Modelling of floc-bubble aggregate rise rates in dissolved air flotation

The use of relatively simple, but conceptually sound mathematical models, is a powerful tool to identify and understand parameters that are critical to a process. In this paper, a model is presented which addresses the rise rate of floc-bubble aggregates in the DAF separation zone. The model uses Stoke's Law as a point of departure, which is then progressively extended to incorporate the non-sphericity of the aggregates, the non-laminar nature of their movement, the fractal nature of the flocs, the physical constraints of attaching bubbles to a floc, and the limit on bubble numbers imposed by a typical air dosing system. The main findings are: There are two distinctly different DAF domains, namely a small floc domain and a large floc domain. In the small floc domain, the bubble size, the air volume, chemical dosing and the degree of flocculation have to be optimized and accurately controlled, while the large floc domain is less sensitive to these parameters. The calculated rise rates are significantly lower than some of the latest pilot testing results reported from the USA; a surprising finding at first. There are, however, numerous modelling simplifications that may explain this discrepancy. The most probable reasons are the further agglomeration of the aggregates in the separation zone due to differential rise rates or the recirculating flow within the white-water blanket, and the complex and poorly understood flow patterns within the separation zone.