Spatial Modeling of Formation of Gel

Abstract

Understanding and predicting colloidal interaction is important in a variety of applications. In this study, we investigate aggregation dynamics of colloidal silica by generating simulated structures and comparing them to experimental data gathered through scanning transmission electroscopy (STEM). More specifically, diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA) models with different functions for the probability of particles sticking upon contact were used. Aside from using a constant sticking probability, the sticking probability was allowed to depend on the masses of the colliding clusters and on the number of particles close to the collision. It was found that in comparison to using a constant sticking probability, both the mass-dependent and neighbordependent sticking probability improved the goodness-of-fit of spatial summary statistics when the simulated data were compared to the experimental data. The models were also compared based on fractal dimensions. Both in terms of goodnessof- fit for the summary statistics and the fractal dimension, the structures generated with a neighbor-dependent sticking probability were the most similar to the experimental data. This model was further analyzed by conducting global envelope tests based on the spatial summary statistics. The tests showed that although the summary statistics are similar for the simulated and experimental structures, there are also systematic deviations. Structures generated with the same model were also compared with the STEM data by simulating flow and diffusion. From this analysis, it was seen that the permeability and the geometry factor of the simulated and experimental structures were relatively similar.