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The fluid dynamics of coughing and sneezing
Keywords: Infectious disease, fluid dynamics, epidemiology, modeling
1 Introduction
In most respiratory diseases, whether viral or
bacterial, the size of the emitted drops of saliva
or mucus is critical in determining the range of
pathogens. Indeed, the size of a drop determines
the distance it can travel before evaporating into
a droplet nucleus (a solid phase containing a
mixture of minerals and pathogens) or settling
under the influence of gravitational forces.
Initially, only large visible droplets were thought
to carry the pathogens of most common diseases
(Chapin 1910). Wells (1934, 1955) challenged
this view, and compared the time for complete
evaporation to the Stokes settling time. Drops
larger than 100 μm were estimated to settle to
the ground in less than a second, while smaller
drops were estimated to evaporate into droplet
nuclei before settling. Such droplet nuclei may
be suspended by any ambient air currents, so
play a critical role in long-range airborne
transmission. Recent studies have been aimed at
refining the measurement of the size distribution
of droplets emitted by various respiratory
functions, such as coughing or sneezing (Yang
et al. 2007, Morawska et al. 2009). The size of
the emitted droplets was found to vary greatly
from a few μm to 1 mm. For most diseases,
there is no consensus on, or rationalization of,
the drop size distribution.
The principal shortcomings of the current
models of respiratory drop dispersal (e.g. that of
Wells) are two-fold. First, they neglect the
multiphase component of the emitted respiratory
cloud, specifically, the fact that the droplets are
suspended in a turbulent buoyant cloud. Second,
they neglect the effect of the ambient flow. In
our recent study (Bourouiba et al. 2012), we
revisit the physical picture and modeling of
violent respiratory events. Here, we focus on the
effect of the turbulent multiphase dynamics on
the range of pathogen-bearing droplets.
2 Materials/Methods
A combination of theoretical and experimental
approaches is used. Violent respiratory events
were visualized using a combination of high
speed imaging and processing. The resulting
observations guided our theoretical modeling.
Analog experiments conducted in a water tank
were also conducted in order to examine the
range of validity of our proposed mathematical
model. These involved the measurement of the
trajectory and settling patterns of particles
suspended in a multiphase buoyant cloud
emitted from a piston.
3 Results and Discussion
Figure 1 shows an example of high speed
camera visualization of a normal sneeze at 1000
frames per second. Image processing techniques
allow us to highlight both (a) the multiphase
cloud and (b) the large droplet ballistic
dynamics (Bourouiba et al. 2012). These
observations indicate that the initial cloud
entrains ambient fluid in a self-similar manner,
leading to the increase of its size and decrease of
its mean speed with distance from the source.
The particles stay suspended within the cloud
until their settling speed exceeds the mean
recirculation speed of the cloud, at which point
they fall out. The analog experiments showed
good agreement with our theoretical predictions
for the settling patterns. The combination of
our observations and mathematical modeling
indicate that the turbulent multiphase cloud is
critical in extending the contamination range of
pathogen-bearing droplets.
Figure 1: High speed camera visualization of a
normal sneeze (1000 frames per second) reveals
simultaneously (a) the multiphase cloud
dynamics (here shown at 0.161 seconds past the
onset of the sneeze) and (b) the large droplet
ballistic dynamics (Bourouiba et al. 2012).
4 Conclusions
Following the introduction of a pathogen in a
population of susceptible hosts, the nature and
duration of the contact between infected and
non-infected members of the population is
critical in shaping the outcome of the epidemics.
Understanding the dynamics of contact is thus
central to the modeling, planning and control of
epidemics. Surprisingly, the definition of contact
for many common diseases remains vague and
its dynamics poorly understood. The results of
the present study show the importance of the
role of fluid dynamics in understanding the full
physical picture of contact for many respiratory
diseases. Indeed, the multiphase component of
the clouds expelled by violent respiratory events
was shown to be critical in extending the spatial
and temporal range of droplet suspensions. Such
modeling represents an important step in
developing a consistent theoretical framework
for respiratory disease transmission.
Acknowledgments
We acknowledge the support of the National
Science Foundation through grant number
1022356.
5 References
Chapin C. V. 1910. The sources and modes of
infection, John Wiley & Sons, New York.
Bourouiba L. Dehandschoewercker E. and Bush
J. W. M. 2012 Spatial spread of respiratory
diseases: importance of the multiphase flow
dynamics. submitted
Morawska L. et al 2009 Size distribution and
sites of origin of droplets expelled from the
human respiratory tract during expiratory. J.
Aerosol. Sc 40, 256-269
Wells W. F. 1934 On air-borne infection. Study
II. Droplet and droplet nuclei, Amer. J.
Hygiene 20, 611-618
Wells W. F. 1955 Airborne contagion and air
hygiene: an ecological study of droplet
infection. Harvard, University Press,
Cambridge, MA.
Yang et al 2007 The size and concentration of
droplets generated by coughing in human
subjects. Aerosol. Med. 20, 484-494.