Cell model of in-cloud scavenging of highly soluble gases

We investigate mass transfer during absorption of highly soluble gases such as HNO₃, H₂O₂ by stagnant cloud droplets in the presence of inert admixtures. Thermophysical properties of the gases and liquids are assumed to be constant. Diffusion interactions between droplets, caused by the overlap of depleted of soluble gas regions around the neighboring droplets, are taken into account in the approximation of a cellular model of a gas-droplet suspension whereby a suspension is viewed as a periodic structure consisting of the identical spherical cells with periodic boundary conditions at the cell boundary. Using this model we determined temporal and spatial dependencies of the concentration of the soluble trace gas in a gaseous phase and in a droplet and calculated the dependence of the scavenging coefficient on time. We found that scavenging coefficient for gas absorption by cloud droplets remains constant and sharply decreases only at the final stage of absorption. In the calculations we employed a Monte Carlo method and assumed gamma size distribution of cloud droplets. It is shown that despite of the comparable values of Henry's law constants for the hydrogen peroxide (H₂O₂) and the nitric acid (HNO₃), the nitric acid is scavenged more effectively by cloud droplets than the hydrogen peroxide due to a major affect of the dissociation reaction on HNO₃ scavenging. It is demonstrated that scavenging of highly soluble gases by cloud droplets leads to strong decrease of soluble trace gas concentration in the interstitial air. We obtained also analytical expressions for the "equilibrium values" of concentration of the soluble trace gas in a gaseous phase and for concentration of the dissolved gas in a liquid phase for the case of hydrogen peroxide and nitric acid absorption by cloud droplets.