COVID-19 in air suspensions

We analyse the stability of virus-carrying particles in air at equilibrium after the dissipation of the initial turbulent process produced by sneezing, coughing, breathing or speaking. Because the viruses are expelled mainly attached to small droplets, with diverse sizes and weights, and the external environmental conditions can also be diverse, the subsequent motion spannes different spatial and temporal scales. For droplet sizes larger than $100\,\mu m$, computing the time of decay to the ground and the distance travelled with a simple free fall model with empirical data extracted from the literature, we obtain distances in the range between $1$ to $3$ meters from the emitter, with a falling time of less than $1\,s$, similar to known recommendations for safe social distancing. For droplets sizes less than $100\,\mu m$ a simple model of motion in a viscous medium predicts that isolated viruses could remain suspended in quiet air for more than a month, while small droplets of $1\,\mu m$ in size can remain suspended for several hours, in agreement with recent experimental results on virus stability in aerosols. These results give solid background for the discussion of prevention strategies, like the use of masks in closed environments.