Size distribution dynamics of fuel-borne catalytic ceria nanoparticles

Ceria-based fuel additives in diesel engines when dosed at above a certain concentration into the fuel have been shown to lead into bimodal exhaust particle size distributions in a previous study. In order to model this complex problem it is assumed that the soot aggregate size distribution (where each aggregate consists of individual primary particles) evolves fast toward a constant total surface area (determined by the “open” non-coalesced fractal aggregate morphology) and this surface represents a sink for the ceria nuclei. The latter undergo kinetic aggregation among them as well as are simultaneously scavenged by the soot particles. The mathematical model is formulated in terms of an aerosol population balance equation for the ceria particles. The governing parameter in the resulting dimensionless population balance equation is the ratio of the total surface area of the soot aerosol over the initial additive surface area. The latter is proportional to the total additive mass if the ceria critical nuclei are assumed to consist of one molecule, an appropriate assumption for high surface tension, metal oxides like ceria. The experimental results show that the critical additive concentration at the onset of the bimodal shape of the exhaust size distribution scales linearly with the exhaust soot mass fraction, hence the soot aggregates must have a quite “open” fractal structure in order for their total area to be proportional to their total mass. Although simple population balance models may provide some insight into the problem of interest, the experimental results show that models accounting for more complex interactions of additive and soot particles (potentially involving incomplete accommodation) must be investigated in the future.