Aerosol agitation: Quantifying the hydrodynamic stressors on particulates encapsulated in small droplets

Lower respiratory tract infections originate from multiple aerosol sources, varying from droplets erupting from bursting bubbles in a toilet or those produced by human speech. A key component of the aerosol-based infection pathway—from source to potential host—is the survival of the pathogen during aerosolization. Due to their finite-time instability, pinch-off processes occurring during aerosolization have the potential to rapidly accelerate the fluid into focused regions of these droplets, stress objects therein, and if powerful enough, disrupt biological life. However, the extent that a pathogen will be exposed to damaging hydrodynamic stressors during the aerosolization process is unknown. Here we compute the probability that particulates will be exposed to a hydrodynamic stressor during the generation of droplets that range in size from one to 100 microns. For example, particulates in water droplets less than 5 $\mu \mathrm{m}$ have a 50% chance of being subjected to an energy dissipation rate in excess of ${10}^{11}$ $\mathrm{W}/{\mathrm{m}}^3$, hydrodynamic stresses in excess of ${10}^4$ Pa, and strain rates in excess of ${10}^7$ ${\mathrm{s}}^{-1}$, values known to damage certain biological cells. Using a combination of numerical simulations and self-similar dynamics, we show how the exposure within a droplet can be generally predicted from its size, surface tension, and density, even across different aerosolization mechanisms. Collectively, these results introduce aerosol agitation as a potential factor in pathogen transmission and implicate the pinch-off singularity flow as setting the distribution of hydrodynamic stressors experienced within the droplet.

Figure 1

Capillary forces generate energy dissipation rates ($\phi$) during drop formation high enough to damage pathogens. (a) A schematic illustrates that pathogens from respiratory and environmental sources can be transferred in drops. Yet whether or not the pathogens are infectious (inset: green-infectious, red-noninfectious) may depend more on drop size than source aerosolization mechanism. (b) One mechanism to generate respiratory aerosols occurs when liquid bridges develop within airways. As the air stretches these thin films, holes nucleate and combine to form ligaments, which then break up into drops. (c) Aerosols also form when bubbles rise to a surface and rupture. (d) Numerical simulations of the rupture can calculate the EDR from hydrodynamic agitation during jet drop generation. [(e) and (f)] Simulations of a cylindrical ligament breakup reveal a comparable EDR when a similarly sized drop is generated. (g)[(i)–(vii)] High-speed images from experiments $(\mathrm{\Delta }t=2.86\mu \mathrm{s})$ during ligament drop $(D_d=28\mu \mathrm{m})$ breakup closely match interface profiles from corresponding numerical simulations (blue lines). (h) The velocity field from numerical simulations—corresponding to experimental frame (iv)—highlights large spatial gradients as the ligament drop retracts.

Figure 2

Lagrangian particle tracking to uncover the maximum energy dissipation rate $\mathrm{\Phi }$ at a particular location. By tracking fluid parcels in the simulations, an exposure map can be computed of the maximum EDR $\mathrm{\Phi }$ experienced at each material point within the drop. Here the jet and ligament drops have diameters approximately $D_d\approx 20\mu \mathrm{m}$.

Figure 3

While generating a drop with diameter $D_d$, there exists an energy dissipation rate ${\mathrm{\Phi }}_{50}$ that is exceeded by 50% of the drop volume. Simulation results for both the jet (circles) and ligament (squares) breakup mechanisms suggest that the majority of fluid in the smallest drops will exceed an EDR previously known to damage bacteria and mammalian cells. Settling time is the measure of time for a drop to fall from a height of 2 m based on a balance of gravitational and air drag forces.

Figure 4

Aggregate simulation data of nondimensional EDR for varying volume fractions $\mathrm{\Omega }/{\mathrm{\Omega }}_d$, where ${\mathrm{\Omega }}_d$ is the volume of the droplet. Here the error bars denote the standard error from the simulations in Fig. 3.