  We develop a model for the thermodynamics and evaporation dynamics of aerosol
droplets of a liquid such as water, surrounded by the gas. When the temperature
and the chemical potential (or equivalently the humidity) are such that the
vapour phase is the thermodynamic equilibrium state, then of course droplets of
the pure liquid evaporate over a relatively short time. However, if the
droplets also contain nanoparticles or any other non-volatile solute, then the
droplets can become thermodynamically stable. We show that the equilibrium
droplet size depends strongly on the amount and solubility of the nanoparticles
within, i.e. on the nature of the particle interactions with the liquid, and of
course also on the vapour temperature and chemical potential. We develop a
simple thermodynamic model for such droplets and compare predictions with
results from a lattice density functional theory that takes as input the same
particle interaction properties, finding very good agreement. We also use
dynamical density functional theory to study the evaporation/condensation
dynamics of liquid from/to droplets as they equilibrate with the vapour,
thereby demonstrating droplet stability.
