Precursor aggregate distributions for particulate gels

We analyze the aggregation process leading to gel formation in colloidal dispersions under quiescent conditions in order to identify possible precursor aggregate distributions for particulate gels. The aggregation process is described with an experimentally validated population balance model, which allows us to calculate how the aggregate mass distribution evolves in time. When the cumulative occupied volume fraction of fractal aggregates reaches a certain limit, the random cluster-cluster aggregation regime crosses over to an interconnection regime, and a gel network forms. The aggregate distribution at the end of the aggregation regime is the precursor for the subsequently formed particulate gel. We demonstrate that, when aggregation proceeds fully in the reaction-limited regime, the precursor aggregate distribution depends only on the solid volume fraction while being insensitive to both the primary particle size and the stability ratio. However, the stability ratio is an important operating parameter controlling the overall aggregation and gelation time. The situation can be significantly changed by entering the diffusion-limited aggregation regime. The interplay among these various factors is illustrated through an example of the optimal design of the precursor aggregate distribution. Primary particle size, solid volume fraction, and stability ratio are used as design parameters, and the objective function is formulated in terms of specific requirements on the precursor cluster mass distribution. These requirements were determined on the basis of qualitative arguments about the relation between the precursor structure and the gel mechanical properties.