10th International Aerosol Conference September 2 - September 7, 2018 America's Center Convention Complex St. Louis, Missouri, USA
Abstract View
Fragmentation of Synthetic Fractal-like Agglomerates via Random Binary Scission
Lorenzo Isella, Anastasios D. Melas, Margaritis Kostoglou, YANNIS DROSSINOS, European Commission, Joint Research Centre
Abstract Number: 472 Working Group: Aerosol Physics
Abstract Particle transport depends sensitively on the particle size distribution and its time evolution via, for example, coagulation or agglomeration and fragmentation. Whereas the dynamics of particle agglomeration, driven, for example, by thermal motion, and the structure of the resulting agglomerates have been extensively studied, the fragmentation of fractal-like agglomerates has not received adequate attention.
We consider morphology-dependent linear fragmentation of synthetic fractal-like agglomerates. Loop-less, power-law agglomerates were generated by a modified tunable cluster-cluster aggregation algorithm that generates agglomerates of specified fractal prefactor and dimension, composed of arbitrary number (size) of spherical, identical, and point-touching monomers.
The simulated fragmentation process is based on mapping the initial agglomerate onto a symmetric adjacency matrix. The adjacency matrix is constructed from all the monomer-monomer Euclidean distances: monomer-monomer links (bonds) are represented by one and the absence of a link by a zero. The binary adjacency matrix, as suggested by graph theory, may be used to determine the connected components (fragments) of a structure. Given the adjacency matrix associated with an agglomerate, a link is randomly removed, according to a uniform probability distribution. The connected components of the resulting structure are determined. If the initial agglomerate fragments, the sizes of the fragments are stored. Only one link is removed per agglomerate, no multiple fragmentation events were considered.
We generated clusters of fractal prefactor 1.3 and variable fractal dimension (1.6, 1.8, 2.1). Their number and size varied from generation 4 clusters (83 to 110 monomers) to generation 7 clusters (730 to 810 monomers) for a total of approximately 400,000 clusters per fractal dimension. We numerically determined the size distribution of the fragments arising from the fragmentation of an initial N-monomer cluster. We found that the fragment size distribution peaks at the smallest (one monomer) and largest (N-1 monomers) fragments: a symmetric U-shaped fragment size distribution was observed.
The modelled fragment size distribution must obey two (inter-related) conservation laws. Mass conservation requires that the sum of monomers in the fragments must equal the number of monomers in the initial agglomerate. Moreover, the expected number of clusters arising from the binary fragmentation of an agglomerate should be two, and their distribution symmetric.
The fragmentation kernel was expressed as the product of the fragmentation rate of an initial agglomerate of size y times the fragment size distribution, i.e., the distribution of particles of size x arising from the break up of a particle of initial size y. For the time-independent fragmentation mechanism we considered, the fragmentation rate was taken to be constant, rendering the fragmentation kernel proportional to the fragment size distribution.
We modelled the homogeneous fragmentation kernel as the properly normalized product of the Brownian coagulation kernel of two fractal-like agglomerates times the beta distribution. The beta distribution models the product of fragment sizes x(y-x) raised to a (negative) power. The proposed empirical fragmentation kernel compares favourably well with the numerical fragment size distribution and with previously proposed U-shaped fragmentation kernels. The effect of the morphology of the initial agglomerate, as described by its fractal dimension, was also studied. We found that the straight-chain limit, uniform fragment size distribution, is reached only for fractal dimensions very close to unity.
A.D. Melas was supported by the Horizon 2020 E.U. Framework Programme SUREAL-23, Project - GA No: 724136