  We study the spreading of viruses, such as SARS-CoV-2, by airborne aerosols,
via a new first-passage-time problem for Lagrangian tracers that are advected
by a turbulent flow: By direct numerical simulations of the three-dimensional
(3D) incompressible, Navier-Stokes equation, we obtain the time $t_R$ at which
a tracer, initially at the origin of a sphere of radius $R$, crosses the
surface of the sphere \textit{for the first time}. We obtain the probability
distribution function $\mathcal{P}(R,t_R)$ and show that it displays two
qualitatively different behaviors: (a) for $R \ll L_{\rm I}$,
$\mathcal{P}(R,t_R)$ has a power-law tail $\sim t_R^{-\alpha}$, with the
exponent $\alpha = 4$ and $L_{\rm I}$ the integral scale of the turbulent flow;
(b) for $l_{\rm I} \lesssim R $, the tail of $\mathcal{P}(R,t_R)$ decays
exponentially. We develop models that allow us to obtain these asymptotic
behaviors analytically. We show how to use $\mathcal{P}(R,t_R)$ to develop
social-distancing guidelines for the mitigation of the spreading of airborne
aerosols with viruses such as SARS-CoV-2.
