Master curves for aggregation and gelation : effects of cluster structure and polydispersity

A parametric study of the effects of cluster structure and polydispersity on the kinetics of aggregation and gelation is presented. The aggregation kinetics is described in terms of master curves characterizing the evolution of suitable dimensionless averages (measurable by light scattering) of the underlying cluster mass distribution (CMD), as a function of a suitable dimensionless time. Such master curves are shown to be dependent only on two dimensionless parameters: the cluster fractal dimension (d(f)) and the ratio between Brownian and shear aggregation rates (kappa). Shear aggregation of fractal clusters leads to higher-order moments of the CMD diverging to infinity in a finite time, which is usually called runaway. It is determined that the parameter space is split into two distinct regions: either where aggregates gel because of space filling before runaway occurs or where gelation occurs as a consequence of runaway. It is also determined that cluster polydispersity and the fractal dimension significantly affect the runaway and gelation times