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

Abstract

A fluid mechanics model of inhaled air gases, nitrogen (N2) and oxygen (O2) 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 μm) 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 O2, N2, and CO2 gases through the porous membrane. An optimum Nr of expressing the flow of the inhaled air gases, O2 and N2, through the porous membrane was determined (NO2 = NN2 = -4.4) when an N95 facial mask of specifications of a = 20 nm, l = 30 μm, and ϵ = 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.