Numerical Analysis of Simultaneous Heat and Mass Transfer During Absorption of Polluted Gases by Cloud Droplets

In this study we performed numerical analysis of heat and mass transfer during evaporation and condensation of a stagnant cloud droplet in the presence of soluble polluted gases. It is assumed that gas absorption is accompanied by subsequent aqueous-phase equilibrium dissociation reactions. We considered liquid and gaseous phase controlled mass transfer. The system of transient conjugate nonlinear energy and mass conservation equations was solved using anelastic approximation and taking into account thermal effect of gas absorption. Using the material balance at the droplet surface we obtained equations for Stefan velocity and the rate of change of the droplet radius taking into account the effect of gas absorption at the gas-liquid interface. We derived also boundary conditions taking into account the effects of gas absorption with subsequent dissociation reactions in the liquid phase and heat of absorption. Numerical analysis was performed for the case of sulfur dioxide dissolution in water droplet with pH values typical for atmospheric clouds. It was shown that thermal effect of absorption and Stefan flow result in the maximum of droplet surface temperature during the transient period of droplet evaporation and affect droplet size evolution. Comparison of the results obtained using the model of physical absorption of sulfur dioxide in water droplet (Elperin and Fominykh, 2005; Elperin et al., 2007) with the predictions of the present model that takes into account the subsequent equilibrium dissociation reactions showed that the model of physical absorption underestimates the droplet surface temperature and overestimates the average concentration of [SO₂ · H₂O] at the transient stage of gas absorption. The developed model allows determining the dependence of pH vs. time for both evaporating and growing droplets. The performed calculations showed that the value of pH increase with the increasing relative humidity (RH).