A simple sticking probability model is used for deducing a kernel capable to describe the kinetics of computer-simulated irreversible aggregation processes. Not only the diffusion-and reaction-limited aggregation regimes were fitted but also the whole transition region. The deduced kernel establishes λ = 0 for the entire range of sticking probabilities and helps to understand how irreversible cluster-cluster aggregation works.

In order to form magnetic filaments or chains, aqueous suspensions of superparamagnetic colloidal particles were aggregated under the action of an external magnetic field in the presence of different amounts of an indifferent 1:1 electrolyte (KBr). This allowed the influence of the anisotropic magnetic and isotropic electrostatic interactions on the aggregation behavior of these electric double-layered magnetic particles to be studied. Dynamic light scattering was used for monitoring the average diffusion coefficient of the magnetic filaments formed. Hydrodynamic equations were employed for obtaining the average chain lengths from the experimental mean diffusion coefficients. The results show that, for the same exposure time to the magnetic field, the average filament size is monotonously related to the amount of electrolyte added. The chain growth behavior was found to follow a power law with a similar exponent for all electrolyte concentrations used in this work. The time evolution of the average filament size can be rescaled such that all the curves collapse on a single master curve. Since the electrolyte added does not have any effect on the scaling behavior, the mechanism of aggregation seems to be completely controlled by the dipolar interaction. However, electrolyte addition not only controls the range of the total interaction between the particles, but also enhances the growth rate of the aggregation process. Taking into account the anisotropic character of these aggregation processes we propose a kernel that depends explicitly on the range of the dipolar interaction. The corresponding solutions of the Smoluchowski equation combined with theoretical models for the diffusion and light scattering by rigid rods reproduce the measured time evolution of the average perpendicular aggregate diffusion coefficient quite satisfactorily.

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