Coagulation effect on the activity size distributions of long lived radon progeny aerosols and its application to atmospheric residence time estimation techniques

The long lived naturally occurring radon progeny species in the atmosphere, namely (210)pb, Bi-210 and Po-210, have been used as important tracers for understanding the atmospheric mixing processes and estimating aerosol residence times. Several observations in the past have shown that the activity size distribution of these species peaks at larger particle sizes as compared to the short lived radon progeny species an effect that has been attributed to the process of coagulation of the background aerosols to which they are attached. To address this issue, a mathematical equation is derived for the activity-size distribution of tracer species by formulating a generalized distribution function for the number of tracer atoms present in coagulating background particles in the presence of radioactive decay and removal. A set of these equations is numerically solved for the progeny chain using Fuchs coagulation kernel combined with a realistic steady-state aerosol size spectrum that includes nucleation, accumulation and coarse mode components. The important findings are: (i) larger shifts in the modal sizes of Pb-210 and Po-210 at higher aerosol concentrations such as that found in certain Asian urban regions (ii) enrichment of tracer specific activity on particles as compared to that predicted by pure attachment laws (iii) sharp decline of daughter-to-parent activity ratios for decreasing particle sizes. The implication of the results to size-fractionated residence time estimation techniques is highlighted. A coagulation corrected graphical approach is presented for estimating the residence times from the size-segregated activity ratios of Bi-210 and Po-210 with respect to Pb-210. The discrepancy between the residence times predicted by conventional formula and the coagulation corrected approach for specified activity ratios increases at higher atmospheric aerosol number concentrations (>1010 #/m(3)) for smaller sizes (