Size and Fractal Dimension of Colloid Deposits in Model Porous Media

Colloids exert significant influence on subsurface hydrology, geochemistry, and microbiology. In particular, colloid deposits reduce permeability, triggering a reduction or realignment of flow. Since many subsurface processes are transport-limited, this reduction or realignment of flow, in turn, influences numerous chemical and biological processes. This work explores a conceptual model linking permeability with colloid deposit morphology, where deposit morphology is quantified by two metrics of the colloid deposit: (1) characteristic size and (2) fractal dimension. These two metrics are measured using static light scattering (SLS) within refractive index matched (RIM) porous media, into which a suspension of 100 nm carboxylate-modified polystyrene microspheres are eluted at constant flow. Scattering data are fitted with a two-parameter model that includes deposit fractal dimension, and with a three-parameter model that also includes deposit size. For each set of scattering measurements, the appropriate model is selected using the Akaike information criterion, and model errors are estimated using the bootstrap with 100 replicates. Results indicate two key findings. First, fractal dimensions generally decrease with time as additional colloids are eluted into the column, indicating a transition from more uniform to more dendritic deposits. Second, permeability reduction is associated with colloid deposits having smaller fractal dimensions, that is, with more dendritic and space-filling deposits. Modeling efforts are currently underway to correlate permeability with the underlying hydrodynamic and geochemical variables that determine colloid deposit morphology.