Ballistic aggregation

Void [52] developed a variety of ballistic deposition models to simulate sedimentation processes. Void used ballistic models to determine deposition densities for spherical particles which traveled via vertical paths and were deposited on horizontal surfaces. Recently, Schmitz et al. [53] used a ballistic aggregation model to describe particle aggregation at the surface of a crossflow microfiltration membrane. Schmitz and co-workers were able to account for interfacial forces empirically, and demonstrated the influence of physical and chemical variables on the resulting morphology of the fouling deposits (such as aggregate density variation with depth, and influence of shear flow and re-entrainment properties on fouling deposit density and porosity). 

Clusters resulting from a ballistic cluster-cluster aggregation process, where... 

However, it is not quite clear whether this relation can be applied for non-Euclidean, ramified structures. Simulation results of carbon black formation under ballistic conditions by Meakin et al. [14] indicate that a scaling equation is fulfilled, approximately, between the number of particles Np in a primary aggregate and the relative cross section area A/Ap ... 

Figure 14. Extinction and scattering spectra for ballistic RF aggregates with different conjugate numbers N = 1-100. All data are averaged over random orientations (T-matrix method) without statistical averaging. Parameters of conjugates are the shell thickness and refractive index s = 2.5 nm, =1.40, respectively, the gold core diameter <7 =15 nm (a,b) and 60 nm (c,d).

Grzegorczyk, M. Rybaezuk, M. and Maruszewski, K. Ballistic aggregation an alternative approach to modeling of silica sol-gel structures Chaos, Solitons and Fractals, 19, 1003-11,2004. 

Meakin, P. and Jullien, R. (1988). The effects of restructuring on the geometry of clusters formed by diffusion-limited, ballistic and reaction-limited cluster-cluster aggregation. J. Chem. Phys., 89, 246-250. 

Jullien, R. and Meakin, P. (1989). Simple models for the restructuring of 3-dimensional ballistic aggregates. J. Colloid Interface Sci., 127, 265-272. 

Ballistic aggregation (Figure 7.10c). This is similar to DLA but the incoming monomers that are trapped by the cluster do not follow a Brownian path but straight lines. The agglomerate that results is a bit more porous than in the case of RLA but it is not fractal the dimension of the cluster is d (3 in space and 2 on a flat screen). 

For a realistic modelling of primary carbon black aggregates by ballistic cluster-cluster aggregation with rff= 1.9 and /)= 1.3, they came out with the following mathematical expression ... 

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