  A model that predicts the outcome of collisions between droplets and
particles in terms of the distribution of the droplet volume post-collision is
lacking, in contrast to the case for droplet-droplet interactions. Taking
existing models that successfully predict the outcomes (coalescence, stretching
or reflexive separation) and post-separation characteristics (sizes, numbers
and velocities of the resulting droplets) of droplet-droplet collisions and
adapting them to take into account an inextensible, non-deformable particle
with varying wettability characteristics, a new model is presented for
droplet-particle collisions. The predictions of the new model agree well with
experimental observations of droplet-particle collisions in low-viscosity
regimes.
  The model is then applied to the case of collisions between respiratory
aerosols generated by breath, speech, cough and sneeze and ambient airborne
particulate material (PM) in order to assess the potential contribution of
these interactions to the enhanced transmission of pathogens contained in the
aerosol, including COVID-19. The results show that under realistic conditions
it is possible for aerosol-PM collisions to enrich the pathogen content of
smaller (and so more persistent) aerosol fractions, and to transfer pathogens
to the surface of PM particles that can travel deep into the respiratory tract.
In the context of better knowledge of the size and velocity distributions of
respiratory aerosols, this model may be used to predict the extent to which
high ambient PM levels may contribute to airborne infection by pathogens such
as COVID-19.
