Population Balance Modelling of Colloidal Aggregates in Laminar Shear Flow
Creators: Andrade Rossi, Ricardo
Publisher: name: University of Alberta Library
Year: 2023

<p>Shear-induced aggregation is an important process in the solid-liquid separation of colloidal particles, i.e., solid particles in the micron size range. In this process, the solid particles are mixed with chemical destabilizers in shear flow to induce the formation of aggregates or flocs, which are easier to separate than individual particles due to their larger size. Depending on the shear rate of the system, the hydrodynamic forces acting on flocs can break them into smaller fragments or induce their restructuring, which leads to the formation of small compact flocs. Aggregate breakage is an undesirable process because it decreases the efficiency of industrial solid-liquid separation systems. In order to prevent floc breakage and enhance the control of the final aggregate size and structure from shear-induced aggregation, it is crucial to quantitatively understand the restructuring and breakage mechanisms in shear flows. Therefore, the objective of the present work is to investigate the breakage and restructuring of populations of aggregates in laminar shear flow via a statistical approach.</p>

<p>A population balance model (PBM) was developed to predict the evolution of the average aggregate size, the floc size distribution, and the morphology of populations of aggregates from breakage experiments that were conducted in a previous study (Gustavo Cifuentes, Aggregate Breakage in Laminar Couette Flow, 2022). These experiments were performed in a Taylor-Couette cell at laminar flow conditions. The aggregates were composed of 2 μm latex spheres, and they were formed in a neutrally buoyant fluid-particle system at a shear rate of 17.6 s-1. Then, the breakage and restructuring of aggregates were facilitated by doing a step increase in the shear rate to values ranging from 28.9 s-1 to 86.8 s-1.</p>

<p>The current work focused on modelling the behaviour of floc populations after the step increase in the shear rate from Cifuentes&#39; breakage experiments. The results from this work proved that the breakage and restructuring of aggregates in laminar flow can be modelled via PBM. It was observed that the shear-induced breakage mechanism of relatively compact aggregates (Df &gt; 2.2) is non-uniform, i.e., fragments of different sizes have different probabilities of occurring. Additionally, the scaling exponent from the aggregate strength power-law relationship was proved to be equal to 0.5. The critical shear rate G<em>{b,i} required to break an aggregate of size R</em>{g,i} was shown to scale with the floc population Reynolds number at steady-state. This relationship can be used to estimate the fitting parameter B of the breakage kernel in PBM simulations. Regarding the modelling of floc collisions, it was noticed that floc permeability must be considered in order to produce accurate predictions of the floc size distribution. Lastly, the initial aggregate restructuring after the step increase in shear rate from Cifuentes&#39; experiments can be assumed to be instantaneous, i.e., it occurs much faster than the observed time scale and measurement sampling time. This assumption allows the PBM to model the long-term floc restructuring and to produce better predictions of the evolution of average floc size and size distribution over time for different shear rates.</p>