Particle Aggregation - Later Stages

Later Stages

As the aggregation process continues, larger clusters form. The growth occurs mainly through encounters between different clusters, and therefore one refers to cluster-cluster aggregation process. The resulting clusters are irregular, but statistically self-similar. They are examples of mass fractals, whereby their mass M grows with their typical size characterized by the radius of gyration R_g as a power-law

where d is the mass fractal dimension. Depending whether the aggregation is fast or slow, one refers to diffusion limited cluster aggregation (DLCA) or reaction limited cluster aggregation (RLCA). The clusters have different characteristics in each regime. DLCA clusters are loose and ramified (d ≈ 1.8), while the RLCA clusters are more compact (d ≈ 2.3). The cluster size distribution is also different in these two regimes. DLCA clusters are relatively monodisperse, while the size distribution of RLCA clusters is very broad.

The larger the cluster size, the faster their settling velocity. Therefore, aggregating particles sediment and this mechanism provides a way for separating them from suspension. At higher particle concentrations, the growing clusters may interlink, and form a particle gel. Such a gel is an elastic solid body, but differs from ordinary solids by having a very low elastic modulus.