Derivation of Flotation Kinetic Model for Activated and Depressed Copper Sulﬁde Minerals

Article Derivation of Flotation Kinetic Model for Activated and Depressed Copper Sulﬁde Minerals

Hidekazu Matsuoka 1, Kohei Mitsuhashi 1, Masanobu Kawata 1 and Chiharu Tokoro 2,*

1 Nittetsu Mining Co., Ltd., Tokyo 190-0182, Japan; [email protected] (H.M.); [email protected] (K.M.); [email protected] (M.K.) 2 Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan * Correspondence: [email protected]; Tel.: +81-3-5286-3320

Received: 24 October 2020; Accepted: 16 November 2020; Published: 18 November 2020

Abstract: The wettability and floatability of oxidized chalcocite, bornite, and chalcopyrite with the conditions of sodium hydrosulfide (NaHS) dosages and pHs were studied by contact angle measurements, and single and mixture mineral flotation tests. To evaluate the results of the flotation, the flotation kinetic model for copper sulfide minerals treated by NaHS was derived. In this study, we focused on the activation and depression by NaHS, a well-known activator and depressant of copper minerals. The flotation results showed that there can be a threshold NaHS dosage to activate the mineral surfaces, as evidenced by the depression of the minerals and reduction of recoveries at higher dosages of NaHS. Chalcocite recoveries increased with an increase of NaHS dosage. Bornite recoveries tended to be depressed with a smaller amount of NaHS as pH increased. The recoveries of chalcopyrite increased as pH increased at an optimum NaHS dosage. Moreover, the flotation kinetic model that includes the surface properties and the reaction rate constant between the copper sulfide minerals and NaHS was derived. The trends of the flotation rate constants and mass fractions with NaHS dosages and pHs could quantitatively well-explain the flotation results.

Keywords: flotation kinetic model; flotation; copper sulfide; activation; depression

1. Introduction Copper is a valuable metal and used in various products such as copper wire and electronic devices. Copper sulfide minerals are widely known as a major source of copper resources. Copper sulfide minerals are separated from other gangue minerals by a flotation method. Flotation utilizes the surface wettability property evaluated by a contact angle degree. Law and Zhao [1] demonstrated that the tangential angle at liquid-solid-air interface can quantitatively describe the wetting of a solid surface by a liquid. Contact angle, θ is defined by Young’s equation as follows [2]:

γSV = γLV cos θ + γSL (1) where γSV is the solid surface tension, γLV is the liquid surface tension, γSL is the liquid-solid interfacial tension. It can be understood that the greater the contact angle the greater is the adhesion force between the particle and bubble [3]. The slightly oxidized surface of copper sulfide mineral, chalcopyrite, is hydrophobic with contact angles around 70◦ because of produced sulfur-rich products ex. sulfur, metal-deficient sulfides, and polysulfides [4–6]. Therefore, the slightly oxidized copper sulfide mineral is easy to recover to the froth phase because of their hydrophobic surface property. As the oxidation progresses or surfaces are more strongly oxidized, however, surfaces become hydrophilic because surfaces are covered with oxides and/or hydroxides [4,7–11], and the contact angle becomes low [4]. Thus, it is difficult to recover because of their hydrophilic surface property.

Minerals 2020, 10, 1027; doi:10.3390/min10111027 www.mdpi.com/journal/minerals Minerals 2020, 10, 1027 2 of 15

To evaluate these minerals’ flotation results, flotation kinetic models are used. Various models have been investigated to evaluate the flotation kinetics as shown in following Table1[12–17].

Table 1. Seven kinds of ﬂotation kinetic models (adapted from [18]).

Name of the Model Formula

Classical first-order model [19] R = 1 exp( k1t) 1− − First-order model with rectangular distribution of floatability [20,21] R = 1 [1 exp( k2t)] h − k2it − − Floatability component model [22,23] R = ϕ 1 exp k t + 1 ϕ [1 exp( kst)] f − − f − f − − Fully mixed reactor model [24] R = 1 1 − 1+t/k3 Improved gas and solid adsorption model [25] R = k4t 1+k4t 1 Second-order model with rectangular distribution of floatability [26,27] R = 1 [ln(1 + k6t)] − k6t R = recovery; k1, 2, 3, 4, 5, 6 = rate constant; kf = fast floating rate constant; ks = slow floating rate constant; ϕf = fast floating mass fraction.

In recent years, secondary sulfide ores (ex. chalcocite) have sometimes been associated with primary sulfide ores (ex. chalcopyrite and bornite), which have been the main ore of copper until now. Secondary sulfide ores and bornite are strongly affected by oxidation, such as on stockpiles and during the grinding process. An activator can be added to increase the recovery of low floatability minerals. Finkelstein [28] and Allison and O’Connor [29] reported the activation of various sulfides by copper ion. Activation of sphalerite by copper ions is widely known as a typical example of copper ion’s activation [30,31]. Moreover, Zhou and Chander [32] indicated that the sulfurizing agent, NaHS, can be used to activate a copper oxide mineral, malachite. By using a sulfurizing agent, an oxidized surface is sulfurized by the following reaction [33].

2 + 2 8CuO + 5S − + 8H 4Cu2S + SO4 − + 4H2O (2)

2 + CuO + S − + 2H CuS + H2O (3) As a result, the hydrophobicity is increased and the adhesiveness with air bubbles is increased to improve the recovery. On the other hand, NaHS also works as a depressant for chalcopyrite in copper and molybdenum selective flotation [3,34,35]. In this study, we focused on the effect of NaHS as both activator and depressant for oxidized copper sulfide minerals and investigated the quantitative conditions of NaHS activation and depression. Pure mineral specimens of chalcocite, bornite, and chalcopyrite as typical primary and secondary sulfide ores were used for contact angle measurements and single mineral flotation tests. Mixture mineral flotation tests were conducted using Chilean copper ore sample that included chalcocite, bornite, and chalcopyrite. Both of the flotation tests were conditioned at several NaHS dosages and alkaline pHs. Moreover, based on the floatability component model and the surface properties of the copper sulfide minerals, the flotation kinetic model for activated and depressed copper sulfide minerals by NaHS was derived. The derived model was constructed with three components (which were based on copper sulfide minerals’ surface properties) and it included the reaction rate constant between the copper sulfide minerals and NaHS. The model was fitted to the flotation results and their results were discussed.

2. Materials and Methods

2.1. Materials

2.1.1. Preparation of Mineral Specimens for Contact Angle Measurements and Single Mineral Flotation Tests Mineral specimens of chalcocite (Flambeau Mine, America), bornite (Leonard Mine, America), and chalcopyrite (Kosaka Mine, Japan) were used. The samples were characterized by X-ray ﬂuorescence (Supermini 200, Rigaku Co., Ltd., Tokyo, Japan) (see Table2). Minerals 2020, 10, 1027 3 of 15

Table 2. Chemical composition of chalcocite, bornite, and chalcopyrite samples.

Cu Fe S Si As Ag Pb Element (Mass%)

Chalcocite, Cu2S 83.9 1.64 14.3 0.04 0.03 -- Bornite, Cu5FeS4 71.5 8.78 19.3 0.12 - 0.19 - Chalcopyrite, CuFeS2 38.2 31.6 28.4 0.05 -- 1.64

Each mineral was cut to 1 cm3 for use in contact angle measurements. The minerals were embedded in an epoxy resin (Epofix, Struers, Tokyo, Japan). After solidification, the surface of each sample was polished with SiC #1200, #2000, and #4000 polishing papers, followed by 3 µm and 1/4 µm diamond pastes on MD Sat and MD Dur (Struers, Tokyo, Japan) fine polishing disks placed on a polishing machine (Laboforce-Mini, Struers, Tokyo, Japan). The samples were ground using an agate mortar to less than 20 µm for use in single mineral flotation tests. To remove oxidized species from the surfaces, 2 g of the minerals were immersed in 20 mL of a 1 M HNO3 solution and sonicated (UT-205S, Sharp Co., Ltd., Osaka, Japan) for 1 min. The minerals were filtered and rinsed three times with pure water to remove nitrates. The samples were freeze-dried (FDU-1200, Tokyo Rikakikai Co., Ltd., Tokyo, Japan) over 12 h and prepared as fresh samples [36]. Before treatment with NaHS, the surfaces of the fresh samples were oxidized slightly in an oven (WFO-520, Tokyo Rikakikai Co., Ltd., Tokyo, Japan) at 90 ◦C for 12 h for use in contact angle measurements and for 96 h to conduct single mineral flotation tests.

2.1.2. Mixed Copper Sulfide Minerals Ore Sample for Mixture Mineral Flotation Tests A Chilean copper ore sample that contained chalcocite, bornite, and chalcopyrite was used in the mixture mineral flotation tests. The mineral composition of the sample analyzed using a Mineral Liberation Analyser (MLA 650, FEI, Tokyo, Japan) is shown in Tables3 and4. The copper grade of the sample was 1.0%, and the sample contained bornite, chalcopyrite, and chalcocite as copper sulfide minerals and calcite, orthoclase, albite, and quartz as gangue minerals. The sample was crushed using a jaw crusher (1032-B, Yoshida Seisakusho Co., Ltd., Tokyo, Japan) to 1.7 mm and divided into 480 g − sub-samples. The divided samples were ground to P80 = 70 µm with a rod mill and ball mill (1140-A-S, Yoshida Seisakusho Co., Ltd., Tokyo, Japan) for the flotation tests [36].

Table 3. Mineral composition of the Chilean copper ore sample.

Minerals Content Ratio (Mass %) Calcite 69.3 Orthoclase 11.2 Albite 6.4 Quartz 5.7 Copper sulﬁdes 2.0 Others 5.4

Table 4. Distribution of bornite, chalcopyrite, and chalcocite in the copper sulﬁdes of the sample.

Copper-Sulﬁde Minerals Content Ratio (Mass %) Bornite 53.9 Chalcopyrite 27.7 Chalcocite 18.4 Minerals 2020, 10, x 4 of 15

Table 4. Distribution of bornite, chalcopyrite, and chalcocite in the copper sulfides of the sample.

Copper-Sulfide Minerals Content Ratio (Mass %) Bornite 53.9 Chalcopyrite 27.7 Minerals 2020, 10, 1027 4 of 15 Chalcocite 18.4

2.2. NaHS Treatments Before Each MeasurementMeasurement andand TestTest

2.2.1. Contact Angle Measurements The block minerals in epoﬁxepofix resins were immersedimmersed in 100 mL NaHSNaHS solutionssolutions of varyingvarying concentrations of of 1.0 1.0 × 1010−9 M,9 M, 7.0 7.0 × 10−109 M,9 1.0M, × 1.0 10−8 10M, 81.2M, × 1.210−6 M,10 and6 M, 1.0 and × 10 1.0−3 M at10 natural3 M at pHs natural for × − × − × − × − × − pHs10 min. for 10 min.

2.2.2. Single Mineral Flotation Tests The surfaces of mineral specimens after oxidation treatment were treated with NaHS to sulfurize surfaces. The solution (100 mL pure water) was adjusted to pH 8, 9, or 10 using 1% NaOH. NaHS was added to the solution to several concentrations, an andd the pH was adjusted to the desired pH using 1% H2SOSO44. .Thereafter, Thereafter, 1 1 g g of of oxidized oxidized pure pure sample sample was was added added to to a solution, the pH was adjusted to the desired values, and the NaHS treatmentstreatments werewere performedperformed forfor 55 minmin [[36].36].

2.2.3. Mixture Mineral Flotation Tests In the conditioning stage, pulps after grinding by by the the rod mill and ball mill had a 37% pulp concentration in a a 1-L 1-L Denver-type Denver-type flotation ﬂotation cell cell (D (D-12-12 Denver, Denver, Colorado, CO, USA). U.S.A.). Pulps werePulps agitated were agitated using an impeller at 900 rpm. The pH was controlled by Ca(OH)2 and H2SO4 to maintain the pH at 8, 9, using an impeller at 900 rpm. The pH was controlled by Ca(OH)2 and H2SO4 to maintain the pH at 8, or9, or 10. 10. Figure Figure1 1shows shows that that copper copper and and ironiron existedexisted inin the form form of of oxides oxides on on the the mineral mineral surfaces surfaces at atthese these pHs. pHs. After After pH pHadjustment, adjustment, NaHS NaHS dosages dosages of 0of g/t, 0 g50/t, g/t, 50 g100/t, 100g/t, gor/t, 200 or 200g/t was g/t was added added to the to thecell, cell, and and the thepH pH was was readjusted readjusted to tothe the desired desired valu value.e. Afterward, Afterward, flotation ﬂotation reagents, reagents, the the collector diisobutyl dithiophosphate (AERO (AERO 3477 3477 promoter, promoter, Solvay S.A., Brussels, Belgium), Belgium), and and the the frother, frother, methyl isobutyl carbinol (MIBC), were added andand conditionedconditioned forfor 55 minmin [[36].36].

Figure 1. pH-EhpH-Eh diagram diagram for for the the Cu–Fe–S–H Cu–Fe–S–H2OO system system with with the the preponderant preponderant copper and iron species shown in each domain [[37].37].

2.3. Contact Angle Measurement Contact angles were measured following thethe steps conducted byby [[38].38]. After oxidation and NaHS treatments, thethe contactcontact anglesangles of of the the mineral mineral surfaces surfaces were were measured measured by by the the captive captive bubble bubble method method in ain goniometer a goniometer (OCA15EC, (OCA15EC, DataPhysics, DataPhysics, San San Jose, Jose CA,, CA, USA). USA). The The air air bubble bubble volume volume was was 7.0 7.0µL. µL. The The air bubbleair bubble was was generated generated by aby microsyringe a microsyringe and and attached attached to eachto each mineral mineral surface. surface. The The contact contact angles angles of untreated, oxidized, and NaHS-treated mineral samples were measured at diﬀerent ﬁve points on the mineral surfaces and the average values were reported in this paper. Minerals 2020, 10, 1027 5 of 15

2.4. Single Mineral Flotation Tests The single mineral flotation tests were conducted using small column flotation cell to evaluate the floatability of each mineral specimen. The 1 g of the sample treated with NaHS at definite pH and NaHS concentration was added into the small column cell and flotation was conducted for 2 min with 0.3 L/min aeration. After the flotation test, recovered froth and tail samples were dried in an oven at 90 ◦C for more than 12 h, then their weights were measured and the recoveries were calculated.

2.5. Mixture Mineral Flotation Tests A Denver-type flotation machine was used for the mixture mineral flotation tests. At impeller speed of 900 rpm, after NaHS treatment at definite pH and NaHS concentration and addition of collector and frother, the air was self-aerated at 1.6 L/min. The froth was recovered at 1, 3, 6, 18, 30, and 45 min and dried in an oven at 90 ◦C for more than 12 h. The dried froth and tail samples were analyzed by ICP-AES and MLA to obtain copper concentrations and recovery of each copper sulfide mineral.

3. Results and Discussion

3.1. Contact Angle Measurements Figure2 shows the results of contact angle measurements of chalcocite, bornite, and chalcopyrite. The contact angles of untreated chalcocite, bornite, and chalcopyrite were 58.4, 65.3, and 73.9 degrees, respectively. After oxidation treatment, the contact angle of each mineral decreased to 43.7, 58.1, and 63.2 degrees, respectively. The decrease in the contact angle after oxidation treatment indicates Mineralsthat untreated 2020, 10, x surfaces changed into hydrophilic, i.e., the ﬂoatability of these minerals decreased.6 of 15

70 ) ° 60

Contact angle ( Contact 40

20 untreated1E-11oxidized 1E-10 1E-09 1E-08 1E-07 1E-06 1E-05 1E-04 1E-03 NaHS concentration (mol/L) Chalcocite Bornite Chalcopyrite

FigureFigure 2. 2. TheThe results results of of contact contact angle angle measurements measurements on on untreated, untreated, oxidized, oxidized, and and NaHS-treated NaHS-treated chalcocite,chalcocite, bornite, bornite, and and chalcopyrite chalcopyrite at at several several NaHS NaHS concentrations. concentrations.

After oxidation treatments, NaHS treatments were conducted. At 1.0 10 9 and 7.0 10 9 M 3.2. Single Mineral Flotation Tests With the Small Column Cell × − × − NaHS treatment to chalcocite, the contact angle of the surface turned from 43.7 degrees to 59.9 degrees. ThatAccording is because to NaHS Figure activated 3, flotation the chalcocitetests at several surface. conditions As the NaHS of oxidation concentration time were was increasedconducted over to decide1.0 10 a condition8 M, the e ffofect oxidation of activation time. was The not results able toof bechalcocite confirmed. showed Moreover, that the when recoveries NaHS concentration during 12 h × − towas 72 h increased maintained to 1.0 high 10recovery,3 M, the while contact the anglerecovery drastically suddenly decreased decreased and at thean oxidation surface of time chalcocite of 96 × − h.became The recoveries hydrophilic. of Thisbornite indicates decreased that highgradually concentration as oxidation NaHS time treatments increased. have Surprisingly, a depressive etheffect 9 recoveryon chalcocite of chalcopyrite flotation. was In the less case than of 20% bornite, at 12 after h and 1.0 kept10 low− M recoveries NaHS treatment, at most of the the contact conditions. angle × 9 Thevalue different of bornite trends did of not the almost minerals’ change, floatability which indicates after oxidation that 1.0 could10− Mcontribute NaHS treatment in the content did not ratio alter × 9 ofthe iron. oxidized Chalcopyrite, bornite which surface. has As a thehigh NaHS iron conten concentrationt, was oxidized was increased and its tosurface 7.0 10was− M,covered the contact with large amount of iron oxides. Dissolution of copper oxides and sulfates led to ×surface exposure of sulfides, but iron oxides remained on surfaces [36]. Therefore, it was considered that the floatability of chalcocite containing no iron was the highest, followed by bornite and chalcopyrite having the highest iron content. Based on Figure 3, the condition for more heavily oxidized copper sulfides, i.e., 96 h, was chosen for use in succeeding flotation tests to evaluate the activation and depression of minerals by NaHS. Figure 4 shows the single mineral flotation results of chalcocite, bornite, and chalcopyrite. Compared to the recovery without NaHS (0 mol/g), the recoveries of chalcocite increased at NaHS dosage of 1.0 × 10−7 mol/g, regardless of pH. On the other hand, as the NaHS dosage further increased, the recoveries decreased sharply. The behaviors of bornite recoveries indicated the dependence on pH. Without NaHS treatment, the recovery at pH 8 was the highest value in all pHs. After NaHS treatments, the recoveries increased within NaHS dosage of 1.0 × 10−7 to 1.0 × 10−6 M, and the result at pH 8 showed the highest recovery. Then the recoveries decreased as NaHS dosage increased. The flotation results of chalcopyrite showed that the floatability was completely low at any condition of NaHS dosage and pH. The floatability of chalcocite increased by the addition of a small amount of NaHS because of activation by NaHS, because oxidized copper species produced on the chalcocite surface were reacted with NaHS, and their species changed into copper sulfides [36]. Bornite recoveries also increased at any pH condition by a small dosage of NaHS. Moreover, the effect of pH was confirmed, and it was found that the floatability at low pH (pH 8) was higher than the high pH condition. This can be because of complex ion, Fe(HS)20 [36]. Iron oxidized species were dissolved into solutions as Fe(HS)20 by NaHS addition, and it was stable at a low pH. Therefore, floatability of bornite was high at low pH compare than the condition at high pH. A heavily oxidized chalcopyrite did not have the effect of activation by NaHS, because chalcopyrite surface after oxidation could be covered with large amount of iron oxides and/or hydroxides.

Minerals 2020, 10, 1027 6 of 15 angle of the bornite surface increased. The contact angle of the bornite decreased with increasing NaHS concentration similar to chalcocite. In the case of chalcopyrite, it was found that the contact angle trend was almost the same as bornite. The results of each mineral’s contact angle measurements indicate that NaHS works differently depending on the concentration. Low concentrations of NaHS (i.e., 1.0 10 9 to 1.0 10 8 M) had the × − × − effect of activation on the oxidized surfaces of copper sulfide minerals, while high concentrations (i.e., over 1.0 10 8 M) contributed to the depression of minerals. × − 3.2. Single Mineral Flotation Tests with the Small Column Cell According to Figure3, flotation tests at several conditions of oxidation time were conducted to decide a condition of oxidation time. The results of chalcocite showed that the recoveries during 12 h to 72 h maintained high recovery, while the recovery suddenly decreased at an oxidation time of 96 h. The recoveries of bornite decreased gradually as oxidation time increased. Surprisingly, the recovery of chalcopyrite was less than 20% at 12 h and kept low recoveries at most of the conditions. The different trends of the minerals’ floatability after oxidation could contribute in the content ratio of iron. Chalcopyrite, which has a high iron content, was oxidized and its surface was covered with large amount of iron oxides. Dissolution of copper oxides and sulfates led to surface exposure of sulfides, but iron oxides remained on surfaces [36]. Therefore, it was considered that the floatability of chalcocite containing no iron was the highest, followed by bornite and chalcopyrite having the highest iron content. Based on Figure3, the condition for more heavily oxidized copper sulfides, i.e., 96 h, was chosen for use in succeeding flotation tests to evaluate the activation and depression of minerals byMinerals NaHS. 2020, 10, x 7 of 15

100 90 80 70 60 50 40

Recovery (%) 30 20 10 0 0 102030405060708090100 Time (hr) Chalcocite Bornite Chalcopyrite

Figure 3. The ﬂotation recoveries of chalcocite, bornite, and chalcopyrite after oxidation treatments at Figure 3. The flotation recoveries of chalcocite, bornite, and chalcopyrite after oxidation treatments at 0, 12, 24, 48, 72, 96 h at pH 9. 0, 12, 24, 48, 72, 96 h at pH 9.

Figure100 4 shows the single mineral ﬂotation results of chalcocite, bornite, and chalcopyrite. Compared90 to the recovery without NaHS(a) (0 mol/g), the recoveries(b) of chalcocite increased at NaHS(c) dosage of80 1.0 10 7 mol/g, regardless of pH. On the other hand, as the NaHS dosage further increased, × − the recoveries70 decreased sharply. The behaviors of bornite recoveries indicated the dependence on pH. 60 Without NaHS50 treatment, the recovery at pH 8 was the highest value in all pHs. After NaHS treatments, 7 6 the recoveries40 increased within NaHS dosage of 1.0 10− to 1.0 10− M, and the result at pH 8

Recovery (%) × × showed the30 highest recovery. Then the recoveries decreased as NaHS dosage increased. The flotation results of20 chalcopyrite showed that the floatability was completely low at any condition of NaHS 10 dosage and pH. The floatability of chalcocite increased by the addition of a small amount of NaHS 0 because of activation010-8 10 by-7 NaHS,10-6 because10-5 10-4 oxidized010-8 copper10-7 10 species-6 10-5 produced10-4 010 on-8 the10 chalcocite-7 10-6 10 surface-5 10-4 were reacted with NaHS, and their species changedNaHS into dosage copper (mol/g) sulfides [36]. Bornite recoveries also pH 8 pH 9 pH 10 Figure 4. The recoveries of the minerals versus several NaHS dosages for (a) chalcocite, (b) bornite, and (c) chalcopyrite at pH 8, 9, and 10 with the small column cell (NaHS 0 M means only oxidation treatment was conducted.).

3.3. Mixture Mineral Flotation Tests Figure 5a shows that the recoveries of chalcocite increased as pH increased and as the amount of NaHS dosage increased. At NaHS dosage of 200 g/t, the chalcocite recovery was more depressed by NaHS at the initial stage of the flotation as shown in Figure 6. Figure 5b suggested that the bornite was activated at low pH and its recovery increased. On the other hand, as pH increased, the bornite was activated only by a small amount addition of NaHS and tended to be depressed even with a relatively small amount of NaHS. In Figure 7, the depression of bornite occurred at NaHS dosage of 200 g/t. The results of chalcopyrite in Figure 5c indicated that chalcopyrite was activated and its recovery increased at high pH and an optimum NaHS dosage. Figure 8 shows that the initial stage of chalcopyrite recoveries decreased at NaHS dosage of 200 g/t by the depression effect of NaHS. Therefore, it was considered that the pH and the NaHS dosage had significant influences on the activation and depression of each mineral. Compared with the results of single mineral flotation tests, the recoveries of the single mineral flotation tests were lower than that of mixture mineral flotation tests, because of the difference in the progress of oxidation. However, it was considered that the trends of activation and depression by NaHS and effect of pH were same between single and mixture mineral tests. The summarized diagrams are shown in Table 5. It was considered that the three minerals had in common trends of positive correlation between the activation and the NaHS dosage. One explanation is that the more the NaHS dosages there were, the more amount of copper oxides changed into copper sulfides, and the surfaces became more

Minerals 2020, 10, x 7 of 15

100 90 80 70 60 50 40 Minerals 2020, 10, 1027 7 of 15 Recovery (%) 30 20 increased at any pH condition10 by a small dosage of NaHS. Moreover, the effect of pH was confirmed, and it was found that the floatability0 at low pH (pH 8) was higher than the high pH condition. This can 0 1020304050607080901000 be because of complex ion, Fe(HS)2 [36]. Iron oxidized species were dissolved into solutions as Time (hr) Fe(HS) 0 by NaHS addition, and it was stable at a low pH. Therefore, floatability of bornite was high 2 Chalcocite Bornite Chalcopyrite at low pH compare than the condition at high pH. A heavily oxidized chalcopyrite did not have the effectFigure of activation 3. The flotation by NaHS, recoveries because of chalcocite, chalcopyrite bornite, surface and afterchalcopyrite oxidation after could oxidation be covered treatments with at large amount0, 12, of 24, iron 48, oxides72, 96 h andat pH/or 9. hydroxides.

100 90 (a) (b) (c) 80 70 60 50 40 Recovery (%) 30 20 10 0 010-8 10-7 10-6 10-5 10-4 010-8 10-7 10-6 10-5 10-4 010-8 10-7 10-6 10-5 10-4 NaHS dosage (mol/g) pH 8 pH 9 pH 10 FigureFigure 4. TheThe recoveries recoveries of of the the minerals minerals ve versusrsus several several NaHS NaHS dosages dosages for for ( (aa)) chalcocite, chalcocite, ( (bb)) bornite, bornite, andand ( (cc)) chalcopyrite chalcopyrite at at pH pH 8, 8, 9, 9, and and 10 with the sm smallall column cell (NaHS 0 M means only oxidation treatmenttreatment was was conducted.). conducted.).

3.3.3.3. Mixture Mixture Mineral Mineral Flotation Flotation Tests Tests FigureFigure 55aa showsshows thatthat the the recoveries recoveries of of chalcocite chalcocite increased increased as as pH pH increased increased and and as as the the amount amount of ofNaHS NaHS dosage dosage increased. increased. At At NaHS NaHS dosage dosage of of 200 20 g0/ t,g/t, the the chalcocite chalcocite recovery recovery was was more more depressed depressed by byNaHS NaHS at theat the initial initial stage stage of of the the flotation flotation as as shown shown in in Figure Figure6 .6. Figure Figure5b 5b suggested suggested that that the the bornite bornite was activated at low pH and its recovery increased. On On the the other other hand, hand, as as pH pH increased, the bornite was activated only by a small amount addition of of NaHS and and tended to to be depressed even with a relativelyrelatively small small amount amount of of NaHS. NaHS. In In Figure Figure 7,7 ,the the depression depression of of bornite bornite occurred occurred at atNaHS NaHS dosage dosage of 200of 200 g/t. g /Thet. The results results of ofchalcopyrite chalcopyrite in inFigure Figure 5c5c indicated indicated that that chalcopyrite chalcopyrite was activated and itsits recoveryrecovery increased increased at at high high pH pH and and an an optimum optimum NaHS NaHS dosage. dosage. Figure Figure 8 8shows shows that that the the initial initial stage stage of chalcopyriteof chalcopyrite recoveries recoveries decreased decreased at atNaHS NaHS dosage dosage of of200 200 g/t g /byt by the the depr depressionession effect effect of of NaHS. NaHS. Therefore, it it was considered that that the pH and th thee NaHS dosage had significant significant influences influences on on the activationactivation and depression depression of each each mineral. mineral. Compared Compared with with the the results results of of single single mineral mineral flotation flotation tests, tests, thethe recoveries recoveries of of the the single single minera minerall flotation flotation tests tests were were lower lower than than that that of of mixture mineral flotation flotation tests,tests, becausebecause ofof thethe di differencefference in in the the progress progress of oxidation.of oxidation. However, However, it was it consideredwas considered that the that trends the trendsof activation of activation and depression and depression by NaHS by andNaHS eff ectand of ef pHfect were of pH same were between same between single and single mixture and mixture mineral mineraltests. The tests. summarized The summarized diagrams diagrams are shown are inshown Table 5in. Table 5. It was considered that the three minerals had in common trends of positive correlation between the activation and the NaHS dosage. One explanation is that the more the NaHS dosages there were, the more amount of copper oxides changed into copper sulfides, and the surfaces became more

MineralsMinerals 20202020,, 1010,, xx 88 ofof 1515

hydrophobic.hydrophobic. OnOn thethe otherother hand,hand, therethere cancan bebe aa thresholdthreshold NaHSNaHS dosagedosage toto activateactivate thethe mineralmineral surfaces,surfaces, asas evidencedevidenced byby thethe depressiondepression ofof thethe minemineralsrals andand reductionreduction ofof theirtheir recoveriesrecoveries afterafter anan observedobserved increasingincreasing recoveryrecovery withwith NaHSNaHS dosagedosage.. InIn termsterms ofof depression,depression, thethe mineralsminerals hadhad inin commoncommon trendstrends ofof aa positivepositive correlationcorrelation betweenbetween thethe depressiondepression andand thethe pHpH andand aa positivepositive correlationcorrelation betweenbetween thethe depressiondepression andand thethe NaHSNaHS dosage.dosage. HSHS-- ionion couldcould bebe moremore stablestable atat higherhigher pHpH andand largerlarger NaHSNaHS dosagedosage inin aa solution.solution. RemainingRemaining largerlarger amountsamounts ofof HSHS-- ionion contributedcontributed toto thethe depressiondepression ofof mineralsminerals byby adsorbingadsorbing toto thethe mineralmineral surfacessurfaces [39].[39]. TheThe excessexcess HSHS-- ionion afterafter aa reactionreaction withwith thethe mineralmineral surfaces,surfaces, whichwhich contributedcontributed toto thethe depression,depression, isis releasedreleased toto thethe atmosphereatmosphere withwith timetime byby thethe influenceinfluence ofof airair oxidation,oxidation, thusthus thethe effecteffect ofof depressiondepression waswas graduallygradually weakerweaker withwith time.time. FigureFigure 99 showsshows thethe finalfinal coppercopper recoveriesrecoveries atat anyany conditioconditionn ofof pHpH andand NaHSNaHS dosage.dosage. TheThe coppercopper recoveriesrecoveries ofof thethe samplesample reflectedreflected thethe mineralmineral compositionscompositions ofof chalcocite,chalcocite, bornite,bornite, andand chalcopyrite.chalcopyrite. TheThe samplesample waswas richrich inin bornitebornite andand chalcopyrite.chalcopyrite. BorniteBornite recoverecoveriesries increasedincreased withwith anan optimumoptimum NaHSNaHS dosagedosage atat Mineralseacheach pH,pH,2020 andand, 10, 1027chalcopyritechalcopyrite recoveriesrecoveries increasedincreased withwith aa smallsmall amountamount ofof NaHSNaHS dosagedosage atat higherhigher 8pH.pH. of 15 Therefore,Therefore, thethe coppercopper recoveriesrecoveries increasedincreased withwith NaHSNaHS dosagedosage ofof 5050 g/tg/t atat pHpH 10.10.

FigureFigureFigure 5. 5.5. FinalFinalFinal recoveriesrecoveries of of ( (aa)) chalcocite, chalcocite, ( (bb)) bornite, bornite, andand and (( (ccc))) chalcopyritechalcopyrite chalcopyrite withoutwithout without NaHSNaHS NaHS andand and withwith with NaHSNaHSNaHS dosages dosagesdosages ofof 5050 gg/t,g/t,/t, 100100 gg/t,g/t,/t, andand 200200 gg/tg/t/t atat pH pH 8, 8, 9, 9, and and 10.

100100 9090 8080 (a)(i)(a)(i) (ii)(b)(ii)(b) (iii)(c)(iii)(c) 7070 6060 5050 4040 Recovery (%) Recovery (%) 3030 2020 1010 00 00 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 4500 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 4500 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 45 TimeTime (min)(min) NaHSNaHS 00 g/tg/t NaHSNaHS 5050 g/tg/t NaHSNaHS 100100 g/tg/t NaHSNaHS 200200 g/tg/t FigureFigureFigure 6. 6.6. ChalcociteChalcociteChalcocite recoveriesrecoveriesrecoveries withoutwithoutwithout NaHSNaHSNaHS andandand with withwith NaHS NaHSNaHS dosages dosagesdosages of ofof 50 5050 g g/t,g/t,/t, 100 100100 g g/t,g/t,/t, and andand 200 200200 g g/tg/t/t at Minerals(ataat) ( pH( a2020a)) pHpH 8,, 10 ( 8,b8,,) x(( pHb b)) pHpH 9, and 9,9, andand (c) (( pHcc)) pHpH 10. 10.10. 9 of 15

100 90 80 (a)(i) (b)(ii) (c)(iii) 70 60 50 40

Recovery (%) 30 20 10 0 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 Time (min) NaHS 0 g/t NaHS 50 g/t NaHS 100 g/t NaHS 200 g/t FigureFigure 7. 7.Bornite Bornite recoveries recoveries withoutwithout NaHSNaHS andand with NaHS dosages of of 50 50 g/t, g/t, 100 100 g/t, g/t, and and 200 200 g/t g/t at at (a()a pH) pH 8, 8, (b (b) pH) pH 9, 9, and and ( c()c) pH pH 10. 10.

100 90 80 70 (b)(ii) (iii)(c) 60 (a)(i) 50 40

Recovery(%) 30 20 10 0 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 Time (min) NaHS 0 g/t NaHS 50 g/t NaHS 100 g/t NaHS 200 g/t Figure 8. Chalcopyrite recoveries without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at (a) pH 8, (b) pH 9, and (c) pH 10.

Figure 9. Final copper recoveries without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at pH 8, 9, and 10.

Minerals 2020, 10, x 9 of 15

100 90 80 (a)(i) (b)(ii) (c)(iii) 70 60 50 40

Recovery (%) 30 20 10 0 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 Time (min) NaHS 0 g/t NaHS 50 g/t NaHS 100 g/t NaHS 200 g/t

MineralsFigure2020, 10 7., 1027Bornite recoveries without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at 9 of 15 (a) pH 8, (b) pH 9, and (c) pH 10.

100 90 80 70 (b)(ii) (iii)(c) 60 (a)(i) 50 40

Recovery(%) 30 20 10 0 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 Time (min) NaHS 0 g/t NaHS 50 g/t NaHS 100 g/t NaHS 200 g/t FigureFigure 8. 8.Chalcopyrite Chalcopyrite recoveries recoveries without without NaHS NaHS and and with with NaHS NaHS dosages dosages of of 50 50 g /g/t,t, 100 100 g/ t,g/t, and and 200 200 g/ t atg/t (a )at pH (a) 8,pH (b 8,) pH (b) 9,pH and 9, and (c) pH (c) 10.pH 10.

Table 5. The relationship between the minerals and the conditions of pH and NaHS dosage. “+” means positive correlation, “ ” means negative correlation. − Minerals pH NaHS Activation + + Chalcocite Depression + + Activation + Bornite − Depression + + Activation + + Chalcopyrite Depression + +

It was considered that the three minerals had in common trends of positive correlation between the activation and the NaHS dosage. One explanation is that the more the NaHS dosages there were, the more amount of copper oxides changed into copper sulfides, and the surfaces became more hydrophobic.Figure 9. OnFinal the copper other recoveries hand, there without can beNaHS a threshold and with NaHSNaHS dosages dosage toof 50 activate g/t, 100 the g/t, mineral and 200 surfaces,g/t as evidencedat pH 8, 9, by and the 10. depression of the minerals and reduction of their recoveries after an observed increasing recovery with NaHS dosage. In terms of depression, the minerals had in common trends of a positive correlation between the depression and the pH and a positive correlation between the depression and the NaHS dosage. HS− ion could be more stable at higher pH and larger NaHS dosage in a solution. Remaining larger amounts of HS− ion contributed to the depression of minerals by adsorbing to the mineral surfaces [39]. The excess HS− ion after a reaction with the mineral surfaces, which contributed to the depression, is released to the atmosphere with time by the influence of air oxidation, thus the effect of depression was gradually weaker with time. Figure9 shows the final copper recoveries at any condition of pH and NaHS dosage. The copper recoveries of the sample reflected the mineral compositions of chalcocite, bornite, and chalcopyrite. The sample was rich in bornite and chalcopyrite. Bornite recoveries increased with an optimum NaHS dosage at each pH, and chalcopyrite recoveries increased with a small amount of NaHS dosage at higher pH. Therefore, the copper recoveries increased with NaHS dosage of 50 g/t at pH 10. Minerals 2020, 10, x 9 of 15

100 90 80 (a)(i) (b)(ii) (c)(iii) 70 60 50 40

Recovery (%) 30 20 10 0 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 Time (min) NaHS 0 g/t NaHS 50 g/t NaHS 100 g/t NaHS 200 g/t Figure 7. Bornite recoveries without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at (a) pH 8, (b) pH 9, and (c) pH 10.

100 90 80 70 (b)(ii) (iii)(c) 60 (a)(i) 50 40

Recovery(%) 30 20 10 0 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 Time (min) NaHS 0 g/t NaHS 50 g/t NaHS 100 g/t NaHS 200 g/t MineralsFigure2020, 8.10 ,Chalcopyrite 1027 recoveries without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 20010 of 15 g/t at (a) pH 8, (b) pH 9, and (c) pH 10.

Figure 9. Final copper recoveries without NaHS and with NaHS dosages of 50 g/t, g/t, 100 g/t, g/t, and 200 g/t g/t at pH 8, 9, and 10. 3.4. Derivation of Flotation Kinetic Model

In a ﬂotation cell, the rate of disappearance of particle mass ( dW/dt) is proportional to the particle − mass in a cell (W), by the following equation [3]:

dW = kW (4) − dt where k is the ﬂotation rate constant. The ﬁrst-order model [11] is given by integrating from time 0 to t when mass in the cell decreases from W0 (initial particle mass) to W [3]: Z Z W dW t = k dt (5) − W0 W 0

W ln = kt (6) W0 − W = W exp( kt) (7) 0 − Equation (7) is rearranged by recovery, where R = (W0 – W)/W0 (R on a fractional basis) gives [3]:

R = 1 exp( kt) (8) − − In this experimental system, NaHS was added to modify the surface properties of the minerals. To derive the ﬂotation kinetic model, it was necessary to consider the rate of NaHS decreasing from the ﬂotation system when NaHS reacted with the minerals. Therefore, the rate of NaHS decreasing, which decreased by the reaction with minerals, was substituted into k in Equation (4):

k = K[1 A exp( B t)] (9) − ∗ − ∗ where K is the flotation rate constant, A is defined as the concentration of NaHS times 103, B is the reaction rate constant between the surfaces and NaHS. The calcurated A and B were shown in Supplementary Tables S1 to S3. The surface properties of the copper sulfide minerals reacted with NaHS were analyzed by [36], and the results of surface analyses by X-ray photoelectron spectroscopy showed that fresh copper sulfide minerals, copper sulfides produced by NaHS, and copper and iron oxides and hydroxides precipitates were generated after NaHS treatments. Therefore, the surface properties were focused on, and the three surfaces: (1) the fresh surfaces, (2) the surfaces activated by NaHS, and (3) Minerals 2020, 10, x 11 of 15

𝑅= 𝜑 ∗𝑅 (11)

𝜑 =1 (12)

where Ki are the flotation rate constants of the three components, Ri are the flotation recovery rates of the three components, φi are the mass fraction of each component. When i = 3, A and B are defined as 0, because oxides and hydroxide were produced by alkalinity of a solution. The equations were fitted Minerals 2020, 10to, each 1027 mineral’s results of batch flotation tests, and each flotation rate constant of chalcocite, bornite, 11 of 15 and chalcopyrite is shown in Figure 10 to Figure 12, respectively. Figure 10(a1,a2) suggested that fresh surface (Cu2S) dominated the floatability of chalcocite. φ2 had a peak at each pH, and the NaHS activation was significantly influenced at pH 8. The correlation oxides and/ortrends hydroxides of all Figure surfaces, 10(a3) K3 were were very defined low values as for floatability all mineralscomponents. because the floatability These of considerations oxides had been reflectedand/or in thehydroxides following was significantly models: low. Figure 10(b3) shows that φ3 gradually decreased as NaHS dosage increased. This trend suggested that the oxidized surface changed into sulfides by NaHS dosage. Figure 11b shows thatdW φ1 graduallyX3 decreased as NaHS dosage increased, while φ2 increased as NaHS dosage increased. This= can be becauseKi[1 of theA activationexp( B oft the)] borniteW surface by NaHS. (10) − dt i=1 − ∗ − ∗ ∗ Figure 11(a2) indicated that K2 increased from NaHS dosage of 0 g/t to 100 g/t, and at higher dosage decreased at pH 8 but increased at pH 9 andX 10.3 Figure 11(b2) shows that φ2 at pH 8 especially increased with the increase of NaHS dosageR = 0 g/t to ϕ200i g/t.Ri The amount of activated surface was (11) i=1 increased by the increase of NaHS dosage and this explains∗ the trend. Figure 11(b3) shows that φ3 at pH 8 drastically decreased from NaHS dosageX3 of 0 g/t to 100 g/t while it decreased from 0 g/t to 50

3 ϕi = 1 (12) g/t at pH 9 and 10. Then, φ at pH 8 increased fromi=1 100 g/t to 200 g/t whereas at pH 9 and 10 increased from 50 g/t to 200 g/t. This is because the oxidized surface was sulfurized by NaHS until NaHS dosage where Ki arereached the flotation an optimum rate value, constants and oxides of and/or the three hydroxides components, might have Rincreasedi are the on flotationthe surface recoveryafter rates of the three components,reaching the optimumϕi are the NaHS mass dosage. fraction Figure of12(a2,b2) each show component. that chalcopyrite When K2i increased= 3, A and with Btheare defined as 0, because oxidesincrease and of pH, hydroxide and φ2 had werethe highest produced point depending by alkalinity on pH. This of apoint solution. of φ2 with The NaHS equations dosage were fitted of 50 g/t at pH 10 was the highest followed by pH 9 and 8. Figure 12(b3) indicated that φ3 at each pH to each mineral’sdecreased results with NaHS of batch dosage flotation of 50 g/t, and tests, increas anded each as NaHS flotation dosage increased. rate constant These trends of chalcocite, were bornite, and chalcopyritesimilar isto shownthe chalcopyrite in Figure results 10 of, copper Figure ore 11 flotation, Figure tests. 12 , respectively.

Minerals 2020, 10, x 12 of 15 Figure 10. The chalcocite results of (a) ﬂotation rate constants, (1) K1, (2) K2, (3) K3, and (b) mass Figure 10. The chalcocite results of (a) flotation rate constants, (1) K1, (2) K2, (3) K3, and (b) mass fraction, (1) ϕ , (2) ϕ , (3) ϕ , without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at fraction,1 (1)2 φ1, (2) φ23, (3) φ3, without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at pH 8, 9, andpH 10. 8, 9, and 10.

25 0.7 (1) (2) (3) 0.6 20 0.5

15 0.4

(a) 0.3 10

0.2 5 0.1 Flotation rate constant (1/min) constant rate Flotation 0 0 1 0.4 (1) (2) (3)

0.8 0.3

0.6 (b) 0.2 0.4

0.1

Mass fraction (fraction) Massfraction 0.2

0 0 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 NaHS dosage (g/t) pH 8 pH 9 pH 10

Figure 11. The bornite results of (a) flotation rate constants, (1) K1, (2) K2, (3) K3, and (b) mass fraction, Figure 11. The bornite results of (a) ﬂotation rate constants, (1) K1, (2) K2, (3) K3, and (b) mass fraction, (1) φ1, (2) φ2, (3) φ3, without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at pH 8, 9, (1) ϕ1, (2) ϕ2and, (3) 10.ϕ 3, without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at pH 8, 9, and 10. 25 0.7 (1) (2) (3) 0.6 20 0.5

15 0.4

(a) 0.3 10

0.2 5 0.1 Flotation rate constant (1/min) constant Flotation rate 0 0 1 0.4 (1) (2) (3) 0.8 0.3

0.6 (b) 0.2 0.4

0.1

Mass fraction (fraction) fraction Mass 0.2

0 0 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 NaHS dosage (g/t) pH 8 pH 9 pH 10

Figure 12. The chalcopyrite results of (a) flotation rate constants, (1) K1, (2) K2, (3) K3, and (b) mass fraction, (1) φ1, (2) φ2, (3) φ3, without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at pH 8, 9, and 10.

Minerals 2020, 10, x 12 of 15

Figure 10. The chalcocite results of (a) flotation rate constants, (1) K1, (2) K2, (3) K3, and (b) mass fraction, (1) φ1, (2) φ2, (3) φ3, without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at pH 8, 9, and 10.

25 0.7 (1) (2) (3) 0.6 20 0.5

15 0.4

(a) 0.3 10

0.2 5 0.1 Flotation rate constant (1/min) constant rate Flotation 0 0 1 0.4 (1) (2) (3)

0.8 0.3

0.6 (b) 0.2 0.4

0.1

Mass fraction (fraction) Massfraction 0.2

0 0 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 NaHS dosage (g/t) pH 8 pH 9 pH 10

Figure 11. The bornite results of (a) flotation rate constants, (1) K1, (2) K2, (3) K3, and (b) mass fraction, Minerals 2020,(1)10 ,φ 10271, (2) φ2, (3) φ3, without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at pH 8, 9, 12 of 15 and 10.

25 0.7 (1) (2) (3) 0.6 20 0.5

15 0.4

(a) 0.3 10

0.2 5 0.1 Flotation rate constant (1/min) constant Flotation rate 0 0 1 0.4 (1) (2) (3) 0.8 0.3

0.6 (b) 0.2 0.4

0.1

Mass fraction (fraction) fraction Mass 0.2

0 0 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 NaHS dosage (g/t) pH 8 pH 9 pH 10

Figure 12. The chalcopyrite results of (a) flotation rate constants, (1) K1, (2) K2, (3) K3, and (b) mass Figure 12. The chalcopyrite results of (a) ﬂotation rate constants, (1) K1, (2) K2, (3) K3, and (b) mass fraction, (1) φ1, (2) φ2, (3) φ3, without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at fraction, (1) ϕ1, (2) ϕ2, (3) ϕ3, without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at pH 8, 9, and 10. pH 8, 9, and 10.

Figure 10(a1,a2) suggested that fresh surface (Cu2S) dominated the floatability of chalcocite. ϕ2 had a peak at each pH, and the NaHS activation was significantly influenced at pH 8. The correlation trends of all Figure 10(a3) K3 were very low values for all minerals because the floatability of oxides and/or hydroxides was significantly low. Figure 10(b3) shows that ϕ3 gradually decreased as NaHS dosage increased. This trend suggested that the oxidized surface changed into sulfides by NaHS dosage. Figure 11b shows that ϕ1 gradually decreased as NaHS dosage increased, while ϕ2 increased as NaHS dosage increased. This can be because of the activation of the bornite surface by NaHS. Figure 11(a2) indicated that K2 increased from NaHS dosage of 0 g/t to 100 g/t, and at higher dosage decreased at pH 8 but increased at pH 9 and 10. Figure 11(b2) shows that ϕ2 at pH 8 especially increased with the increase of NaHS dosage 0 g/t to 200 g/t. The amount of activated surface was increased by the increase of NaHS dosage and this explains the trend. Figure 11(b3) shows that ϕ3 at pH 8 drastically decreased from NaHS dosage of 0 g/t to 100 g/t while it decreased from 0 g/t to 50 g/t at pH 9 and 10. Then, ϕ3 at pH 8 increased from 100 g/t to 200 g/t whereas at pH 9 and 10 increased from 50 g/t to 200 g/t. This is because the oxidized surface was sulfurized by NaHS until NaHS dosage reached an optimum value, and oxides and/or hydroxides might have increased on the surface after reaching the optimum NaHS dosage. Figure 12(a2,b2) show that chalcopyrite K2 increased with the increase of pH, and ϕ2 had the highest point depending on pH. This point of ϕ2 with NaHS dosage of 50 g/t at pH 10 was the highest followed by pH 9 and 8. Figure 12(b3) indicated that ϕ3 at each pH decreased with NaHS dosage of 50 g/t, and increased as NaHS dosage increased. These trends were similar to the chalcopyrite results of copper ore flotation tests.

4. Conclusions The surface wettability and floatability of chalcocite, bornite, and chalcopyrite affected by NaHS dosage and pH were investigated. The results of the contact angle measurement showed that NaHS works differently depending on the concentration. The NaHS activation was observed at low concentrations of NaHS, while the depression of each mineral occurred at high concentrations. The floatability of chalcocite was affected by NaHS dosage, and the recoveries increased with the increase of NaHS dosage. The bornite floatability at lower pH was the highest compared to high pHs, and bornite recoveries tended to be depressed with a smaller amount of NaHS as pH increased. The recoveries of chalcopyrite increased as pH increased at an optimum NaHS dosage. Moreover, Minerals 2020, 10, 1027 13 of 15 it was suggested that there can be a threshold NaHS dosage to activate the surface, as evidenced by the depression of the minerals and reduction of recoveries at higher dosages of NaHS. The well-fitted flotation kinetic model to the results of the mixture mineral flotation tests based on the floatability component model and the surface properties of the minerals was generated. The trends of the flotation rate constants and mass fractions with NaHS dosages and pHs could be similar trends with the flotation results. Therefore, considering the surface properties of the copper sulfide minerals affected by NaHS and the reaction rate between NaHS and the minerals, the model which could produce the behavior of activation and depression was created successfully.

Supplementary Materials: The following are available online at http://www.mdpi.com/2075-163X/10/11/1027/s1, Table S1: The chalcocite results of the concentration of NaHS, A and the reaction rate constant, B, without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at pH 8, 9, and 10; Table S2: The bornite results of the concentration of NaHS, A and the reaction rate constant, B, without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at pH 8, 9, and 10; Table S3: The chalcopyrite results of the concentration of NaHS, A and the reaction rate constant, B, without NaHS and with NaHS dosages of 50 g/t, 100 g/t, and 200 g/t at pH 8, 9, and 10. Author Contributions: Conceptualization, H.M. and C.T.; methodology, H.M., K.M. and C.T.; validation, H.M. and C.T.; formal analysis, H.M.; investigation, H.M.; writing—original draft preparation, H.M.; writing—review and editing, H.M.; supervision, C.T.; project administration, M.K. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors would like to thank Satur, J.V. for editing a draft of this manuscript. We also thank Ebisu, Y. for valuable comments for this paper. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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