, fitting the shape of the N95 facemask. This study is to find an expression for air flow visualisation and to make a more precise calculation of filtration efficiency. In this paper, the velocity profile is given great accuracy to allow a more quantitative assessment of filtration efficiency for various mask designs. The three-dimensional (3D) profile of velocity distribution for air flow within a rectangular section duct is examined in connection with the filtration efficiency of face masks.