Mathematical modelling of the flotation deinking process

The overall flotation deinking process can be divided into four basic microprocesses: 1.(1) collision or capture of an (ink) particle by an air bubble 2.(2) adhesion of an (ink) particle to the air bubble by sliding 3.(3) development of a three-phase contact at the air bubble/water/particle interface, and 4.(4) bubble/particle stability or instability after an aggregate is formed each of these microprocesses have an associated probability that they will occur successfully in a flotation cell. In this paper, the associated probabilities of each microprocess are employed in the development of a kinetic- or population balance-type model of the overall flotation process. The overall model contains two kinetic constants: the first, k"1 governs the overall probability of a free ink particle successfully intercepting and adhering to an air bubble; the second, k"2 is a measure of the probability that a bubble/particle aggregate pair will become unstable and split to yield a ''new'' free ink particle. The solution to the kinetic model is presented in terms of k"1 and k"2, which are themselves functions of system parameters such as bubble and particle physical properties (e.g., diameter, density), fluid properties (e.g., viscosity, surface tension), etc. From this solution, a definition of a theoretical flotation efficiency, as well as other system performance parameters are presented.

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