Heat and Mass Transfer Around a Viral Load: Mathematical Modelling of Respiratory Droplet Evaporation

The COVID-19 pandemic renewed scientific interest in the physics of respiratory droplet transmission. This work presents a mathematical model for heat and mass transfer around an isolated liquid droplet carrying a viral load, ejected from an infected host during coughing or sneezing. Under a quasi-stationary framework with spherical symmetry, coupled mass and energy balance equations are solved for both steady-state and transient regimes. Two limiting cases are treated — low and high mass-transfer rates — yielding closed-form expressions for the droplet lifetime td. Numerical applications for summer (T∞ = 25 °C) and winter (T∞ = 18 °C) ambient conditions over a range of relative humidities (30–80 %) and droplet equilibrium temperatures (18–32 °C) are reported for an initial diameter D0 = 10 μm. Results show that lower relative humidity accelerates evaporation, and that the transient thermal regime is 55–110 times shorter than the evaporation lifetime, confirming the quasi-stationary assumption. A complete parametric results table is provided.