Application of Depletion Attraction in Mineral Flotation: II

minerals

Article Application of Depletion Attraction in Mineral Flotation: II. Effects of Depletant Concentration

Gahee Kim 1, Junhyun Choi 1, Sowon Choi 1, KyuHan Kim 2, Yosep Han 1 , Scott A. Bradford 3, Siyoung Q. Choi 4,* and Hyunjung Kim 1,3,*

1 Department of Mineral Resources and Energy Engineering, Chonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju, Jeonbuk 54896, Korea; [email protected] (G.K.); [email protected] (J.C.); [email protected] (S.C.); [email protected] (Y.H.) 2 Department of Chemical & Biomolecular Engineering, Seoul National University of Science & Technology, 232 Gongneung-ro, Nowon-gu, Seoul 01811, Korea; [email protected] 3 U.S. Salinity Laboratory, USDA, ARS, Riverside, CA 92507, USA; [email protected] 4 Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Korea * Correspondence: [email protected] (S.Q.C.); [email protected] (H.K.); Tel.: +82-42-350-4369 (S.Q.C.); +82-63-270-2370 (H.K.); Fax: +82-63-270-2366 (H.K.) Received: 29 August 2018; Accepted: 10 October 2018; Published: 14 October 2018

Abstract: Along with the accompanying theory article, we experimentally investigate the effect of the depletion attraction force on the flotation of malachite. While varying the concentration of the depletion agent (polyethylene glycol), three different systems are studied: pure malachite, pure silica and a 1:1 mass ratio of malachite and silica binary system. We find that the recovery increases significantly as the concentration of the depletion reagents increases for all three systems. However, the recovery suddenly decreases in a certain concentration range, which corresponds to the onset of the decreased surface tension when high concentrations of the depletion agent are used. The decreased surface tension of the air/water interface suggests that the recovery rate is lowered due to the adsorption of the depletion agent to the bubble surface, acting as a polymer brush. We also perform experiments in the presence of a small amount of a collector, sodium oleate. An extremely small amount of the collector (10−10–10−5 M) leads to the increase in the overall recovery, which eventually reaches nearly 100 percent. Nevertheless, the grade worsens as the depletant provides the force to silica particles as well as target malachite particles.

Keywords: ﬂotation; malachite; silica; binary mixture; depletion attraction; PEG

1. Introduction In the field of mineral processing, froth flotation has been the most widely used technique to improve the quality of low-grade minerals [1–6]. During this process, a collector is used to impart hydrophobicity to desired mineral particles; these hydrophobic particles are then better attached onto the surface of a bubble, leaving undesired particles in the bulk solution. Among these collectors is xanthate, which is a typical collector used for sulfide minerals and for oxide minerals after the sulfidization process [7–10]. Although this collector has been exploited extensively over the last several decades, a reduction in its use is desired because it is environmentally harmful [11–13]. Accordingly, several groups have attempted to find environmentally friendly collectors [14–19]. In this regard, collector-less flotation would be the best option if shown to be feasible. In fact, attempts have been made to separate particles without a collector [10,20–23]. For example, several groups have investigated the flotation behavior of sulfide minerals without collectors (e.g., galena (PbS), pyrite (FeS2), arsenopyrite

Minerals 2018, 8, 450; doi:10.3390/min8100450 www.mdpi.com/journal/minerals Minerals 2018, 8, x FOR PEER REVIEW 2 of 11 Minerals 2018, 8, 450 2 of 11 ((Zn,Fe)S)) [10,20,23–25]. These studies showed that sulfide minerals could provide better floatability(FeAsS), chalcopyrite in certain oxidation (CuFeS2), chalcocite and reduction (Cu2S) and potential sphalerite ranges ((Zn,Fe)S)) by adjusting [10,20,23–25 the]. These solution studies pH, at whichshowed elemental that sulfide sulfur minerals forms a could hydrophobi providec better surface floatability of sulfide in certain minerals. oxidation However, and reduction these studies exploitedpotential only ranges certain by adjusting properties the solution of sulfide pH, mineralsat which elemental and are sulfur thus formslimited a hydrophobic to them. Furthermore, surface theseof techniques sulfide minerals. still However,require a thesechange studies of the exploited surface only properties certain properties in the same of sulfide ways mineralsa collector and does. Hencaree, thusconsiderable limited to them.amounts Furthermore, of chemical these reagents techniques are stillrequired require to a changeachieve of suitable the surface pHs. properties inWe the suggest same ways a route a collector that enhances does. Hence, the considerableflotation efficiency amounts by of chemicalphysically reagents changing are required the interaction to betweenachieve a suitable bubble pHs. and a mineral particle without changing the surface chemistry. Interaction We suggest a route that enhances the flotation efficiency by physically changing the interaction between a bubble and a particle is crucial to enhance the floatability of a particle, as it is a critical step between a bubble and a mineral particle without changing the surface chemistry. Interaction between in the flotation process. However, it remains difficult to explain the exact mechanism of such an a bubble and a particle is crucial to enhance the floatability of a particle, as it is a critical step in the attachmentflotation process. process, However, as it invo it remainslves complicated difficult to explain multiphase the exact components mechanism of (liquid such an-air attachment-solid) in the presenceprocess, of as a it involvesrapid flow. complicated Accordingly, multiphase many components researchers (liquid-air-solid) have focused in the on presence bubble of-particle a interactionsrapid flow. rather Accordingly, than considering many researchers the entire have complicated focused on bubble-particleprocess [5,26– interactions31]. rather than consideringOur strategy the entire to change complicated the process bubble [-5particle,26–31]. interaction is termed “depletion attraction.” DepletionOur attraction strategy to is change an osmotic the bubble-particle force exerted interaction on larger is termed objects “depletion (e.g., colloids attraction.” and Depletion droplets) by smallerattraction objects is an(small osmotic molecules, force exerted polymer on largers and objects surfactant (e.g., colloids micelles) and [32 droplets)–35]. This by smaller attractiv objectse force is employed(small molecules,only when polymers the distance and surfactant between micelles)two larger [32 objects–35]. This is closer attractive than force the issize employed of the depletant, only wherewhen the the symmetry distance betweenof the osmotic two larger pressure objects is is broken. closer than Otherwise, the size ofosmotic the depletant, force is where isotropic the and symmetry of the osmotic pressure is broken. Otherwise, osmotic force is isotropic and therefore does therefore does not affect the interaction between larger objects, as described in Figure 1. In terms of not affect the interaction between larger objects, as described in Figure1. In terms of flotation, we can flotation, we can regard a mineral particle and a bubble as two large objects, with small polymer regard a mineral particle and a bubble as two large objects, with small polymer molecules added as moleculessmall objects. added By as addingsmall objects. polymer By molecules, adding alsopolymer termed molecules, as a depletion also agenttermed or aas depletant, a depletion we canagent or a depletant,increase thewe attractive can increase interaction the attractive between interaction a mineral particle between and a mineral bubble. particle and a bubble.

Figure 1. Schematic illustration of the depletion attraction between a bubble and minerals. Figure 1. Schematic illustration of the depletion attraction between a bubble and minerals. The The bubble-particle interaction has a huge energy barrier without a depletant, making it difﬁcult bubblefor- particlesparticle to interaction attach the has bubble a huge surface energy (a). On barrier the other without hand, a depletiondepletant, attraction making pushes it difficult the for particlesparticles to attach to the bubblethe bubble surface surface (b). (a). On the other hand, depletion attraction pushes the particles to the bubble surface (b).

In this study, we experimentally explore the effects of depletion agents on mineral flotation. Two hydrophilic minerals were considered for the present work: first, malachite was selected as a valuable mineral because this mineral has been actively studied in our group [5,36–38]. Second, silica

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In this study, we experimentally explore the effects of depletion agents on mineral flotation. Two hydrophilic minerals were considered for the present work: first, malachite was selected as a valuable mineral because this mineral has been actively studied in our group [5,36–38]. Second, silica is normally considered as a gangue mineral for metallic mineral flotation, thus we chose this for a gangue mineral. Using polyethylene glycol (PEG), a biocompatible polymer, as a depletion agent, pure malachite and silica particles are floated. The flotation tests were conducted at pH 7 where the bubble-particle interaction is expected to be electrostatically favorable for malachite [5,38] while electrostatically unfavorable for silica [39,40]. We hypothesized that this control would vary the attachment probability of each mineral in the presence of depletants to different degree. Malachite particle experiments show increased flotation efficiency with an increase in the concentration of PEG, whereas the floatability of silica particles increases only slightly. The flotation efficiency of malachite also increases significantly for the mixed system of malachite and silica. Furthermore, we study the effect of depletion attraction on the flotation of malachite in the presence of low concentrations of sodium oleate. The floatability becomes remarkably higher relative to that in the absence of PEG, eventually becoming close to 100 percent.

2. Materials and Methods

2.1. Samples and Reagents

In this study, malachite (Cu2(OH)2CO3), considered to be a valuable mineral, was obtained from Junsei Chemical Co., Ltd. (Tokyo, Japan). The malachite contained a minimum of 55% of Cu and 95% of CuCO3. Silica sand (99.5% purity, Sibelco Korea Co., Ltd., Nonsan, Korea) was used as a gangue mineral. For ﬂotation experiments, the particle size of both malachite and silica was set using −270 + 325 mesh (45–53 µm, Tyler Standard). Polyethylene glycol (PEG) with an average molecular weight of 10,000 was obtained from Sigma-Aldrich (St. Louis, MO, USA) as a depletant and sodium oleate (SO) was purchased from Sigma-Aldrich as a collector for microﬂotation.

2.2. Characterization of the Samples

Surface Tension of PEG In order to evaluate the change in the surface tension depending on the concentration of PEG during the ﬂotation test, the surface tension was measured using a surface tension analyzer (DST60, SEO Co., Ltd., Suwon, Korea). In this study, we determined the surface tension through the Du Noüy ring method using a Pt ring [41]. The concentration of the PEG solution was ﬁxed at 5 × 10−5–30 wt %.

2.3. Flotation

2.3.1. Depletion Effects (Single Minerals of Silica and Malachite, Respectively and a Mixture of the Two) The flotation efficiency values of silica and malachite individually and a mixture of these two minerals were investigated depending on the concentration of PEG (5 × 10−5–5 wt %). Flotation experiments were carried out using a well-controlled and modified Hallimond tube [42]. The samples included malachite at 1 g, silica at 1 g and a mixture (malachite 0.5 g and silica 0.5 g), separated in a Hallimond tube with 150 mL of a PEG solution. The flotation conditions were characterized by a stirring rate of 340 rpm (PC-410D, Corning Life Sciences, Tewksbury, MA, USA) with 30 mL/min of nitrogen gas of 99.99% purity for 10 min. After flotation, the concentrate—which refers to the froth and tailing as a result of flotation—was dried in a dryer (J-IB2, Jicico Co., Ltd., Seoul, Korea) at 45 ◦C for one day to determine the floatability, recovery and grade. The floatability was calculated by the weight ratio of the concentrate to the total mineral and the recovery was estimated according to the weight ratio of the target mineral (silica or malachite) in the concentrate to the total mineral. The grade was determined by the weight ratio of the target mineral in the concentrate to the concentrate. Minerals 2018, 8, 450 4 of 11

2.3.2. Added Collector with PEG in a Binary System After fixing the concentration of PEG at 5 × 10−3 wt %, the flotation efficiency of the malachite and silica mixture was investigated as a function of the concentration of sodium oleate (SO). A mixture of malachite 0.5 g and silica 0.5 g as a sample was used. The concentration of SO was fixed at 10−10–10−5 M. Flotation was performed using a Hallimond tube with 30 mL/min of nitrogen gas and at an agitation speed of 340 rpm (PC-410D, Corning Life Sciences, Tewksbury, MA, USA) for 10 min, identical to the conditions used earlier. After flotation, the concentrate and tailing as a result of flotation were dried in a dryer (J-IB2, Jicico Co., Ltd., Seoul, Korea) at 45 ◦C for one day to determine the recovery and grade. The recovery and grade were calculated in the same manner as the flotation under depletion force without a collector.

2.4. Adsorption Experiments for PEG on Minerals In order to examine whether or not PEG was adsorbed onto the mineral surface during the microﬂotation process, adsorption tests were performed using a spectrophotometer (HS-3300, Humas Co., Ltd., Daejeon, Korea). The adsorption test proceeded in the same manner as the ﬂotation assessment, with 150 mL of PEG solution per 1 g of sample stirred for 10 min at a stirring speed of 340 rpm in a Hallimond tube. The supernatant of the suspension was then taken to measure the absorbance at 194 nm. The adsorption tests were conducted at least three times per sample.

2.5. Viscosity Measurement of PEG Solution Rheological property of PEG solution was further examined by measuring solution viscosity with different PEG concentrations. Shear stress of PEG solution was measured as a function of shear rate using a Brookﬁeld viscometer (DV2TCP, Brookﬁeld AMETEK, Middleboro, MA, USA). The measurements were carried out at constant room temperature (~25 ◦C).

3. Results and Discussion

3.1. Flotation Results

3.1.1. Single Minerals of Silica and Malachite The floatability measurements of each pure mineral, that is, malachite and silica particles, were taken first. Figure2 shows the floatability as a function of the PEG concentration. In general, malachite shows higher floatability than silica over all concentrations of PEG; this results from the differences in an electrostatic force of malachite and silica to the bubble because identical depletion force is expected to be present for both minerals at the same PEG concentration [1]. For malachite particles, the natural floatability is roughly 20% and adding a small amount of PEG, 5 × 10−5 wt %, does not change this value. However, as the concentration of PEG was increased, the floatability increased sharply to approximately 80% at 5 × 10−3 wt %, appearing to remain constant at 5 × 10−2 wt %. The floatability of malachite suddenly dropped to 35%, which is still higher than the natural floatability. However, this represents a twofold decrease compared to lower concentrations. At an even higher concentration of 5 wt %, floatability increased to nearly 90%. Solutions with more than 5 wt % of PEG became too viscous; therefore, we conducted experiments only up to 5 wt %. On the other hand, the silica floatability remains very low for the entire concentration range of PEG, except at 5 wt %. It showed a similar trend, although it was not as clear as that of malachite due to the low floatability. Minerals 2018, 8, x FOR PEER REVIEW 5 of 11 Minerals 2018, 8, 450 5 of 11

FigureFigure 2. 2.Microflotation Microflotation measurements measurements of of malachite malachite and and silica silica for for 10 10 min min at at pH pH 7 7 using using a a Hallimond Hallimond tube.tube. An An increase increase in in the the concentration concentration of of PEG PEG results results in in an an increase increase in in the the overall overall floatability floatability for for both both particles,particles, although although the the floatability floatability of of malachite malachite is is far far higher higher than than that that of of silica. silica. The The floatability floatability at at the the PEGPEG concentration concentration of of 0 0 wt wt % % means means natural natural floatability. floatability. To explain this interesting flotation behavior of both particles, we first performed the adsorption To explain this interesting flotation behavior of both particles, we first performed the test of PEG onto the minerals, as it may act as a collector by being adsorbed on the mineral surface. adsorption test of PEG onto the minerals, as it may act as a collector by being adsorbed on the In particular, we focused on higher concentrations of PEG because we could not measure the mineral surface. In particular, we focused on higher concentrations of PEG because we could not absorbance reliably at lower concentrations. The absorbance values of PEG suspension before and measure the absorbance reliably at lower concentrations. The absorbance values of PEG suspension after adsorption tests are presented in Table1. The trends obtained suggest that PEG adsorption before and after adsorption tests are presented in Table 1. The trends obtained suggest that PEG onto malachite or silica surfaces is almost negligible. To further support the adsorption test results, adsorption onto malachite or silica surfaces is almost negligible. To further support the adsorption we conducted a flotation test using the suspension with PEG-adsorbed malachite yet without test results, we conducted a flotation test using the suspension with PEG-adsorbed malachite yet non-adsorbed PEG in solution by filtering the mixture of malachite and PEG using a membrane without non-adsorbed PEG in solution by filtering the mixture of malachite and PEG using a filter with a pore size of 0.45 µm. The test was carried out at 5 wt % PEG concentration where greatest membrane filter with a pore size of 0.45 μm. The test was carried out at 5 wt % PEG concentration PEG adsorption is expected if any. The floatability of the filtered malachite (i.e., adsorbed PEG on where greatest PEG adsorption is expected if any. The floatability of the filtered malachite (i.e., the malachite) was determined to be about 20%; this value was similar to the natural floatability of adsorbed PEG on the malachite) was determined to be about 20%; this value was similar to the malachite, clearly supporting the observations obtained from the adsorption tests. Moreover, contact natural floatability of malachite, clearly supporting the observations obtained from the adsorption angle values measured by a bubble captive method [38,43] show negligible changes with different PEG tests. Moreover, contact angle values measured by a bubble captive method [38,43] show negligible concentrations: 27.4◦, 30.7◦ and 27.1◦ for no PEG, 5 × 10−5 wt % PEG and 5 wt % PEG. Accordingly, changes with different PEG concentrations: 27.4°, 30.7° and 27.1° for no PEG, 5 × 10−5 wt % PEG and 5 all of these test results are in agreement with the characteristics of PEG, which is a neutral polymer wt % PEG. Accordingly, all of these test results are in agreement with the characteristics of PEG, and known as a weakly-adsorbing polymer on the solid surface [44,45]. which is a neutral polymer and known as a weakly-adsorbing polymer on the solid surface [44,45].

Table 1. UV-vis absorbance value of PEG suspension at 194 nm before and after adsorption tests onto Table 1. UV-vis absorbance value of PEG suspension at 194 nm before and after adsorption tests onto the mineral surface. the mineral surface. Concentration of PEG (wt %) Before Adsorption After Adsorption onto Silica After Adsorption onto Malachite Concentration of PEG Before After Adsorption onto After Adsorption onto 5 × 10−2 0.093 ± 0.006 0.100 ± 0.012 0.101 ± 0.002 5 × 10(wt−1 %) 0.743Adsorption± 0.011 0.759Silica± 0.003 Malachite 0.773 ± 0.010 55 × 10−2 1.4170.093± 0.068± 0.006 0.100 1.432 ±± 0.010.0282 0.101 1.558 ± 0.00± 0.1252 5 × 10−1 0.743 ± 0.011 0.759 ± 0.003 0.773 ± 0.010 5 1.417 ± 0.068 1.432 ± 0.028 1.558 ± 0.125 Therefore, we turned our attention to the surface of a bubble and tested whether PEG could be adsorbed onto to the bubble surface. Although we used water-soluble polymers, their surface Therefore, we turned our attention to the surface of a bubble and tested whether PEG could be activities at the air/water interface were known and measured beforehand. Because the surface activity adsorbed onto to the bubble surface. Although we used water-soluble polymers, their surface depends on many factors, such as the molecular weight and concentration [44,46], we measured our activities at the air/water interface were known and measured beforehand. Because the surface own 104 Da PEG as a function of the concentration, as shown in Figure3. For all concentrations of PEG, activity depends on many factors, such as the molecular weight and concentration [44,46], we the surface activity was found to be very weak compared to a typical surfactant. The surface tension measured our own 104 Da PEG as a function of the concentration, as shown in Figure 3. For all immediately decreased to 65 mN/m after an addition of 5 × 10−4 wt % of PEG, remaining constant concentrations of PEG, the surface activity was found to be very weak compared to a typical at a concentration range of nearly three orders of magnitude, from 5 × 10−4 wt % to 5 × 10−1 wt %. surfactant. The surface tension immediately decreased to 65 mN/m after an addition of 5 × 10−4 wt % Subsequently, it started to decrease slightly again from 5 × 10−1 wt %. of PEG, remaining constant at a concentration range of nearly three orders of magnitude, from 5 × 10−4 wt % to 5 × 10−1 wt %. Subsequently, it started to decrease slightly again from 5 × 10−1 wt %.

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FigureFigure 3. 3.Measurements Measurements of of the the surface surface tension tension for for various various PEG PEG concentrations concentrations at at room room temperature temperature ◦ (~25(~25 °CC).). These These were were averaged averaged from from at at least least three three individual individual measurements. measurements.

This surface tension behavior of PEG was previously investigated. PEG is a nonionic polymer that This surface tension behavior of PEG was previously investigated. PEG is a nonionic polymer is however soluble in water. Active materials on a soluble surface typically form a Gibbs monolayer. that is however soluble in water. Active materials on a soluble surface typically form a Gibbs Generally, this monotonically reduces the surface tension, after which it becomes constant, which is monolayer. Generally, this monotonically reduces the surface tension, after which it becomes the typical indication of micelle formation. However, previous studies showed that PEG does not form constant, which is the typical indication of micelle formation. However, previous studies showed micelles [47]. One previous study showed that the constant surface tension of PEG at intermediate that PEG does not form micelles [47]. One previous study showed that the constant surface tension concentrations is likely to be a sublayer which is formed from excess molecules [46]. It was proven of PEG at intermediate concentrations is likely to be a sublayer which is formed from excess that a semi-dilute monolayer forms at the interface at these concentrations. Although the bubble molecules [46]. It was proven that a semi-dilute monolayer forms at the interface at these interface accepts more PEG molecules with an increase in the concentration, the surface tension can concentrations. Although the bubble interface accepts more PEG molecules with an increase in the remain constant due to the formation of a layer underneath the semi-dilute monolayer, hindering the concentration, the surface tension can remain constant due to the formation of a layer underneath adsorption of more PEG to bubble surface. This also explains why the increased floatability begins to the semi-dilute monolayer, hindering the adsorption of more PEG to bubble surface. This also slow down in this regime. The decreased surface tension after the constant regime was previously explains why the increased floatability begins to slow down in this regime. The decreased surface explained in terms of the solubility of PEG; this additional decrease in the surface tension depends tension after the constant regime was previously explained in terms of the solubility of PEG; this on its solubility in water. This second decrease in the surface tension at higher PEC concentration additional decrease in the surface tension depends on its solubility in water. This second decrease in indicates that PEG occupies a greater free interfacial area on bubbles, thus reducing the probability of the surface tension at higher PEC concentration indicates that PEG occupies a greater free interfacial successful particle attachment to a bubble surface. This onset of a decrease in the surface tension is area on bubbles, thus reducing the probability of successful particle attachment to a bubble surface. This in good agreement with the floatability measurements; the floatability decreases sharply at the point onset of a decrease in the surface tension is in good agreement with the floatability measurements; the wherefloatability the surface decreases tension sharply decreases at the point again. where the surface tension decreases again. 3.1.2. Mixture of Malachite and Silica 3.1.2. Mixture of Malachite and Silica We successfully demonstrated that depletion attraction could result in high floatability of each We successfully demonstrated that depletion attraction could result in high floatability of each mineral individually. We then tested a mixed system of both particles. Figure4a shows the overall mineral individually. We then tested a mixed system of both particles. Figure 4a shows the overall floatability at a 1 to 1 mass ratio of malachite and silica. It is immediately noticeable that the overall floatability at a 1 to 1 mass ratio of malachite and silica. It is immediately noticeable that the overall trend is nearly identical to those of the individual results. This is important because it proves that trend is nearly identical to those of the individual results. This is important because it proves that many factors, such as particle-particle interactions and flow effects, are negligible. Figure4b shows the many factors, such as particle-particle interactions and flow effects, are negligible. Figure 4b shows grade of the concentrate. The grade worsens as the concentration of PEG increases. In fact, the overall the grade of the concentrate. The grade worsens as the concentration of PEG increases. In fact, the trend is precisely opposite to that noted with the floatability. The grade decreases slightly and then overall trend is precisely opposite to that noted with the floatability. The grade decreases slightly increases suddenly at the point the floatability becomes severely decreased. Eventually, it reaches its and then increases suddenly at the point the floatability becomes severely decreased. Eventually, it worst point at the highest concentration, because the depletion force at that point is large enough and reaches its worst point at the highest concentration, because the depletion force at that point is large allows both particles to be attached onto the bubble surface. This is likely to stem from the fact that enough and allows both particles to be attached onto the bubble surface. This is likely to stem from stronger depletion attraction leads to a reduction of the energy barrier and thus to an increase in the the fact that stronger depletion attraction leads to a reduction of the energy barrier and thus to an attachment probability of silica particles. increase in the attachment probability of silica particles.

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Figure 4. (a) Overall recovery of malachite (square) and silica (circle) from a mixture with a 1:1 mass ratio using a Hallimond tube for 10 min at pH 7 while increasing the PEG concentration and (b) FigureFigure 4. ((aa)) Overall recovery recovery of of malachite malachite (square) (square) and and silica silica (circle) (circle) from from a a mixture mixture with with a a 1:1 1:1 mass mass grade of malachite (triangle). ratioratio using aa Hallimond Hallimond tube tube for for 10 10 min min at pHat pH 7 while 7 while increasing increasing the PEG the PEG concentration concentration and ( band) grade (b) of malachite (triangle). 3.2. Flotationgrade of malachitewith a Small (triangle). Amount of Collector with PEG in a Binary System 3.2. Flotation with a Small Amount of Collector with PEG in a Binary System 3.2. FlotationIn some with cases, a Small a considerable Amount of gradeCollector with with very PEG high in arecovery Binary System is required. For example, precious metalIn minerals some cases, must a considerablebe fully recovered grade even with with very a high slight recovery grade improvement. is required. For To example, achieve preciousthis, we In some cases, a considerable grade with very high recovery is required. For example, precious metalmeasured minerals the floatability must be fully of malachite recovered in even a silica with mixturea slight grade in the improvement. presence of 10 To-10– achieve10−5 M this,SO as we a metal minerals must be fully recovered even with a slight grade improvement. To achieve this, we measuredcollector. It the should floatability be noted of malachite that this concentration in a silica mixture range in used the presence can be considered of 10-10–10 extremely−5 M SO as low a measured the floatability of malachite in a silica mixture in the presence of 10-10–10−5 M SO as a collector.because previous It should studies be noted used that at least this concentration10−5 M SO for rangeoxide usedmineral can flotation be considered [38,48– extremely50]. Figure low 5a collector. It should be noted that this concentration range used can be considered extremely low becauseshows the previous floatability studies of theused silica at least and 10 malachite−5 M SO formixture oxide while mineral varying flotation the [ concentration38,48–50]. Figure of the5a because previous studies used at least 10−5 M SO for oxide mineral flotation [38,48–50]. Figure 5a showsanionic the surfactant floatability SO ofwith the a silica fixed and concentration malachite mixture of 5 × 10 while−3 wt varying% of PEG. the As concentration expected, the of recovery the anionic of shows the floatability of the silica and malachite mixture while varying the concentration of the surfactantmalachite becomes SO with significantly a fixed concentration higher compared of 5 × 10to −the3 wt entire % of SO PEG. concentration As expected, in all the cases. recovery At a SO of anionic surfactant SO with a fixed concentration of 5 × 10−3 wt % of PEG. As expected, the recovery of malachiteconcentration becomes of 10 significantly−5 M, malachite higher is almostcompared completely to the entire recovered. SO concentration For comparison, in all cases. the same At a malachite becomes significantly higher compared to the entire SO concentration in all cases. At a SO SOmalachite/silica concentration system of 10 −is5 testedM, malachite without is PEG almost and completely is presented recovered. in Figure For5a. It comparison, should be noted the same that concentration of 10−5 M, malachite is almost completely recovered. For comparison, the same malachite/silicafor concentrations system of <10 is−5 tested M, malachite without PEGshowed and natural is presented floatability in Figure without5a. It should PEG, indicating be noted that that malachite/silica system is tested without PEG and is presented in Figure 5a. It should be noted that forlower concentrations concentrations of <10of SO−5 doesM, malachite not serve showed as a collector natural until floatability it reaches without to 10−5 PEG,M. Figure indicating 5b shows that for concentrations of <10−5 M, malachite showed natural floatability without PEG, indicating that lowerthe computed concentrations grade ofof SOthis does system. not serve It decreases as a collector slightly until as it SO reaches is added to 10 but−5 M. remains Figure 5atb showsa constant the lower concentrations of SO does not serve as a collector until it reaches to 10−5 M. Figure 5b shows computed(~80%) for gradethe entire of this range system. of our It SO decreases concentrations. slightly as SO is added but remains at a constant (~80%) the computed grade of this system. It decreases slightly as SO is added but remains at a constant for the entire range of our SO concentrations. (~80%) for the entire range of our SO concentrations.

Figure 5. (a) Recovery measurements of malachite (square) and silica (circle) from a mixture with a 1:1 Figure 5. (a) Recovery measurements of malachite (square) and silica (circle) from a mixture with a mass ratio at a ﬁxed PEG concentration of 5 × 10−3 wt % while varying the concentration of SO and 1:1 mass ratio at a fixed PEG concentration of 5 × 10−3 wt % while varying the concentration of SO and Figurerecovery 5. of(a) malachite Recovery (opened measurements square) of in malachite the absence (square) of PEG and and silica (b) the (circle) grade from of malachite a mixture (triangle). with a recovery of malachite (opened square) in the absence of PEG and (b) the grade of malachite 1:1 mass ratio at a fixed PEG concentration of 5 × 10−3 wt % while varying the concentration of SO and 3.3. Viscosity(triangle). Effect of a High PEG Concentration and Polyelectrolytes as a Depletant recovery of malachite (opened square) in the absence of PEG and (b) the grade of malachite 3.3. Viscosity(triangle).Our experimental Effect of a High ﬁndings PEG Concentration may be well and explained Polyelectrolytes by the as theoreticala Depletant calculation from the accompanying article [1]. The bubble surface adsorption of depletion agents hinders mineral 3.3attachment. Viscosity and Effect this of occursa High inPEG a certain Concentration some PEG and concentration Polyelectrolytes range. as a Depletant One must be careful when PEG is used, as various molecular weights and different end groups can lead to distinctly different surface

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Our experimental findings may be well explained by the theoretical calculation from the accompanying article [1]. The bubble surface adsorption of depletion agents hinders mineral attachment and this occurs in a certain some PEG concentration range. One must be careful when PEG is used, as various molecular weights and different end groups can lead to distinctly different Minerals 2018, 8, 450 8 of 11 surface activities [51]. However, we found that an increase of the PEG concentration to 5 wt % can overcome the energy barrier created by polymer brushes, implying that other mechanisms are activitiesinvolved [ in51 ]. this However, process. we Hence, found we that measured an increase viscosity of the PEG of PEG concentration suspension to as 5 wt a function % can overcome of PEG theconcentration energy barrier and created the results by polymer are presented brushes, in implying Figure 6.that The other result mechanisms suggests are that involved the abnormal in this process.increase Hence,in floatability we measured at 5 wt viscosity % PEG is of due PEG to suspension the sudden as increase a function of of solution PEG concentration viscosity, which and the in resultsturn would are presented provide in longer Figure residence6. The result time suggests of bubbles that the and abnormal particles increase and eventually in ﬂoatability increase at 5 wt the % PEGprobability is due toof thebubble sudden-particle increase interaction. of solution However, viscosity, too which high in a turnconcentration would provide of PEG longer increas residencees the timeviscosity of bubbles of solution and particles significantly, and eventually resulting in increase an unsuccessful the probability process. of bubble-particle This indicates interaction. that there However,exists an optimum too high aconcentration concentration for of this PEG process. increases the viscosity of solution signiﬁcantly, resulting in an unsuccessful process. This indicates that there exists an optimum concentration for this process.

Figure 6. (a)(a) SShearhear stress and ( (b)b) solutionsolution viscosity as a function of shear rate with differentdifferent PEG ◦ × −5 × −3 concentrations atat constantconstant room room temperature temperature (~25 (~25C). °C ). 5 5 ×10 10−5 wtwt %% (inverted (inverted triangle), triangle),5 5 ×10 10−3 wt % (triangle), 5 × 10−1 wt % (circle) and 5 wt % (square) PEG were used. (triangle), 5 × 10−1 wt % (circle) and 5 wt % (square) PEG were used. In principle, polymers that are not adsorbed onto a bubble surface and which are soluble in In principle, polymers that are not adsorbed onto a bubble surface and which are soluble in water simultaneously are available, such as polyelectrolytes. In addition, they may provide better water simultaneously are available, such as polyelectrolytes. In addition, they may provide better results at high concentrations. Moreover, polyelectrolytes have a larger radius of gyration for the same results at high concentrations. Moreover, polyelectrolytes have a larger radius of gyration for the molecular weight and their charges increase their effective size. This larger size would result in higher same molecular weight and their charges increase their effective size. This larger size would result in depletion force. However, polyelectrolytes can also stick to oppositely charged patches or particle higher depletion force. However, polyelectrolytes can also stick to oppositely charged patches or surfaces. This would worsen the floatability, as it such action also acts as a polymer brush. particle surfaces. This would worsen the floatability, as it such action also acts as a polymer brush. 4. Conclusions 4. Conclusions In conclusion, we experimentally investigated how depletion interaction affects mineral floatability.In conclusion, Malachite, we silica experimentally and a mixture investigated of these two how minerals depletion were interaction each tested affects while varyingmineral thefloatability. concentration Malachite, of PEG silica as and a depletion a mixture agent. of these We foundtwo minerals that the were floatability each tested generally while increasesvarying the as PEGconcentration is added whileof PEG the as gradea depletion remains agent. nearly We identical, found that except the floatability at very high generally concentrations. increases However, as PEG ouris added experiments while the revealed grade remains two important nearly identical, features: except (1) because at very PEG high itself concentrations. is a surface-active However, material, our itexperiments can be adsorbed revealed onto two a bubble important surface, features: acting ( as1) abecause polymer PEG brush. itself This is polymera surface brush-active hampers material, the it attachmentcan be adsorbed of mineral onto a particles, bubble surface, reducing acting the floatability. as a polymer (2) brush. If too muchThis polymer PEG is added, brush ithampers aggravates the theattachment grade because of mineral the particles, depletion reducing interaction the beginsfloatability. to facilitate (2) If too the much attachment PEG is added, of silica it particlesaggravates as wellthe grade as malachite because particles. the depletion Furthermore, interaction we foundbegins that to facilitate adding an the extremely attachment low of amount silica particles of collector as increaseswell as malachite the floatability particles. even more,Furthermore, allowing we it ultimately found that to reach adding nearly an extremely 100 percent low despite amount the fact of thatcollector the grade increases decreases the floatability slightly. Flotation even more, using allowing depletion it attraction ultimately with to minimalreach nearly use of 100 a collector percent coulddespite be th eco-friendlye fact that the and grade it would decreases be particularly slightly. Flotation useful in systemsusing depletion that require attraction a high with recovery minimal rate withuse of a a considerable collector could grade. be eco-friendly and it would be particularly useful in systems that require a high recovery rate with a considerable grade. Author Contributions: G.K. and S.Q.C. compiled the information and wrote the manuscript; J.C., S.C., K.K. and Y.H. collaborated in the edition of the manuscript; S.A.B. reviewed the manuscript and gave feedback for improvement; and, H.K. assisted in all of the aforementioned activities as academic supervisor. Minerals 2018, 8, 450 9 of 11

Funding: This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF-2012R1A6A3A040395) and by the Korea Energy and Mineral Resources Engineering Program (KEMREP). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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