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The incorporation of particle inertia into the usual mean field theory for particle aggregation and fragmentation in fluid flows is still an unsolved problem. We therefore suggest an alternative approach that is based on the dynamics of individual inertial particles and apply this to study steady state particle size distributions in a 3-d synthetic turbulent flow. We show how a fractal-like structure, typical of aggregates in natural systems, can be incorporated in an approximate way into the aggregation and fragmentation model by introducing effective densities and radii. We apply this model to the special case of marine aggregates in coastal areas and investigate numerically the impact of three different modes of fragmentation: large-scale splitting, where fragments have similar sizes, erosion, where one of the fragments is much smaller than the other and uniform fragmentation, where all sizes of fragments occur with the same probability. We find that the steady state particle size distribution depends strongly on the mode of fragmentation. The resulting size distribution for large-scale fragmentation is exponential. As some aggregate distributions found in published measurements share this latter characteristic, this may indicate that large-scale fragmentation is the primary mode of fragmentation in these cases.

The cellular automaton model is used to simulate diffusion and aggregation with dissociation of point particles in 2D. A continuous phase transition is found that separates creation of compact aggregates and fractal ones. The transition is the function of pair-interaction energy ($E_b$), type of neighborhood and temperature $T$. Manifestations of the transition in real physical systems are discussed.