The dependence of new particle formation rates on the interaction between cluster growth, evaporation, and condensation sink

New particle formation (NPF) is one of the major contributors to atmospheric aerosol number concentrations. The initial step of NPF includes the formation and growth of small clusters, their evaporation and loss to pre-existing particles (characterized by the condensation sink, CS). In the polluted atmospheric boundary layer, the high environmental CS suppresses NPF and it can work synergistically with evaporation to further reduce the NPF rates. In this study, to quantitatively include CS into NPF analysis, we make simplifications to the cluster balance equations and develop approximate equations for the NPF rates in the presence of pre-existing particles, which are applicable to nucleation mechanisms that can be represented by a nonbranched nucleation pathway. The developed equations show that the proportion of clusters that finally lead to new particle formation is given by the cluster-specific ratio of growth rate/CS | evaporation rate | growth rate. As a result, the cumulative product of this ratio for all clusters in the nucleation pathway determines the NPF rates. By comparing with benchmark cluster dynamics simulations of sulfuric acid-dimethylamine and sulfuric acid-ammonia nucleation systems, the developed equations were confirmed to give good estimates of the NPF rates and approximately capture the dependency of NPF rates on CS and nucleating vapor concentrations. The CS dependency predicted by the developed equations shows larger deviations from the simulations when the cluster evaporation rates are high, i.e., when the underlying assumptions of the equations are not satisfied. The equations were also found to be in good agreement with atmospheric NPF rates measured in long-term field observations in urban Beijing.