947
Simulation of Flotation Circuits Using a Model Derived from
First Principles
Mohit Gupta, Holden Lim, Aaron Noble, and Roe-Hoan Yoon
Center of Advanced Separation Technologies, Virginia Tech, Blacksburg, Virginia, USA
ABSTRACT: Fuerstenau (1957) showed that the flotation recovery of quartz reaches a maximum when the
collector-coated mineral particles have zero ζ-potentials. A few years later, Derjaguin and Dukhin (1961)
developed a model to show that the repulsive electrical double-layer (EDL) forces in wetting films constitute
kinetic energy barriers (E1) for bubble-particle interactions. Thus, these investigators were the first to recognize
that the surface forces in wetting films control the kinetics of bubble-particle attachment in flotations. Yoon
and Mao (1996) extended the concept by considering the role of attractive hydrophobic forces that can reduce
E1 and, hence, increase the kinetics. This approach has been extended further by considering the role of
hydrophobic forces in both the pulp and froth phase of a flotation cell to predict the grade vs. recovery curves
and to optimize flotation circuits (Huang et al., 2022 Gupta el al, 2023). A user-friendly computer simulator
has been developed for practitioners.
INTRODUCTION
Sulman and Picard (1905) were the first to disclose a method
of using air bubbles to selectively collect hydrophobic par-
ticles on the surface and rise out of an aqueous phase, leav-
ing hydrophilic particles behind (US Patent 793,808). The
process known as ‘forced air’ flotation is recognized as the
best available method of separating fine particles to produce
high-grade concentrates at high recoveries. In this process,
a target mineral (e.g., chalcopyrite) is rendered hydropho-
bic using a hydrophobizing agent called collector so that
the mineral particles can attach themselves to rising stream
of air bubbles. Thus, control of particle hydrophobicity is
critical for the separation process.
It is difficult, however, to model flotation using hydro-
phobicity—a thermodynamic property—as a parameter for
a kinetic process. It would be better to use the attractive
hydrophobic (HP) force to model the movement of hydro-
phobic particles toward air bubbles in wetting films (Huang
et al., 2022 Gupta &Yoon, 2024). There are two other
forces controlling particle movement, i.e., electrical dou-
ble-layer (EDL) and van der Waals (vdW) forces. However,
these forces are usually repulsive and, hence, are not con-
ducive to bubble-particle attachment. Fuerstenau (1957)
was the first to report that flotation recovery reached a
maximum under conditions of zero ζ-potentials, which led
Derjaguin and Dukhin (1961) to develop a model showing
that EDL forces create kinetic energy barriers (E1) to flota-
tion. Thus, flotation is driven by the HP force, which in
turn is closely related to contact angles (θ)—a measure of
particle hydrophobicity.
Many investigators took samples from an operating flo-
tation bank and analyzed them using a 2-D mineral libera-
tion analyzer to determine the size(i)-by-class (j) flotation
rate constants (kij) of various composite particles. Results
showed that the rate constants increased with surface libera-
tion, which was a simple manifestation of increased contact
angles at higher surface liberations (Jameson, 2012 Huang
et al., 2022). This finding has a significant implication for
Simulation of Flotation Circuits Using a Model Derived from
First Principles
Mohit Gupta, Holden Lim, Aaron Noble, and Roe-Hoan Yoon
Center of Advanced Separation Technologies, Virginia Tech, Blacksburg, Virginia, USA
ABSTRACT: Fuerstenau (1957) showed that the flotation recovery of quartz reaches a maximum when the
collector-coated mineral particles have zero ζ-potentials. A few years later, Derjaguin and Dukhin (1961)
developed a model to show that the repulsive electrical double-layer (EDL) forces in wetting films constitute
kinetic energy barriers (E1) for bubble-particle interactions. Thus, these investigators were the first to recognize
that the surface forces in wetting films control the kinetics of bubble-particle attachment in flotations. Yoon
and Mao (1996) extended the concept by considering the role of attractive hydrophobic forces that can reduce
E1 and, hence, increase the kinetics. This approach has been extended further by considering the role of
hydrophobic forces in both the pulp and froth phase of a flotation cell to predict the grade vs. recovery curves
and to optimize flotation circuits (Huang et al., 2022 Gupta el al, 2023). A user-friendly computer simulator
has been developed for practitioners.
INTRODUCTION
Sulman and Picard (1905) were the first to disclose a method
of using air bubbles to selectively collect hydrophobic par-
ticles on the surface and rise out of an aqueous phase, leav-
ing hydrophilic particles behind (US Patent 793,808). The
process known as ‘forced air’ flotation is recognized as the
best available method of separating fine particles to produce
high-grade concentrates at high recoveries. In this process,
a target mineral (e.g., chalcopyrite) is rendered hydropho-
bic using a hydrophobizing agent called collector so that
the mineral particles can attach themselves to rising stream
of air bubbles. Thus, control of particle hydrophobicity is
critical for the separation process.
It is difficult, however, to model flotation using hydro-
phobicity—a thermodynamic property—as a parameter for
a kinetic process. It would be better to use the attractive
hydrophobic (HP) force to model the movement of hydro-
phobic particles toward air bubbles in wetting films (Huang
et al., 2022 Gupta &Yoon, 2024). There are two other
forces controlling particle movement, i.e., electrical dou-
ble-layer (EDL) and van der Waals (vdW) forces. However,
these forces are usually repulsive and, hence, are not con-
ducive to bubble-particle attachment. Fuerstenau (1957)
was the first to report that flotation recovery reached a
maximum under conditions of zero ζ-potentials, which led
Derjaguin and Dukhin (1961) to develop a model showing
that EDL forces create kinetic energy barriers (E1) to flota-
tion. Thus, flotation is driven by the HP force, which in
turn is closely related to contact angles (θ)—a measure of
particle hydrophobicity.
Many investigators took samples from an operating flo-
tation bank and analyzed them using a 2-D mineral libera-
tion analyzer to determine the size(i)-by-class (j) flotation
rate constants (kij) of various composite particles. Results
showed that the rate constants increased with surface libera-
tion, which was a simple manifestation of increased contact
angles at higher surface liberations (Jameson, 2012 Huang
et al., 2022). This finding has a significant implication for