Elsevier

Minerals Engineering

Volume 159, 1 December 2020, 106607
Minerals Engineering

A new paradigm of bubble-particle detachment interaction: How and where do the bubble and the particle detach?

https://doi.org/10.1016/j.mineng.2020.106607Get rights and content

Highlights

  • A new paradigm of the bubble-particle detachment is discovered.

  • Bubble and particle do not detach at their triple contact line.

  • Detachment occurs at capillary neck of air-water interface near solid surface.

  • Detachment always leaves tiny residual volume of air on solid surface.

  • It contradicts traditional theories, urging further investigations.

Abstract

The flotation of coarse in particular partially liberated particles has attracted both industry and research interests in recent years as it can bring several benefits to existing operations, including the decrease in grinding energy and media consumption, the increase in plant throughput, and environmental benefits. The bubble-particle detachment is critical to this flotation process. Here, we have investigated the physics underlying the bubble-particle detachment and discovered a new paradigm, i.e., the bubble and particle do not detach at the three-phase gas-liquid-solid contact (TPC) line between the bubble and the particle, which contradicts the conventional consideration in the available theories. Our high-speed video movies show that the bubble-particle detachment does take place at a capillary neck of the air-water interface near the solid surface. The detachment always leaves a tiny residual volume of gas on the solid surface. Our experiments also show that the detachment interaction does not simply follow the slip mode of the TPC motion but rather a combined slip-stick mode of the TPC line relaxation. We rationalize our observations by considering the contact angle hysteresis, which always exists on the real particle surfaces having morphological roughness and chemical heterogeneity. The new evidence challenges the existing theories about the bubble-particle detachment interaction in flotation and urges further investigations to overcome the inconsistent predictions.

Introduction

Flotation is a key separation process that has been used in the mining industry for over a century and continues to be an essential technology for maintaining production efficiencies as ore quality declines (Fuerstenau et al., 2007, Nagaraj and Farinato, 2016). Flotation separates wanted minerals from unwanted ones (gangue) using air bubbles. Hydrophobic particles attach to air bubbles and are lifted to the surface of the pulp phase where they are collected as a concentrate, leaving hydrophilic particles settling to the cell bottom to be discharged as tailings. Crucial parameters determining the efficiency of flotation separation are the size, surface morphology, and chemistry of the particles. Conventional flotation is efficient only for fully liberated minerals having sizes between 20 and 70 μm (Gontijo, 2007, Jameson et al., 2007, Jowett, 1980). In the copper mining industry, for example, the ores containing typically 1% copper and 99% gangue have to be milled to around 50 μm to fully liberate copper for conventional flotation. Mineral liberation accounts for the largest part of the energy consumption in flotation (Curry et al., 2014). Consequently, significant research efforts have recently focused on coarse composite particle flotation which does not require fully liberated minerals and therefore greatly reducing the energy consumption while significantly increasing the plant throughput (Jameson et al., 2020, Jameson and Emer, 2019). However, coarse composite particle flotation differs from conventional flotation in a few aspects that the uneven (composite) surface morphology and chemistry of coarse particle surfaces become critical factors affecting bubble-particle aggregation and stability.

Generally, only those particles that adhere strongly to air bubbles are lifted to the froth surface and become floated. The bubble-particle adhesion and detachment can be analysed based on a classical geometry of the bubble-particle aggregate as depicted in Fig. 1. This model was developed in the 1930s (Gaudin, 1939) and then having been extended to various variants to suit specific conditions (Nguyen et al., 2016, Nguyen and Schulze, 2004, Wang et al., 2016b). Even though, the original model still serves as a standard one for studying bubble-particle aggregation.

The bubble-particle aggregation is supported by many forces including the capillary force, which is of paramount importance. The force is proportional to the water-air surface tension, σWA, and the wetting perimeter of the bubble-particle contact, 2πrsinα, as per Fig. 1. The vertical component of the capillary force, F, can hold the particle adhered to the bubble surface during its rise to the froth surface. We obtain the following prediction for the supporting force (Gaudin, 1939):F=2πrσWAsinαsinθ-αwhere θ is the contact angle as described in Fig. 1. Eq. (1) shows that the supporting force is not constant but does change with the three-phase contact (TPC) between the bubble and the particle, as characterised by the half apical angle, α, shown in Fig. 1. Indeed, Gaudin (1939) analysed the supporting force mathematically and showed that the force has a maximum at αm=θ/2 which is mathematically defined as follows:dFdαα=αm=0αm=θ2

A fuller analysis by considering the bubble radius, rb, shows that the critical angle is still significantly dependent on the contact angle as per the following equation (Nguyen, 2003, Nguyen and Schulze, 2004):sinθ-2αm+rbrL2-rrbsin2αm+OrL2=0where L is the capillary length (L=2.71mmfor a clean water-air interface) and the symbol O... describes the order of magnitude of the cut-off terms.

Eq. (2) constitutes the foundation of the bubble-particle aggregate stability as founded by Gaudin, advanced by many researchers, and has been the cornerstone of the modern flotation theory. It is mathematically correct. However, it does require the satisfaction of two key conditions, namely,

  • (1)

    The function Fα must be continuous (smooth) for determining the first derivative (Otherwise, the derivative does not exist), and

  • (2)

    The contact angle must be independent of α, i.e., the TPC position on the particle surface.

Meeting these two key conditions in practice can be a big challenge as the physics of the wetting and dewetting processes and the relaxation of the TPC lines on real solid surfaces significantly deviates from the mathematics. The contact angle is known to be a multiple-value variable, ranging from the receding contact angle (the minimum value) to the advancing contact angle (the maximum value) on morphologically and chemically heterogeneous solid surfaces (Chau et al., 2009, Eral et al., 2013, Feng and Nguyen, 2017). For instance, the distribution of contact angle on spherical glass particles attached to a flat air-water interface can follow the Gaussian normal distribution, changing linearly with α, and, therefore, has to be considered when taking the derivative as described by Eq. (3) (Feng and Nguyen, 2017). The slip-stick mode of the TPC line motion on solid surfaces is rather more common than unique in reality and does not warrant the satisfaction of the mathematical condition of the continuity for the first derivative. Due to the slip-stick motion of the TPC lines, the apical angle may not be a continuous variable since the TPC lines may not slide smoothly over the particle surface. Instead, the significant effect of the pinning of TPC line at the crystal edges on the particle and topologically rough surfaces on the supporting force has been recently evidenced (Ally et al., 2012, Feng and Nguyen, 2016, Gautam and Jameson, 2012, Pitois and Chateau, 2002). These physical conditions become more pronounced in the flotation of coarse and/or composite particles which have greater surface roughness and chemical heterogeneity. Therefore, addressing this gap in the literature is of profound importance for both theoretical development and applications of flotation. Significantly, the consequence of violating the two key mathematical conditions and the deviation from the real physics of dewetting and wetting on mineral surfaces from the mathematics of the existing bubble-particle stability/detachment theory has raised several important questions. One of them is “How and where do the bubble and the particle detach?”

Here, we have conducted special experiments and provide experimental results and evidence obtained by high-speed video microscopy to address the key fundamental question about the actual bubble-particle detachment. A new paradigm has emerged, showing that the bubble-particle detachment does not occur at bubble-particle contact points as traditionally theorised. The detachment happens at the capillary neck of the air-water interface near the solid surface. We argue that the available models while being mathematically valid, appear to be deficient for capturing the physics of the bubble-particle detachment interaction. Further investigations to overcome the deficiencies are urgently needed.

Section snippets

Experimental details

Fig. 2 shows two experimental setups with high-speed video microscopy to probe the bubble-surface and bubble-particle detachment interactions. The bubble detachment from the inclined solid surface in the first setup provides great details of the detachment but can be argued for being far away from mineral flotation. Therefore, the second setup for investigating the detachment between a bubble and a particle is used to confirm the key findings of the experiments using the first setup.

Bubble detachment from planar surfaces

Fig. 3 shows sequential images of an air bubble (100 μL) interacting with and detaching from a hydrophobic silicon wafer surface. Thousands of sequential images are generated by one single experiment. Therefore, only selected images are presented in Fig. 3. At the beginning (φ=0), the bubble has an axisymmetric shape with a contact angle of θ = 110° on the surface. As the inclined angle (φ) increases, the bubble starts deforming and sliding upward on the surface. A neck is formed at an

Conclusions

We have shown a new paradigm of bubble-particle detachment interaction. Three novel findings have been presented in this paper. Firstly, the motion of the three-phase contact (TPC) line during bubble-particle detachment interaction does not simply follow a continuous slip mode as conventionally assumed. Instead, it follows a combined slip-stick mode. Secondly, the bubble detaching the solid surface (or the particle) through forming and subsequently rupturing a capillary neck at the air-water

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors acknowledge the Australia Research Council for financial support (Project numbers DP150100395 and DP190103459).

References (24)

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1

Current addresses: Department of Physics at Interfaces, Max Planck Institute for Polymer Research, 55128 Mainz, Germany.

2

Current addresses: Hatch, 61 Petrie Terrace, Brisbane, QLD 4000, Australia.

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