Modeling Aerial Transmission of Pathogens (Including the SARS-CoV-2 Virus) through Aerosol Emissions from E-Cigarettes

We examine the plausibility of aerial transmission of pathogens (including the SARS-CoV-2 virus) through respiratory droplets that might be carried by exhaled e-cigarette aerosol (ECA). Given the lack of empiric evidence on this phenomenon, we consider available evidence on cigarette smoking and respiratory droplet emission from mouth breathing through a mouthpiece as convenient proxies to infer the capacity of vaping to transport pathogens in respiratory droplets. Since both exhaled droplets and ECA droplets are within the Stokes regime, the ECA flow acts effectively as a visual tracer of the expiratory flow. To infer quantitatively the direct exposure distance, we consider a model that approximates exhaled ECA flow as an axially symmetric intermittent steady starting jet evolving into an unstable puff, an evolution that we corroborate by comparison with photographs and videos of actual vapers. On the grounds of all this theoretical modeling, we estimate for low-intensity vaping (practiced by 80–90% of vapers) the emission of 6–210 (median 39.9, median deviation 67.3) respiratory submicron droplets per puff and a horizontal distance spread of 1–2 m, with intense vaping possibly emitting up to 1000 droplets per puff in the submicron range with a distance spread over 2 m. The optical visibility of the ECA flow has important safety implications, as bystanders become instinctively aware of the scope and distance of possible direct contagion through the vaping jet.

Unsteady two-dimensional jet with flexible flaps at the channel exit

The present work studies the effect of passive exit flexibility on a two-dimensional starting jet. The exit flexibility is introduced by attaching two flexible (deformable) flaps at the jet exit of a high aspect ratio rectangular duct with the flaps initially being parallel to the channel walls. A controlled piston motion is used to generate the starting jet, which is composed of a rapid acceleration to a constant velocity ($U_{p}$) that is maintained for a given duration of time, after which it is brought to rest impulsively. The parameters which are varied include the flexural rigidity ($EI$) of the flaps, flap length ($L_{f}$) and piston speed ($U_{p}$), with measurements of the flap kinematics and flow field in each case. The flaps initially bulge due to the acceleration of the piston from rest, with this bulge growing in size and moving downstream as the flow develops, culminating in a large opening at the flap exit. Subsequently, the flaps return to their initial parallel position and remain there as long as the piston is in motion. Once the piston stops, the flaps collapse inwards due to fluid deceleration causing additional flow out of the flap region in the form of a jet that adds to the net amount of fluid pushed by the piston. We find that the flap kinematics is affected by the flap $EI$ and $L_{f}$ besides $U_{p}$. We define a non-dimensional flexural rigidity $EI^{\ast }=EI_{eq}/(1/2\unicode[STIX]{x1D70C}U_{p}^{2}L_{f}^{2}d)$, where $EI_{eq}$ is an equivalent flexural rigidity which takes the self-weight of the flaps into account ($d=\text{channel width}$; $\unicode[STIX]{x1D70C}=$ fluid density). We find that across different $EI_{eq}$, $L_{f}$, and piston speeds, the maximum opening of the flap tip and the time taken to reach this maximum opening in terms of $L/L_{f}$ (where $L=\text{fluid slug length}$) fall on a single curve for all the cases studied, when plotted with $EI^{\ast }$. Particle image velocimetry measurements show that the motion of the flaps results in the formation of additional pairs of vortices when compared to the single vortex pair formed in the absence of flaps. The total final circulation coming out of the flap region remains nearly the same as that of the rigid exit case. However, the final fluid impulse is always found to be higher in the flap cases, with the fluid impulse in most flap cases being approximately two times the fluid impulse of the rigid exit case. This increase in impulse is shown to be linked to the fact that the centroids of vorticity get spread out more in the lateral direction due to the opening of the flaps. The increased impulse and the higher time rate of change of impulse, which is linked with force, suggest that introduction of flexible flaps can help improve thrust performance when looked at from a propulsion point of view.

Compressible starting jet: pinch-off and vortex ring–trailing jet interaction

The dominant feature of the compressible starting jet is the interaction between the emerging vortex ring and the trailing jet. There are two types of interaction: the shock–shear layer–vortex interaction and the shear layer–vortex interaction. The former is clearly not present in the incompressible case, since there are no shocks. The shear layer–vortex interaction has been reported in the literature in the incompressible case and it was found that compressibility reduces the critical Reynolds number for the interaction. Four governing parameters describe the compressible starting jet: the non-dimensional mass supply, the Reynolds number, the reservoir to unbounded chamber temperature ratio and the reservoir to unbounded chamber pressure ratio. The latter parameter does not exist in the incompressible case. For large Reynolds numbers, the vortex pinch-off takes place in a multiple way. We studied the compressible starting jet numerically and found that the interaction strongly links the vortex ring and the trailing jet. The shear layer–vortex interaction leads to a rapid breakdown of the head vortex ring when the flow impacted by the Kelvin–Helmholtz instabilities is ingested into the head vortex ring. The shock–shear layer–vortex interaction is similar to the noise generation mechanism of broadband shock noise in a continuously blowing jet and results in similar sound pressure amplitudes in the far field.