  In this paper, we address the well-posedness of an evaporation model for a
spherical liquid droplet taking into account the convective impact of an air
flow in the ambient gas phase. From a mathematical perspective, we are dealing
with a coupled ODE-PDE system for the droplet radius, the temperature
distribution, and the vapor concentration. The nonlinear coupling arises from
the evaporation rate modeled by the Hertz-Knudsen equation. Under physically
meaningful assumptions, we prove existence and uniqueness of a weak solution
until the droplet has evaporated completely. Numerical simulations are
performed to illustrate how different air flows affect the evaporation process.
