Aggregation and Sedimentation of Fine Solids

Abstract

In many applications, it is desired to separate unwanted fine particulates from a liquid by gravity settling. An efficient separation, however, will be feasible only if a combination of aggregation and sedimentation occurs. To understand the kinetics of such a process, a mathematical model that accounted for aggregation and sedimentation was developed. The simulation was based on Smoluchowski’s equation of population balance, with the collision frequency determined by Brownian motion and differential settling, while treating the aggregates as fractal objects as the particles collide and aggregate. One of the most important issues here is that aggregating systems, especially those encountered in particle technology and separation processes, often involve non-uniform particle distributions. Situations with evenly distributed aggregates are very rare in practice, but this continues to be the “default assumption” in many theoretical treatments. This study addressed this issue by developing a series of experiments and numerical model to properly account for non-uniform particle sizes and their spatial variations. Our results showed that the rate of settling could be improved significantly if the particles aggregated (the settling time may be reduced from hours to minutes). Experimentally, we showed that, depending on the strength of interaction between the particles, different settling regimes were observed. It was also observed that under certain experimental conditions, an initial ‘induction time’ appeared before the apparent onset of sedimentation. It appears that the particles required some ‘waiting time’ before commencement of aggregation. Our simulations showed that the observed ‘induction period’ may in fact be a kinetic phenomenon that was independent of the nature of the inter-particle forces (i.e. on the microscopic scale, the particles began to aggregate immediately without any delay). Our simulation showed that inter-particle attraction could significantly affect the rate of aggregation and sedimentation. Larger attractive forces also resulted in a perceptible clear liquid-suspension interface; as such forces diminished, the clear liquid-suspension interface became more diffuse and eventually appeared as a gradual concentration gradient. A novel approach was used to predict formation of this ‘mud line.’ We have also demonstrated that sedimentation kinetics are largely insensitive to the initial particle size distribution; an explanation for this observation is discussed.