Influence of Energy Dissipation on the Efficiency of Air Flotation: Analogy with Flocculation
Dissolved air flotation units are generally designed on the basis of two parameters: the mA/mS ratio of the air mass to the solid mass in reaction, and the contact time between the gas phase and the solid phase. The insufficiency of this approach, which neglects energy dissipation, is demonstrated. Five units, the efficiencies of which were quantified by turbidimetry, were operated with a bentonite suspension previously flocculated with WAC or ferric chloride. Batch flotator 1 was a commercial unit designed to evaluate flotation feasibility (Fig.1). Flotators 2 and 3 were used to establish flotation efficiency as a function of the mA/mS ratio in continuous operation (Figs. 2 and 3). The influence of contact time was determined with batch flotator 4 (Fig. 4). Continuous flotators 3 and 5 were identical rectangular reactors but the latter was designed to allow the injection of pressurized water through five different points (Fig. 3). Turbidity abatement increases as a function of mA/mS, reaching a plateau, the curve having a classical sigmoidal shape in batch or in continuous operation (Fig. 5). However the important air requirement (mA/mS=1) to attain 70% abatement would hamper industrial applications. The contact time is the residence time of the gas phase through a batch cell or the residence time of the solid phase through a continuous flotator. Its influence is displayed in Fig. 6 where a sigmoidal curve shows that a 100 second contact time is required to reach a significant abatement even with a low mA/mS of 0.1. However, flotator 3 operated with a 108 second contact time and 0.1 mA/mS ratio afforded only 40% abatement (Fig. 7). Efficiency is not therefore determined by the two classical parameters only but also by energy dissipation. The energetic conditions can be quantified by velocity gradient measurements, of classical use in flocculation; this parameter is 3100 s-1 in flotator 3 and between 590 and 1670 s-1 in flotator 4. Flotation kinetics are classically considered first-order with respect to the particle concentration (Eqn. 3). In fact there is an analogy between flotation and flocculation which allows one to extend the well-known flocculation kinetics (Eqn. 4) to the flotation process (Eqn. 5). The steadiness of the bubble concentration permits the derivation of Eqn. 6, which enables one to calculate the efficiency of a batch or a plug-flow reactor as a function of the Camp number Gt (Eqn. 9). In fact there is an optimum range of velocity gradients between 3000 and 4000 s-1 and an optimum range of Camp number between 105 and 106 (Fig. 9). The difference with the range currently observed in flocculation could be explained by the contact efficiencies in each process and by the probable existence of two ranges of optimal conditions. The model accuracy can be verified and the rate constant calculated (Figs. 8 and 10). This approach should be extended by testing particles exhibiting different degrees of hydrophobicity.