## 2 Background
### Inhaled and Exhaled E-Cigarette Aerosol (ECA)
The estimation \(N_{p}\sim 10^{10}\)-\(10^{11}\) is reasonable given a particle number concentration of \(n_{p}\sim 10^{9}\)/cm\({}^{3}\) and \(V_{b}=20\)-100 mL of low-intensity vaping, with \(N_{p}\sim 10^{12}\) for high-intensity vaping with \(V_{b}=500\) mL. Data on the gas/particle phase partition of the aerosol mass yield that \(m_{b}\) is roughly 50% Total Particulate Matter (TPM), 40% PG/VG gas phase, 7% water vapor and \(<\)3% nicotine [45], roughly a similar gas/particulate phase partition to that of tobacco smoke [46]. As shown in [36; 38], the presence of compounds in gas or PM form depends on their vapor pressure, with PG tending to be gaseous, VG in PM, for nicotine it depends on its Ph, while some aldehydes (e.g., formaldehyde) are most likely in the gas phase. Values of particle numbers and densities for the exhaled ECA can be estimated by considering its retention by the respiratory system. Compound specific retention percentages were reported by [PERSON] et al. [47] for a wide variety of devices and e-liquids: 86% VG, 92% PG and 94% nicotine. [PERSON] et al. [48] reported 97% total aldehyde retention. These high retention percentages are consistent with the mass distribution of inhaled ECA dominated by larger micron-sized droplets which tend to be efficiently deposited in the upper respiratory tracts [35]. Assuming equal retention rate for the particulate and gas phases, we take as total mass of exhaled aerosol and total numbers of exhaled ECA droplet to be 10% of the values of \(m_{b}\) listed in Table 1 and 10% of the values of \(N_{p}=6.7\times 10^{10}\) reported in [44] for a 2 s machine inhalation puff and 50 mL puff volume. Droplet number density of ECA as it is exhaled can be estimated from these values of \(N_{p}\) bearing in mind that the exhaled ECA is now diluted in tidal volumes \(V_{T}\) listed in Table 1 for the various vaping topographies. This yields number densities in the approximate range \(n_{p}=10^{6}\)-\(10^{7}\) cm\({}^{-3}\) (lower to higher vaping intensities). Exhaled ECA dilutes and disperses very fast. Its chemical composition is similar to that of inhaled ECA, in both the gas phase and the droplets [35], with PG and water in the latter evaporating rapidly. Since hyperfine nanometer-sized droplets deposit efficiently by diffusion in the alveolar region and larger micron-sized droplets (which tend to grow from hygroscopic coagulation [33; 35]) deposit by impaction in the upper respiratory tracts [33; 39; 41; 44], the CMD distribution of ECA as it is exhaled should be dominated by modes in intermediate ranges 0.1-0.5 \(\upmu\)m. Since there are no ECA measurements at the exhalation point (the vapor's mouth), we can estimate the representative droplet diameter by a rough order of magnitude calculation: assuming an aerosol mass yield of 5 mg of inhaled ECA for a low-powered device and a 90% retention of aerosol mass with 50% made of PM, the total droplet mass of exhaled ECA should be around \(M_{p}=0.25\) mg. Assuming a 90% retention of inhaled droplets, the total number of exhaled droplets should be \(N_{p}=7.6\,\times 10^{9}\) droplets (from inhaled numbers in [44]), leading to a median droplet mass of \(m_{p}=M_{p}/N_{p}=3.9\times 10^{-14}\,\text{gm}=(\pi/6)\rho_{p}\,d_{p}^{3}\), where \(\rho_{p}\) is the droplets density that we can assume to be close to VG density \(\rho_{p}=1.3\,\text{gm}/\text{cm}^{3}\), leading to \(d_{p}=0.38\,\upmu\)m. Similar order of magnitude values are obtained for the parameters of high-intensity vaping. The fact that CMD chamber measurements are in the range \(d_{p}=0.1\)-0.2 \(\upmu\)m can be explained by the fact that detectors are located 1-2 m from the exhalation source, thus measured ECA droplets have already undergone significant degree of dilution and evaporation (as shown in [36], droplets' mass can decrease by one third in just 1 s by evaporation of its PG content).