Modification of the Köhler Equation to Include Soluble Trace Gases and Slightly Soluble Substances

A generalized reformulation of the Köhler theory to include the effect of soluble gases and slightly soluble aerosol substances is presented. A single equation is derived that takes into account 1) the Kelvin effect; 2) the Raoult effect caused by highly soluble aerosol material (salt); 3) increase in droplet radius due to an undissolved, insoluble, or slightly soluble core; 4) contribution of solute into the droplet by a slightly soluble substance; and 5) contribution of hygroscopic material into the droplet by a soluble trace gas allowed to deplete from the gas phase because of the condensational growth of the droplets (assuming a monodisperse size distribution). Model calculations are presented for a system in which the aerosol is composed of a slightly soluble CaSO4 core coated with ammonium sulfate, and the gas phase contains HNO3. It is shown that the resulting equilibrium curves allow the occurrence of stable, unactivated droplets with radii up to about 10 μm at realistic ambient conditions. The equilibrium curves show in some cases local minima and maxima, the reasons for and consequences of which are discussed. The results of this study suggest that a new definition for “activated droplet” is needed.