Toward a Multiphase Local Approach in the Modeling of Flotation and Mass Transferin Gas-Liquid Contacting Systems

Abstract

This chapter comprises two major parts: The first part is devoted to the development of a kinetic model of flotation based on the theory of mass transfer in gas liquid bubbly flows. The second part presents some requirements in order to go forward in implementing multiphase local approach in the modeling of flotation and mass transfer in gas-liquid contacting systems. The common kinetic models applied to the flotation process are first order and they are validated on the basis of experimental analysis. Classical kinetics model of flotation cannot represent the bubble carrying capacity because their solution supposes that for long contact time, the concentration of the slurry have to vanish whatever the rate of the superficial bubbles loading may be. The bubble carrying capacity, which can be interpreted as a superficial saturation of the bubbles, cannot be represented by simple first order models. However, saturation phenomena have been observed in some flotation devises. For example the experiments of the flotation column of Bensley et al., (1985) show that, for a given flux of bubbles, the recovery of particles in the slurry may still be constant at a relatively low value whatever the height of the flotation column may be. This is similar to what it happens in common gasliquid mass transfer devices. Gas-liquid mass transfer theory indicates that the flux of mass through the gas-liquid interface is proportional to the gas-liquid contact area. It indicates also that the resistance to the interfacial transfer of low solubility gases may be described by a first order kinetics law where the main variable is the difference between the local concentration of the gas in the liquid and the concentration at saturation in the same thermodynamic conditions. For long contact time, this difference vanishes: the mass transfer is stopped up when the concentration of saturation in the liquid is reached. A kinetic model inspired from the theory of mass transfer in gas liquid medium is presented. This model, developed to describe flotation in a bubble column, is interpreted with regard to the effect of the superficial saturation of the bubbles on the kinetics of flotation. The second part of the chapter is devoted to local analysis and modeling of gas-liquid turbulent flows. The local description of gas-liquid contacting systems (average velocity, turbulence, void fraction etc.) represents an important scientific challenge and creates a