Growth of atmospheric clusters involving cluster–cluster collisions: comparison of different growth rate methods

Abstract

Abstract. We simulated the time evolution of atmospheric cluster concentrations in a one-component system where not only do clusters grow by condensation of monomers, but cluster-cluster collisions also significantly contribute to the growth of the clusters. Our aim was to investigate the consistency of the growth rates of sub-3 nm clusters determined with different methods and the validity of the common approach to use them to estimate particle formation rates. We compared the growth rate corresponding to particle fluxes (FGR), the growth rate derived from the appearance times of clusters (AGR), and the growth rate calculated based on irreversible vapor condensation (CGR). We found that the relation between the different growth rates depends strongly on the external conditions and the properties of the model substance. The difference between the different growth rates was typically highest at the smallest, sub-2 nm sizes. FGR was generally lower than AGR and CGR; at the smallest sizes the difference was often very large, while at sizes larger than 2 nm the growth rates were closer to each other. AGR and CGR were in most cases close to each other at all sizes. The difference between the growth rates was generally lower in conditions where cluster concentrations were high, and evaporation and other losses were thus less significant. Furthermore, our results show that the conventional method used to determine particle formation rates from growth rates may give estimates far from the true values. Thus, care must be taken not only in how the growth rate is determined but also in how it is applied.

Atmospheric new particle formation and growth: review of field observations

“…The GR defined by equation (5) was recently named as the flux-equivalent GR, since the GR of a particle population can be determined in different ways (Kontkanen et al 2016b; see also section 2.3.2). It should be noted that equation (5) is strictly valid only when the particle number concentration around the size dp is conserved, i.e.…”

“…There is no method for the treatment of measurement data that can accurately reproduce the fluxequivalent particle GR defined by equation (5). For example, it has been shown using numerical simulations that the appearance time method discussed above systematically gives values of GR that exceed the corresponding flux-equivalent particle GR, and that this difference increases rapidly when going to sub-3 nm particle sizes (Olenius et al 2014, Kontkanen et al 2016b.…”

Laboratory observations of temperature and humidity dependencies of nucleation and growth rates of sub‐3 nm particles

“…k G,cond was calculated following equation (8) of Nieminen et al [2010]. It was noted that our observed k G,obs , the apparent growth rate, may also include the contribution of particle self-coagulation [Leppä et al, 2011;Kontkanen et al, 2016]. The nucleation mode growth rate due to self-coagulation can be calculated using an analytical resolution by Stolzenburg et al [2005].…”

Errors in nanoparticle growth rates inferred from measurements in chemically reacting aerosol systems

“…The aerosol general dynamic equation (GDE) (Friedlander, 2000;Seinfeld, 1979, 1980) describes the time rate of change of size-dependent particle concentration and composition by such processes. Recent work has focused on understanding processes that affect growth rates (GRs) of freshly nucleated atmospheric nanoparticles (Smith et al, 2008(Smith et al, , 2010Riipinen et al, 2012;Hodshire et al, 2016;Kontkanen et al, 2016;Tröstl et al, 2016). This is important because a particle's survival probability increases with GRs (McMurry and Friedlander, 1979;Weber et al, 1997;Kerminen and Kulmala, 2002;Kuang et al, 2010).…”

“…For example, Kontkanen et al (2016) used simulations to show that discrepancies between measured GR based on appearance time (AGR) and GR based on irreversible vapor condensation (CGR) can be significant. (Note that GR true used in this paper differs from CGR in that GR true also incorporates evaporation.)…”