\label{EQ}$$

This 1D-model allows the computation of the gap flow rate $F_{\mathrm{g}}$ as a function of gap width $B_{\mathrm{g}}$, gap height $H_{\mathrm{g}}$ and gap length $L_{\mathrm{g}}$.

Simulation Setup {#SECsetup}
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Except for the largest particles, most droplets exhaled during breathing are in the range of typical tracer particles used in optical flow measurement techniques. For example, typical droplet diameters used in gas flows lie within $0.5\, \mathrm{\mu m}$ to $5\, \mathrm{\mu m}$ (cf. Tropea and Yarin, 2007). Thus, the droplets of interest in this work can be assumed to follow the airflow and need not be resolved in the simulations.

In order to validate the analytical model from Sect. \[SECtheory\], simulations are performed for using a 2D-geometry and a commercial computational fluid dynamics (CFD) software. The governing equations for the single-phase flow simulations are the equation for mass conservation and the three equations for momentum conservation, collectively called the Navier-Stokes equations: $$\frac{\partial }{\partial t} \int_{V} \rho \ \mathrm{d}V + \int_{S} \rho \textbf{u}  \cdot \textbf{n} \ \mathrm{d}S =  0  \quad ,
\label{EQcontiacc}$$ $$\begin{aligned}
\frac{\partial }{\partial t}  \int_{V} \rho u_{i} \ \mathrm{d}V 
+ \int_{S} \rho u_{i} \textbf{u}  \cdot \textbf{n} \ \mathrm{d}S =  \nonumber \\ 
\int_{S} (\tau_{ij}\textbf{i}_{j} - p\textbf{i}_{i}) \cdot \textbf{n} \ \mathrm{d}S 
