Numerical calculation of the condensational growth of liquid particles in non-dilute and non-ideal media

Condensational growth in aerosols involves simultaneous heat and mass transfer between particles and their surrounding medium. There are several ways of modelling this phenomenon: dilute medium in the vapour species, ideal gas behaviour, ideal mixture, constant thermophysical properties, etc. Most of the solutions proposed for this problem are analytical, at the cost of simplifying many aspects of the phenomenon. This study develops a numerical method for the solution of the steady-state condensational growth of aerosol liquid particles submerged in a gaseous mixture of condensable vapour and inert (non-condensing) gas. Following the principles of the finite volume method, the mass and energy conservation and the droplet heat balance equations are discretized in a spherical mesh around the particle, obtaining their solution by means of a matrix procedure. Heat and mass are transferred satisfying the first-order phenomenological equations. Transport and thermophysical properties of the mixture can be calculated independently, avoiding other assumptions required in analytical procedures. In order to test the method, it was compared with two analytical solutions for the non-dilute condensational growth problem. One of these methods was applied as formulated in the literature, but the other was significantly improved, applying new factors to separate heat and mass transfer as functions of temperature and composition, respectively. The comparison was performed for four condensing substances (H2OH2O, R-134a, n-pentane and n-octane) with air as the inert gas. The results show good agreement under conditions for the ideal gas law, with differences in the case that deviates slightly from this behaviour.