Enthalpy effect on the kinetics of concurrent nucleation and chemical aging of aqueous organic aerosols: The stage of thermal relaxation

The size and composition distribution of an ensemble of aqueous organic droplets, evolving via nucleation and concomitant chemical aging, may be affected by the latent heat of condensation and enthalpy of heterogeneous chemical reactions, so the temperature of the droplet may deviate from the air temperature and thus become an independent variable of its state (additional to its size and composition variables). Using the formalism of the classical nucleation theory, we derive a partial differential equation for the temporal evolution of the distribution of an ensemble of such droplets with respect to all their variables of state via Taylor series expansions of the corresponding multidimensional discrete equation of balance, describing the material and heat exchange between droplets and air. The resulting kinetic equation goes beyond the framework of the Fokker–Planck approximation with respect to the temperature variable. A hierarchy of time scales of nonisothermal nucleation and concomitant chemical aging of aqueous organic aerosols is established and an analytical description of their thermal relaxation stage is developed, allowing one to estimate the characteristic time of the establishment of the equilibrium distribution of aerosol particles with respect to their temperatures. Theoretical results are illustrated with numerical calculations for the concurrent nucleation and chemical aging of model aqueous hydrophilic–hydrophobic organic aerosols in air.