Fluid mechanics of facial masks as personal protection equipment (PPE) of COVID-19 virus

A fluid mechanics model of inhaled air gases, nitrogen (N-2) and oxygen (O-2) gases, and exhaled gas components (CO2 and water vapor particles) through a facial mask (membrane) to shield the COVID-19 virus is established. The model was developed based on several gas flux contributions that normally take place through membranes. Semiempirical solutions of the mathematical model were predicted for the N95 facial mask accounting on several parameters, such as a range of porosity size (i.e., 1-30 nm), void fraction (i.e., 10(-3)%-0.3%), and thickness of the membrane (i.e., 10-40 mu m) in comparison to the size of the COVID-19 virus. A unitless number (Nr) was introduced for the first time to describe semiempirical solutions of O-2, N-2, and CO2 gases through the porous membrane. An optimum Nr of expressing the flow of the inhaled air gases, O-2 and N-2, through the porous membrane was determined (NO2 = NN2 = -4.4) when an N95 facial mask of specifications of a = 20 nm, l = 30 mu m, and epsilon = 30% was used as a personal protection equipment (PPE). The concept of the optimum number Nr can be standardized not only for testing commercially available facial masks as PPEs but also for designing new masks for protecting humans from the COVID-19 virus.

Automated summary

A fluid mechanics model was established to study the protection of COVID-19 virus through a facial mask, with semiempirical solutions predicting the efficiency of N95 masks under various parameters. The concept of an optimum unitless number Nr was introduced to describe gas flow through porous membranes, aiding in testing mask performance and designing new protective equipment.