Deviations from classical droplet evaporation theory

Nonisothermal evaporation

Evaporation of a liquid layer on a substrate is examined without the often-used isothermality assumption, i.e., temperature variations are accounted for. Qualitative estimates show that nonisothermality makes the evaporation rate depend on the conditions at which the substrate is maintained. If it is thermally insulated, evaporative cooling dramatically slows evaporation down; the evaporation rate tends to zero with time and cannot be determined by measuring the external parameters only. If, however, the substrate is maintained at a fixed temperature, the heat flux coming from below sustains evaporation at a finite rate, deducible from the fluid's characteristics, relative humidity, and the layer's depth. The qualitative predictions are quantified using the diffuse-interface model applied to a liquid evaporating into its own vapor.

Respiratory pandemic and indoor aeraulics of classrooms

Respiratory pandemics, such as COVID19, may be transmitted by several modes. The present work focuses on the transmission through small droplets released by people from their mouth by breathing, speaking, coughing, sneering, and possibly aspirated by other people around through their respiration. An analysis of droplet evolution in simplified situations shows that the droplets reach very quickly a quasi-equilibrium temperature before encompassing an isothermal evaporation process. The removal of droplets from suspension is thus piloted by balance between evaporation and sedimentation. It is shown that ambient relative humidity is a major factor influencing the lifetime of droplets and the distance they may travel. As a consequence, and independently of any other health consideration linked to ambient humidity, it is seen that a dry air is a favourable factor for limiting risk of contamination from COVID19. Further investigation is made using computational fluid dynamics (CFD) in a classroom geometry. Several ventilation strategies are investigated: classical regulatory mechanical ventilation, open window natural ventilation and displacement natural ventilation. Ventilation has several effects which influence contamination risk: by introducing fresh air, it reduces droplet concentration; humidity released by human occupants is also limited. However, these effects are not uniform in space, and depend on ventilation strategy. Application of a dose-effect model calibrated for COVID19 to CFD results allows to estimate contamination risk. It is shown that contamination risk is higher for regulatory mechanical ventilation, and may be reduced, using natural ventilation in the absence of wind, by a factor 2.3 to nearly 3 when the teacher is sick, and by a factor 6 to 500 when a student is sick. In the presence of wind, the reduction factor is as high as 13 when the teacher is sick and 17 when a student is sick.