An agglomeration-based model for colloid filtration

This paper develops a model for colloid filtration which accounts for the possibility of aggregation of the colloidal particles in the aqueous phase. Depth-wise variation of liquid-phase colloid concentration, C(x), is measured experimentally in the presence of monovalent cations at different concentrations and divalent cations, which confirm that log of C(x) deviates significantly from linearity for all of the above cases. It is also observed that in all systems showing significant removal, preaggregation of the colloids is observed, which confirms the correlation between aggregation of colloids with their retention in saturated porous media, which has been reported earlier. A new model for depth filtration which is based on material balances of the different sized aggregates, which could be present in the colloidal dispersion, is developed. This resulting model, based on differential deposition rates for different sized aggregates, shows good match with the experimentally observed variation of C(x) with depth, for all of the above conditions. A method for estimating model parameters from data is developed. This model remains independent of the actual deposition mechanism, which could be secondary minima attachment of these colloidal aggregates or the entrapment of these colloidal aggregates in regions of confined geometry. This model can be extended to predict the transport of colloids in groundwater.