Colloid generation/elimination dynamic processes: Toward a pseudo-equilibrium?

A mathematical model describing the evolution of a colloidal suspension over a colloid bed in a batch reactor is presented and tested experimentally. The model is based on population balance equations and takes into account the particle fluxes due to generation, diffusion, aggregation and sedimentation. These processes are combined with two novel processes of colloid creation. These are suggested by adding terms related to spontaneous diffusion from the colloid bed as well as a term reflecting generation by the impact of settling particles on the colloid bed. The effect of the second process is however very limited during the transient period and is absent when the pseudo-equilibrium is reached. The modelling of both generation and elimination mechanisms is performed until this pseudo-equilibrium is reached. The results are displayed on a size distribution scale determining the colloid population from a concentrated suspension with a colloid population deleting the large colloids by sedimentation. Alternatively, the description of the model may be carried out from a depleted colloid suspension which reaches similar pseudo-equilibrium by small colloid generation via spontaneous diffusion from the bed. The model was applied to Clay Suspensions in batch experiments carried out in generation or sedimentation mode and in the groundwater system. In laboratory hydrogeological systems, the colloid size normalised concentration reaches values of the order of 10(-7) ml(-1) min(-1) for attachment values of 10(-G) and for colloid sizes of 50 nm, 10 cm over the colloid bed. The small colloids (similar to 10 nm) are more generated than the large ones (similar to 1000 run) that may be faster eliminated, however, some aggregates survive in the suspension because of lower density than the bulk colloids due to their gel like structure. (c) 2008 Elsevier B.V. All rights reserved.