Theoretical modelling of an infinitely dilute irreversibly aggregating suspension

Abstract

The structure factor of a coagulating monodisperse spherical suspension has been calculated by computer-simulation methods, assuming cluster–cluster and ballistic particle–cluster aggregation schemes, in both cases subject to the constraint of Smoluchowski kinetics and the Rayleigh–Gans–Debye (RGD) approximation. This is compared with earlier theoretical estimates and experimental data. The simulations can be parametrised using theoretical expressions first derived in polymer theory for a ‘blob’ model together with the concept of fractal packing. Good agreement is found for the radius of gyration, hydrodynamic radius and form factor by using a ‘blob’ size of 1.5 in all cases together with the appropriate fractal dimension obtained from the computer simulations (d_f= 1.9 for the cluster–cluster model and 3.0 for the ballistic model). It is noteworthy that this parametrisation extends right across the aggregation range from initial-pair aggregates to large clusters and therefore should prove of practical value in the modelling of kinetic studies of aggregation.