The role of fragmentation in defining the signature size distribution of diesel soot

The addition of fragmentation to the Schmoluchowski aerosol coagulation model significantly improves the prediction of the signature size distribution recently observed for light duty diesel exhaust particulate matter. Allowing fragmentation largely eliminates the asymmetric shape that is characteristic of self-preserving size distributions predicted by models that consider only coagulation and yields a very nearly lognormal distribution, in excellent agreement with diesel soot mobility size measurements. Interestingly, the addition of fragmentation does not really introduce any new adjustable parameters. The model assumes continuum dynamics, as appropriate for diesel engine combustion. The shape and width of the size distribution are independent of the overall fragmentation rate and only slightly dependent on whether the particles break into two equal pieces or pieces with a 2:1 mass ratio. Finally, the size dependencies of both the coagulation rate and the fragmentation rate are tied to the soot fractal dimension, which in agreement with the literature is chosen to equal 1.8.