Respiratory droplets interception in fibrous porous media

Abstract

We investigate, by means of pore-scale lattice Boltzmann simulations, the mechanisms of interception of respiratory droplets within fibrous porous media composing face masks. We simulate the dynamics, coalescence, and collection of droplets of the size comparable with the fiber and pore size in typical fluid-dynamic conditions that represent common expiratory events. We discern the fibrous microstructure into three categories of pores: small, large, and medium-sized pores, where we find that within the latter, the incoming droplets tend to be more likely intercepted. The size of the medium-sized pores relative to the fiber size is placed between the droplet-to-fiber size ratio and a porosity-dependent microstructural parameter $L_{ϵ}^{*}=ϵ/(1-ϵ)$ , with ϵ being the porosity. In larger pores, droplets collection is instead inhibited by the small pore-throat-to-fiber size ratio that characterizes the pore perimeter, limiting their access. The efficiency of the fibrous media in intercepting droplets without compromising breathability, for a given droplet-to-fiber size ratio, can be estimated by knowing the parameter $L_{ϵ}^{*}$ . We propose a simple model that predicts the average penetration of droplets into the fibrous media, showing a sublinear growth with $L_{ϵ}^{*}$ . Permeability is shown also to scale well with $L_{ϵ}^{*}$ but following a superlinear growth, which indicates the possibility of increasing the medium permeability at a little cost in terms of interception efficiency for high values of porosity. As a general design guideline, the results also suggest that a fibrous layer thickness relative to the fiber size should exceed the value $L_{ϵ}^{*}$ in order to ensure effective droplets filtration.