Effect of microturbulence on bubble-particle collision during the bubble rise in a flotation cell

doi:10.1016/j.mineng.2020.106418

Minerals Engineering

Volume 155, 15 August 2020, 106418

https://doi.org/10.1016/j.mineng.2020.106418 Get rights and content

Highlights

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Microturbulence effect on bubble-particle collision during bubble rise is investigated.
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Asymmetry of water flow depends on turbulence intensity and bubble surface mobility.
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Negative effects of the turbulence on collision interaction are unexpected but justified.

Abstract

Holistically, air bubbles in flotation must rise to the top surface while free solid particles must settle to the cell bottom. Inside the stator-rotor space of the mechanical flotation cells, the turbulence of mixing can surpass the gravity-driven motion of the bubble-particle suspension. Outside the space, the bubbles rise to the surface, but it is not known how the turbulence affects the bubble-particle interaction during the bubble rise. Here we numerically investigate the effect of microturbulence on the bubble-particle collision during the bubble rise. The focus is on the interaction asymmetry caused by the inertial forces and bubbles with fully mobile (MBS) or immobile (IMBS) surfaces at intermediate bubble Reynolds number (Re). The Reynolds-Averaged Navier-Stokes equations with the RNG k-ɛ turbulence model are solved for the mean water flow. Its fluctuating components are predicted using the stochastic formulation that is adopted with the discrete phase formulation for determining the particle grazing trajectories. The results show microturbulence influences the bubble-particle collision interaction. The asymmetry of the collision interaction is also affected by the microturbulence intensity. Its negative effects are found for the CCA (the critical collision angle, which also affects the bubble-particle attachment) and the overall collision efficiency. These negative effects are unexpected because turbulence has been postulated to enhance the collision interaction. Numerical results agree with the MBS model for overall collision efficiency and show some significant deviations for the IMBS model. This paper provides a potential technique to examine the microturbulence effect on attachment efficiency via the CCA.

Graphical abstract

Asymmetry increases with Re, I and particle density.

Introduction

Flotation is a separation process of fine particles using air bubbles which are commonly used in the mining industry, wastewater treatment, and wastepaper deinking (Nguyen and Schulze, 2004, Rubio et al., 2002, Vashisth et al., 2011). It typically involves mixing a suspension of particles with air bubbles in a mechanically agitated cell. In this typical application in the mining industry, turbulence generated by mixing is critical to flotation (Schubert, 1999) as macroturbulence is used to control the dispersion of solid particles in the cell, while microturbulence controls the splitting of air into small bubbles and the bubble-particle interactions. Air is commonly supplied to the impeller at the cell bottom to produce small bubbles that collect hydrophobic particles and rise through the suspension and the froth phase to concentrate launder, while the hydrophilic particles do not attach to the bubbles, settle down by gravity to the cell bottom, where they are discharged. Given the strong mixing, turbulence can chaotically move the bubbles and particles, in particular, near the impeller zone, and the modeling of bubble-particle interactions in mechanical cells remains a challenge. Observations often show large-scale recirculation of water in the cell that is capable of entraining air bubbles and particles downward in large zones, in particular, near the cell center above the impeller. Far away from this central zone, the air bubbles rise together with the upward water recirculation to the pulp surface. The downward recirculation is detrimental to flotation and, therefore, the manufacturers of flotation cells have designed many special structures to minimize or eliminate the downward recirculation. The bubble rise in the upward recirculation zone to transport the hydrophobic particles attached to air bubbles is important to flotation; otherwise, hydrophobic particles that are collected by air bubbles would not be transported from the pulp phase to the froth phase. Likewise, the unattached (predominately hydrophilic) particles have to settle to the cell bottom; otherwise, there would not be the flotation selectivity. Since air bubbles rise to the pulp surface and particles settle to the cell bottom, there would be counter-motion between bubbles and particles in the direction of gravity in a flotation cell. However, it is less known how microturbulence influences the bubble-particle counter-motion and its interactions in flotation (Nguyen et al., 2016).

The bubble-particle interactions have been conventionally categorized into the collision, attachment, and detachment interactions (Nguyen and Schulze, 2004), and many works have shown that the collision and detachment interactions are affected by microturbulence (Nguyen et al., 2016, Liu and Schwarz, 2009, Liu and Schwarz, 2009). For example, the bubble-particle collision process is governed by the water flow and hence is expected to be influenced by turbulence. The detachment process is controlled by the so-called machine acceleration which is a representation of microturbulence (Xie et al., 2016, Ngo-Cong and Nguyen, 2020). The attachment is controlled by the particle hydrophobicity and the intermolecular forces and is not known to be affected by turbulence yet.

There are several models to predict the bubble-particle collision interaction in non-turbulent environments (Loglio et al., 2011), where the particle motion relative to the bubble is deterministic and its grazing trajectories around the bubble can be applied to determine the collision efficiency using the critical collision angle (CCA), $θ_{C}$ . It is the polar angle of the contact point between the bubble surface and the particle grazing trajectory as measured from the bubble-particle inter-center line. The CCA is also one of the key parameters of the flotation theory for predicting attachment efficiency (Nguyen et al., 2006, Nguyen and Nguyen, 2009, Nguyen et al., 1998).

There are several theoretical investigations of turbulent collision interactions in other fields outside flotation that include the collision between two identical air bubbles (Saffman and Turner, 1956, Pinsky et al., 1999, Franklin et al., 2005) and two identical particles (Abrahamson, 1975, Yuu, 1984, Zhou et al., 1998). The outcomes of these studies cannot be applied to the bubble-particle collision in flotation because the sizes and densities of mineral particles and air bubbles are different by at least one order of magnitude. Therefore, researchers have taken different approaches to modeling the bubble-particle turbulent collision in flotation. For example, Liu and Schwarz (Liu and Schwarz, 2009, Liu and Schwarz, 2009) investigated the bubble-particle collision in a turbulent flow employing a multiscale modeling approach. At the macro (cell) scale, they quantified complicated turbulent flows being influenced by many macroscopic parameters (the cell geometry and structure, impeller geometry/structure and speed, inlet and out fluid flow rates, the fluid properties, etc.) using a 3D computational fluid dynamics (CFD) model. Since there are numerous numbers of air bubbles and particles in the flotation cell which make a direct 3D numerical modeling of the bubble-particle collision in the turbulent flow impossible, the authors applied the bubble-particle (micro) scale modeling to describe the motions of bubbles and particles (in terms of the drag forces and the microhydrodynamics functions) and quantify the collision interaction. The authors also designed numerical experiments by employing the particle-tracking scheme to calculate the bubble-particle collision efficiency in a developed turbulent flow. In the numerical experiments, the bubble-slurry relative motion was considered due to buoyancy (upward motion) or turbulence (arbitrary direction), and the collision efficiency was determined by the ratio of actual collisions number to collisions expected based on the linear interception kinematics. It was shown that the turbulent bubble-particle collision efficiency with bubble surface effect (i.e., immobile bubble surface or IMBS) first increases with the turbulence energy dissipation rate, reaching a peak and then decreases (Liu and Schwarz, 2009). In the case of the mobile bubble surface (MBS), the turbulent collision efficiency was found to increase with the turbulence energy dissipation rate (Liu and Schwarz, 2009).

Recently, Ngo-Cong et al. (Ngo-Cong et al., 2018) applied the stochastic modeling approach to investigating the turbulent bubble-particle collision in the stator-rotor space of the mechanical cells. It is shown that microturbulence can increase collision efficiency, surpassing the effect of gravity on the collision interaction. This influence of turbulence on the collision interaction is not unexpected (but often neglected) and is in line with the numerical experiments (Liu and Schwarz, 2009, Liu and Schwarz, 2009). It also agrees with the fact that turbulence of mixing is often used to overcome the effect of gravity on settling and presents an efficient way to disperse solid particles in flotation.

In this paper, we have applied a combined approach to designing numerical experiments to study the effect of microturbulence on the bubble-particle collision during the bubble rise in a flotation cell. Specifically, we follow the traditional arrangement of the bubble-particle counter-motion, impose the microscale turbulent fluctuating motion of particles along their trajectories toward the bubble surface, and apply the multiscale modeling approach outlined in the recent publications (Liu and Schwarz, 2009, Liu and Schwarz, 2009). We solve the fluid flow problem at the macro (cell domain) scale using CFD and the bubble and particle dynamics at the bubble and particle microscales by employing various drag forces. Our collision modeling cannot describe the turbulent collision in the stator-rotor space of the mechanical cells, where the stochastic nature of flows is predominant. Away from the stator-rotor space, the modeling developed by Liu and Schwarz (Liu and Schwarz, 2009, Liu and Schwarz, 2009) is perhaps useful. Finally, further away from the flotation cell center, our model would be useful for describing the interactions in the upward recirculation flow which can be extended to the wall of flotation mechanical cells. Ideally, our model would fit describing the bubble-particle collision in flotation columns. Our special focus here is on the effect of microturbulence on the CCA, which is critical to the prediction of the bubble-particle attachment efficiency as discussed previously (We expect that this approach can help us quantify the effect of turbulence on the bubble-particle attachment interaction in flotation).

Regarding the hydrodynamics of the terminal bubble rise, it is noted that the water flow field around the bubble can only be described analytically for two cases, i.e., the Stokes flow (the bubble Reynolds number, Re, is close to zero) and the potential flow (Re is high) (Phan et al., 2003). For these flows, the water streamlines around the bubble are fore-and-aft symmetric, and the CCA is equal to 90° if the particles move with the water streamlines around the bubble (referred to as the interception collision). When Re < 10, the water flow around a bubble, known as the creeping flow, is dominated by viscous forces, and the streamlines around the bubble are nearly fore-and-aft symmetric. This symmetry decreases with increasing Re. Mathematically, the non-linear terms (due to the fluid inertial forces) of the Navier-Stokes equations produce the fore-and-aft asymmetry (FAA) of water streamlines around the bubble with intermediate bubble Reynolds numbers (Nguyen, 1999, Islam and Nguyen, 2019). In these cases, the streamlines are compressed toward the leading hemispherical surface of the bubble and are relaxed in the rear. In this case, the CCA by the interception mechanism is smaller than 90° as the contact point of the particle grazing trajectories with the bubble surface is shifted toward its leading pole. In addition to the fluid inertial forces (Dobby and Finch, 1986, Nguyen and Schulze, 2004), the FAA of the bubble-particle collision can be caused by the centrifugal force of the particle motion around the bubble (Dai et al., 1998) and the other inertial forces (Nguyen and Schulze, 2004, Ralston et al., 1999). It is noted that since the non-linear behavior of the Navier-Stokes equations cannot be derived by a linear combination of predictions for the Stokes and potential flows, the bubble-particle collision theories based on the linear combination to estimate the water flow around a bubble with intermediate Re (Yoon and Luttrell, 1989) cannot produce the FAA of the bubble-particle collision. The FAA aspect and the CCA of the bubble-particle collision interaction due to microturbulence is unknown in the flotation literature. Therefore, this paper aims to investigate how microturbulence influence bubble-particle collision during the bubble rise.

Section snippets

Computational model

We have adopted a multiscale approach to describing the turbulent water flow around the bubble at the macro scale using the CFD model, and the motion of particles and their collision interaction with the bubble at the microscale. We have applied the traditional arrangement of the bubble-particle counter-motion but considered the microscale turbulent fluctuating motion of particles along their trajectories toward the bubble surface. Analysis of such an arrangement has allowed us to quantify the

Asymmetry of water flow and collision interaction

The effect of water flow asymmetry on the bubble-particle collision is examined at the condition of extremely fine particle (i.e., R_p = 5 µm) with density is equal to the water density, $ρ = δ$ (i.e., the inertialess collision). Fig. 2 shows the trajectory of a particle around fully MBS and IMBS under turbulent conditions. For the MBS (Fig. 2a), a low fluctuation of the trajectory is observed for Re = 10 and 100. After that, the changes in the trajectory with increasing Re are less significant. For

Conclusions

The effect of microturbulence on bubble-particle collision with a fully MBS and a fully IMBS bubble during the bubble rise in the recirculation water flow outside the stator-rotor space of a mechanical flotation cell has been examined using the CFD method. The stochastic formulation is used with the discrete phase model to find the fluctuating grazing trajectory of the particle around the bubble, the CCA, and the overall collision efficiency of bubble-particle interaction at intermediate Re

CRediT authorship contribution statement

Md. Tariqul Islam: Methodology, Investigation, Validation, Writing - original draft. Anh V. Nguyen: Project administration, Supervision, Conceptualization, Methodology, Writing - review & editing.

Declaration of Competing Interest

The authors declared that there is no conflict of interest.

Acknowledgments

The authors acknowledge the Australia Research Council for financial support (Project numbers DP150100395 and DP190103459). We gratefully thank the anonymous reviewer for the detailed feedback and comments which greatly improved our paper.

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Effect of microturbulence on bubble-particle collision during the bubble rise in a flotation cell

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Computational model

Asymmetry of water flow and collision interaction

Conclusions

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgments

Chem. Eng. Sci.

J. Colloid Interface Sci.

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