Influence of Particle Size on Flotation Separation of Ilmenite and Forsterite

Abstract

In addition to bubble–particle interaction, particle–particle interaction also has a significant influence on mineral flotation. Fine particles that coat the mineral surface prevent direct contact with collectors and/or air bubbles, thereby lowering flotation recovery. Calculating the particle interaction energy can help in evaluating the interaction behavior of particles. In this study, the floatability of coarse ilmenite (−151 + 74 μm) and different particle sizes (−45 + 25, −25 + 19, −19 μm) of forsterite with NaOL as a collector was investigated. The results showed that forsterite sizes of −45 + 25 and −25 + 19 μm had no effect on the ilmenite floatability, whereas −19 μm forsterite significantly reduced ilmenite floatability. A particle size analysis of artificially mixed minerals and a scanning electron microscopy (SEM) analysis of the flotation products showed that heterogeneous aggregation occurred between ilmenite and −19 μm forsterite particles. The extended DLVO (Derjaguin–Landau–Verwey–Overbeek) theory was applied to calculate the interaction energy between mineral particles using data from zeta potential and contact angle measurements. The results showed that the interaction barriers between ilmenite (−151 + 74 μm) and forsterite (−45 + 25, −25 + 19, and −19 μm) were 11.94 × 10³ kT, 8.23 × 10³ kT and 4.09 × 10³ kT, respectively. Additionally, the interaction barrier between forsterite particles smaller than 19 μm was 0.51 × 10³ kT. The strength of the barrier decreased as the size of the forsterite decreased. Therefore, fine forsterite particles and aggregated forsterite can easily overcome the energy barrier, coating the ilmenite particle surface. This explains the effect of different forsterite sizes on the floatability of ilmenite and the underlying mechanism of particle interaction.

1. Introduction

Titanium is widely distributed around the world and is used in strategic emerging fields such as aerospace, navigation, energy, construction, transportation, medicine, and materials [1,2,3]. Ilmenite is an important titanium-bearing mineral with the molecular formula FeTiO₃. It has been reported that more than 90% of the world’s titanium resources come from ilmenite [4]. China’s titanium reserves rank among the largest in the world, and the country has developed into the world’s largest producer of titanium concentrate. Titanium resources in China are mainly found in the Panxi area, and it is reported that this area contains up to 93% of China’s total titanium reserves [5,6]. However, most of the ores in the Panxi area are difficult to recover ilmenite from [7]. As the mining process progresses deeper, the original gabbro-type iron ore is gradually transformed into forsterite (Mg₂SiO₄) pyroxene-type iron ore. This transformation results in a finer particle size distribution of ilmenite, a notable increase in forsterite content, and a more intricate mineral composition [8]. Therefore, it is necessary to investigate the influence of forsterite particle size on ilmenite recovery.

Increasing attention has been paid to the effect of fine particles on mineral flotation separation. Fine particles have a relatively high surface area, and more reagents are needed for processing. Prior studies showed that the collision probability between fine particles and bubbles is low [9], and fine particles exhibit a reduced tendency of adhesion to bubbles, necessitating greater kinetic energy and a prolonged induction time [10,11,12]. Therefore, flotation recovery and selectivity are deteriorated under normal conditions [13,14]. This circumstance is unfavorable for flotation separation from non-target minerals. On the other hand, fine gangue particles can coat the surface of useful minerals, preventing agents or bubbles from acting on them, thereby reducing flotation recovery [15,16]. The influence of fine particles on the flotation process and improvement methods has been studied in slime coating [17,18], carrier flotation [19,20], and flocculation flotation [21].

Zhu et al. [22] studied the autogenous-carrier flotation of ilmenite. They measured the particle size distribution before and after conditioning with NaOL at a concentration of 1 × 10⁻⁴ M, an ilmenite autogenous-carrier particle size of −38 + 74 µm, and a pH range of 4.5–5.5 using a laser particle size analyzer. They found that fine and coarse ilmenite particles can aggregate, thereby improving the recovery rate of fine ilmenite. Yang et al. [23] studied the influence of pyroxene and olivine particle size on the flotation recovery of ilmenite from the Panxi area. They found that the fine particle content has a significant deterioration effect on the flotation recovery of ilmenite, and they suggested that a narrow particle size distribution of minerals is beneficial to flotation recovery. Fan and Cao [24] calculated the interaction force between ilmenite and titanaugite particles through extended DLVO. Their results showed that aggregation occurs easily between ilmenite and fine titanaugite particles, thus reducing the recovery rate of ilmenite. To date, there has been extended research on the interaction between titanaugite and ilmenite particles. However, the interaction between fine forsterite, another main gangue mineral, and ilmenite particles, along with its mechanism, has not been studied.

Lange et al. [25] used an online particle size distribution technique to obtain the change in particle size in conditioning and used optical microscopy to observe the flotation products. Their results showed that there is aggregation between coarse and fine particles. Due to the difference in elemental composition between valuable minerals and gangue minerals, SEM/EDS is used as a combined technique involving scanning electron microscopy and energy-dispersive X-ray spectroscopy to distinguish these minerals. Many researchers have observed the aggregation of flotation products using SEM-EDS analysis [15,16,26,27]. Derjaguin–Landau–Verwey–Overbeek theory [28,29,30] (E-DLVO theory), which considers hydrophobic and hydrophilic interactions, can be applied to calculate the interaction energies between mineral particles. It can explain the dispersion and aggregation between mineral particles and the flotation performance of minerals [31,32,33]. The above research methods have been widely used to study particle interactions in the flotation process, such as those for coal [34,35,36], hematite [37,38], magnesite [15,16], and phosphate rock [39,40]. However, these methods have not been used in the flotation system of fine forsterite and ilmenite.

In this study, the aggregation/dispersion behavior of forsterite and ilmenite of different particle sizes was studied, and the interaction mechanism was explored by calculating the interaction potential energy profiles. Based on the contact angle and zeta potential data, E-DLVO theory was applied to calculate the interaction energy between mineral particles before and after collector treatment. Particle size and SEM analyses were used to observe the particle aggregation directly. In our previous work [23], the influence of different particle sizes of forsterite on ilmenite flotation recovery was investigated, explaining the mechanism in terms of agent adsorption. In this paper, the intrinsic mechanism is explained by means of the particle interaction microscopic force.

2. Materials and Methods

2.1. Materials

After the repeated application of magnetic separation and gravity separation to vanadium–titanium magnetite ore from Panzhihua (Sichuan province, China), purified ilmenite and forsterite samples were obtained. These purified samples were subjected to grinding and wet screening to obtain different particle sizes (−151 + 74, −45 + 25, −25 + 19, −19 μm). Then, these samples were washed three times using deionized (DI) water to remove impurity ions such as Ca²⁺ and Mg²⁺, produced during the preparation process, and dried at room temperature.

Table 1. Results of multi-element chemical analysis of ilmenite and forsterite samples (mass fraction, %).

Sample	TiO2	Fe2O3	CaO	SiO2	Al2O3	MgO
Ilmenite	50.64	46.48	0.19	0.56	0.30	4.13
Forsterite	0.01	9.89	0.13	40.00	0.14	49.30

and Figure 1 show the multi-element chemical analysis and X-ray diffraction (XRD) characterization results, respectively, for the purified samples. The theoretical TiO₂ content in ilmenite is 52.7%, indicating a purity of 96.09% for the ilmenite sample. Additionally, the theoretical (Fe+Mg)O content in forsterite is 57.2%, indicating a purity of 93.96% for the forsterite sample.

Sodium oleate (NaOL, analytical grade) obtained from ChengDu Chron Chemicals Co, Ltd. (Chengdu, China), was used as an anionic collector in ilmenite flotation. Sulfuric acid and sodium hydroxide (H₂SO₄, NaOH, analytical grade), obtained from ChengDu Chron Chemicals Co, Ltd. (Chengdu, China), were used to regulate the pH. Deionized (DI) water with a resistivity of 18.25 MΩ·cm was used in the related experiments.

2.2. Methods

2.2.1. Micro-Flotation Experiments

Micro-flotation experiments with pure and artificial mixed minerals were performed using an XFGCII flotation machine (Jitan Machinery Co., Ltd., Changchun, China). Flotation was operated at an airflow rate of 0 L/min. The speed of the impeller was kept constant at 1602 rpm. In the purified mineral micro-flotation experiments, 2 g of purified mineral was suspended in 40 mL of DI water. Before the addition of the reagents, the slurry was conditioned for 1 min. The prepared H₂SO₄ solution or NaOH solution was added to adjust the pH to different levels (ranging from 2 to 12) with 3 min of agitation. Subsequently, a NaOL solution was added to form suspensions with varying NaOL concentrations (0, 1, 2, 3, 4, 5 × 10⁻⁴ M), followed by an additional 3 min of stirring. The froth product was then collected by scraping every 5 s for 5 min. Finally, the separated froth product and tailing were filtered and dried in a drying oven at 60 °C.

In the artificial mixed mineral experiments, 2 g samples of purified ilmenite and forsterite were mixed in different ratios (ilmenite/forsterite = 9:1, 8:2, 7:3, and 5:5). After the same operation following the purified mineral micro-flotation experiments, the froth product was assessed by means of chemical analysis. Each experiment was operated three times under the same conditions, and the reported result was the average of standard deviations in three experiments. The standard deviation for each test was calculated and presented as the error bar to illustrate the deviation of the three flotation results in the test relative to the average value.

2.2.2. Zeta Potential Measurements

The zeta potential values of the minerals were measured using a Nano-ZS90 Micro-Electrophoresis Apparatus (Malvern, UK). In each measurement, 30 mg of powdered single-mineral sample (−19 μm) and 40 mL of DI water were mixed in a beaker. A NaOL solution was introduced to achieve a NaOL concentration of 3 × 10⁻⁴ M in the suspension, followed by 10 min of stirring, and the pH was adjusted to different levels (ranging from 2 to 12). The suspension was allowed to settle for an additional 10 min, after which the zeta potential values of the particles in the liquid supernatant were measured. The reported result was the average of standard deviations in three repeated tests. The standard deviation for each test was calculated and presented as an error bar to describe the deviation of the three flotation results in the test relative to the average value.

2.2.3. Contact Angle Measurements

A Surface Analyzer LSA 100 LSA100 (Lauda, German) was used for the contact angle measurements. The single-mineral powdered samples (−19 μm) treated with NaOL solution (3 × 10⁻⁴ M) were filtered, dried, and tableted with a pressure of 10 MPa. Then, the liquid drops were dropped onto the tablet using a microsyringe, with a droplet volume of 4 μL. In each test, a treated sample was used to capture the contact process image of the liquid drop. At least three different locations of samples were measured, and the average value of the contact angle was reported. The error range of the average was controlled within ±2 degrees to ensure the validity of the data.

2.2.4. Particle Size Measurements

The particle size distribution of the minerals was determined using an LS 13 320 Laser Diffraction Particle Size Analyzer (Beckman Coulter, Indianapolis, Indiana, USA). Forsterite with different particle sizes (−45 + 25, −25 + 19, −19 μm) and coarse ilmenite (−151 + 74 μm) were mixed at a mass ratio of 1:1. After the same procedures were performed as for the micro-flotation experiments, the samples were directly taken from in the mixed slurry for particle size measurement.

2.2.5. SEM and EDS Analysis

A Sigma300 (Zessie, Oberkochen, Germany) scanning electron microscope (SEM) was used to observe the aggregation of the fine forsterite on the coarse ilmenite particles. An XFlash 6160 (Bruker, Berlin, Germany) energy-dispersive X-ray spectroscope (EDS) was used to analyze the elementary composition to distinguish the mineral particles in the SEM images.

2.2.6. DLVO Theoretical

The classical DLVO theory was developed by Derjaguin and Landau in Russia in 1941 and Verwey and Overbeek in 1948 [41], respectively. It is based on the sum ($V_{\mathrm{T}}^{\mathrm{D}}$) of the electrostatic energy ($V_{\mathrm{E}}$) and van der Waals energy ($V_{\mathrm{W}}$) between mineral particles to predict the aggregation/dispersion behavior.

$$\begin{array}{c}{V}_{\mathrm{T}}^{\mathrm{D}}=V_{\mathrm{W}}+V_{\mathrm{E}}\end{array}$$

(1)

However, flotation reagents can make the surface of mineral particles more hydrophilic or hydrophobic, resulting in polar interfacial interaction between mineral particles. To explain this phenomenon, the extended DLVO theory has been put forward. Compared with the classical DLVO theory, the extended DLVO theory considers the hydration or hydrophobic interactions ($V_{\mathrm{H}}$) that play a decisive role in the aggregation/dispersion behavior between mineral particles [42]:

$$\begin{array}{c}{V}_{\mathrm{T}}^{\mathrm{ED}}=V_{\mathrm{W}}+V_{\mathrm{E}}+V_{\mathrm{H}}\end{array}$$

(2)

(a) Van der Waals interaction, $V_{\mathrm{W}}$ [43,44]

$$\begin{array}{c}{V}_{\mathrm{W}}=-{\displaystyle \frac{A_{132}}{6H}}{\displaystyle \frac{R_1{R}_2}{R_1+R_2}}\end{array}$$

(3)

Here,

$$\begin{array}{c}{A}_{132}=\left(\sqrt{A_{11}}-\sqrt{A_{33}}\right)\left(\sqrt{A_{22}}-\sqrt{A_{33}}\right)\end{array}$$

(4)

(b) Electrical interaction, $V_{\mathrm{E}}$ [45,46]

For the same particle surface charge ball–ball models:

$$\begin{array}{c}{V}_{\mathrm{E}}=2ᴨ{\epsilon }_0{\epsilon }_{\mathrm{r}}R{\mathrm{\Psi }}^2\ln \left[1+\exp \left(-\kappa H\right)\right]\end{array}$$

(5)

For ball–flat models:

$$\begin{array}{c}{V}_{\mathrm{E}}=ᴨ{\epsilon }_0{\epsilon }_{\mathrm{r}}{\displaystyle \frac{R_1{R}_2}{R_1+R_2}}{\left({\displaystyle \frac{kT}{Ze}}\right)}^2\left({\mathrm{\Psi }}_1^2+{\mathrm{\Psi }}_2^2\right)\left[{\displaystyle \frac{2{\phi }_1{\phi }_2}{{\phi }_1^2+{\phi }_2^2}}p+q\right]\end{array}$$

(6)

where

$$\begin{array}{c}p=\ln \left[{\displaystyle \frac{1+\exp \left(-\kappa H\right)}{1-\exp \left(-\kappa H\right)}}\right]\end{array}$$

(7)

$$\begin{array}{c}q=\ln \left[1-\exp \left(-2\kappa H\right)\right]\end{array}$$

(8)

$$\begin{array}{c}\kappa ={\left({\displaystyle \frac{2e^2{n}_0{Z}^2}{{\epsilon }_0{\epsilon }_{r}kT}}\right)}^{1/2}={\left({\displaystyle \frac{2e^2{N}_{\mathrm{A}}C{Z}^2}{{\epsilon }_0{\epsilon }_{r}kT}}\right)}^{1/2}\end{array}$$

(9)

(c) Polar interfacial interaction, $V_{\mathrm{H}}$ [47,48]

$$\begin{array}{c}{V}_{\mathrm{H}}=2ᴨ{\displaystyle \frac{R_1{R}_2}{R_1+R_2}}{h}_0{V}_{\mathrm{H}}^0\exp {\displaystyle \frac{H_0-H}{h_0}}\end{array}$$

(10)

In order to calculate the hydrophobic force $V_{\mathrm{H}}$, the “decay length” $h_0$ must be determined. According to the general literature, $h_0$ = 1~10 nm; in this study, the $h_0$ value was assumed to be 2 nm. $H_0$ is the minimum equilibrium distance; according to the literature, $H_0$ = 0.1677 nm in a water medium [49]. $V_{\mathrm{H}}^0$ is the polar interface interaction energy constant, which can be calculated using Equation (11):

$$\begin{array}{c}{V}_{\mathrm{H}}^0=2\left[\sqrt{{\gamma }_3^{+}}\left(\sqrt{{\gamma }_1^{-}}+\sqrt{{\gamma }_2^{-}}-\sqrt{{\gamma }_3^{-}}\right)+\sqrt{{\gamma }_3^{-}}\left(\sqrt{{\gamma }_1^{+}}+\sqrt{{\gamma }_2^{+}}-\sqrt{{\gamma }_3^{+}}\right)-\sqrt{{\gamma }_1^{+}{\gamma }_2^{-}}-\sqrt{{\gamma }_1^{-}{\gamma }_2^{+}}\right]\end{array}$$

(11)

where ${\gamma }^{+}$ is for the electron-acceptor parameter and ${\gamma }^{-}$ is for the electron-donor parameter of the surface energy of the substance.

According to Van Oss et al. [50,51,52,53,54], the contact angle is related to the polar (Lewis acid-base, ${\gamma }^{+}$ or ${\gamma }^{-}$) and apolar (Lifshitz–van der Waals, ${\gamma }^{LW}$) components of the surface energy of solids, as well as the solid–liquid interfacial energy. They derived Equation (12):

$$\begin{array}{c}\left(1+\cos \mathrm{\theta }\right)\left({\gamma }_{\mathrm{L}}+\sqrt{{\gamma }_{\mathrm{L}}^{-}{\gamma }_{\mathrm{L}}^{+}}\right)=2\left(\sqrt{{\gamma }_{\mathrm{S}}^{LW}{\gamma }_{\mathrm{L}}^{LW}}+\sqrt{{\gamma }_{\mathrm{S}}^{+}{\gamma }_{\mathrm{L}}^{-}}+\sqrt{{\gamma }_{\mathrm{S}}^{-}{\gamma }_{\mathrm{L}}^{+}}\right)\end{array}$$

(12)

Most oxidized ores can be considered as monopolar surfaces, for which ${\gamma }_{\mathrm{S}}^{+}\approx 0$; Equation (13) can be simplified as follows:

$$\begin{array}{c}\left(1+\cos \mathrm{\theta }\right)\left({\gamma }_{\mathrm{L}}+\sqrt{{\gamma }_{\mathrm{L}}^{-}{\gamma }_{\mathrm{L}}^{+}}\right)=2\left(\sqrt{{\gamma }_{\mathrm{S}}^{LW}{\gamma }_{\mathrm{L}}^{LW}}+\sqrt{{\gamma }_{\mathrm{S}}^{-}{\gamma }_{\mathrm{L}}^{+}}\right)\end{array}$$

(13)

Through Equation (13), we only need to know the contact angles of the two polar liquids; then, we can calculate the values of ${\gamma }_{\mathrm{S}}^{LW}$ and ${\gamma }_{\mathrm{S}}^{-}$ of the different minerals. By substituting them into Equation (11), the polar interfacial interaction energy constants $V_{\mathrm{H}}^0$ can be calculated. In the end, the polar interfacial interaction $V_{\mathrm{H}}$ can be calculated using Equation (10).

In addition, the Hamaker constant and ${\gamma }_{\mathrm{S}}^{LW}$ of minerals have a corresponding relationship. ${\gamma }_{\mathrm{S}}^{LW}$ can be calculated using the polar interfacial interaction $V_{\mathrm{H}}$, and $V_{\mathrm{H}}$ can be calculated from ${\gamma }_{\mathrm{S}}^{LW}$ of the minerals using Equation (14) [55]:

$$\begin{array}{c}A=1.51\times {10}^{-21}{\gamma }_{\mathrm{S}}^{LW}\end{array}$$

(14)

3. Results and Discussion

3.1. Micro-Flotation Experiments

Figure 2a shows the results of the effects of different NaOL concentrations on the recovery of ilmenite and forsterite at a pH of 7.0 ± 0.5. Figure 2a illustrates that the recovery of coarse ilmenite (−151 + 74 μm) and forsterite at different sizes reached the maximum with a NaOL concentration of 3 × 10⁻⁴ M. Even at a high concentration of NaOL, the recovery did not increase significantly. This trend in flotation recovery is consistent with our previous work report [23].

Figure 2b shows the results of the effect of pH on the recovery of ilmenite and forsterite when the concentration of NaOL was 2 × 10⁻⁴ M. It shows that the floatability of coarse ilmenite (−151 + 74 μm) and different-sized forsterite had different variations within a wide pH range. The coarse ilmenite recovery first increased and then decreased with the increase in pH, and the maximum recovery was 86.35% at pH 10. In a highly alkaline environment, the chemical interaction between NaOL and Fe³⁺ weakened, while the interaction with Ca²⁺ and Mg²⁺ strengthened [56]. As a result, the ilmenite recovery decreased rapidly, and the forsterite recovery increased at pH 12.

Considering the results of the micro-flotation experiments and cost efficiency, the experiment of the artificial mixed mineral was carried out under the conditions of pH = 7.0 ± 0.5 and NaOL = 3 × 10⁻⁴ M. The experimental results are shown in Figure 3. The results show that the ilmenite recovery remains unchanged with the increase in the forsterite (−45 + 25, −25 + 19 μm) content. This indicates that conventional-sized forsterite (−45 + 25, −25 + 19 μm) had no effect on the floatability of coarse ilmenite. The reason for the decrease in ilmenite recovery was that conventional-sized forsterite (−45 + 25, −25 + 19 μm) has good floatability and entered the concentrate. However, with an increase in the fine forsterite (−19 μm) content, the recovery of coarse ilmenite decreased gradually. Aggregation between fine forsterite and coarse ilmenite may have occurred, resulting in lower ilmenite recovery.

3.2. Zeta Potential Measurements

The zeta potential is an important parameter for calculating the electrostatic interactions of particles in solution; it also can indicate the degree of adsorption between mineral particles and flotation agents [57,58]. Figure 4 shows the pH effect on the zeta potential of ilmenite and forsterite in the presence and absence of NaOL (3 × 10⁻⁴ M). The results show that the pH_zpc values of ilmenite and forsterite are approximately 4.1 and 2.8, respectively. The results are similar to those reported in [59]. After mixing with NaOL, the zeta potential of both of them shifted towards negative, and the degree of the negative shift was similar. This indicates that there was a slight difference in the adsorption amount of NaOL between them, and it was difficult to separate them with flotation. In addition, ilmenite and forsterite are negatively charged in the pH range of 2–12, indicating that there is electrostatic repulsion between them.

3.3. Contact Angle Measurements

The wettability of a solid surface is usually characterized by the contact angle; thus, the value of the contact angle of a mineral can directly reflect its floatability [60,61].

Table 2. The average contact angles with and without NaOL in deionized water and glycerin (θ°).

Minerals	Ilmenite		Forsterite
	Without NaOL	With NaOL	Without NaOL	With NaOL
DI water	30.22	88.15	34.72	87.63
Glycerin	39.72	51.93	27.70	46.97

presents the contact angles of the samples with different polar liquids in the presence and absence of NaOL (3 × 10⁻⁴ M). The results showed that the contact angle of ilmenite was 30.22° and that of forsterite was 34.72° in DI water, indicating that there was no natural floatability. After NaOL treatment, the contact angle of ilmenite and forsterite increased significantly, and there was slight difference in the extent of the contact angle increase between ilmenite and forsterite. This suggests that there is little difference in the degree of NaOL adsorption, which is consistent with the zeta potential measurements.

According to the contact angle data in the two polar liquids and the known surface energy parameters of water and glycerin, the components of surface energy parameters and the Hamaker constants of the minerals can be calculated using Equations (13) and (14). The calculated results for A, ${\gamma }_{\mathrm{S}}^{LW}$, and ${\gamma }_{\mathrm{S}}^{-}$ are shown in

Table 3. Values of components of surface energies and Hamaker constants of ilmenite and forsterite.

Minerals	A (10−20 J)	${\mathit{\gamma }}_{\mathbf{S}}^{\mathit{L}\mathit{W}}$ (mJ/m2)		${\mathit{\gamma }}_{\mathbf{S}}^{-}$ (mJ/m2)
		Without NaOL	With NaOL	Without NaOL	With NaOL
Ilmenite	13.56	89.80	162.07	198.49	0.780
Forsterite	18.59	123.14	180.85	145.77	0.109

.

3.4. Particle Size Measurements

Variations in particle sizes provide compelling evidence when assessing changes in the agglomeration or dispersion state of particles in a solution. Figure 5 shows the experimental results of the influence of fine forsterite on the particle size of mixed minerals. When conventional-sized forsterite particles (−45 + 25, −25 + 19 μm) were added, the volume-average particle size of coarse ilmenite remained unchanged, at approximately 103.68 μm. However, upon the addition of fine forsterite (−19 μm), the volume-average particle size increased to 108.86 μm, with an increase in the proportion of particles exceeding 74 μm. The data suggest that the addition of conventional-sized forsterite particles has no impact on the particle size of coarse ilmenite. However, the addition of fine forsterite (−19 μm) led to an increase in the volume-average size of coarse ilmenite particles. This indicates that fine forsterite can adsorb onto the surface of coarse ilmenite, resulting in the enlargement of ilmenite particles, thereby affecting the flotation recovery of ilmenite. These findings are consistent with the results of artificial mixed mineral flotation tests.

3.5. SEM and EDS Analysis

SEM images of flotation products can used to observe the dispersion/aggregation state between particles [62]. Figure 6a–c show SEM images of flotation tailings with coarse ilmenite particles and −45 + 25, −25 + 19, and −19 μm forsterite particles, respectively. In addition, Figure 6d shows a partial enlargement image of (c). Figure 6a,b show that the conventional-sized forsterite particles (−45 + 25, −25 + 19 μm) and coarse ilmenite particles were dispersed, and the surface of the ilmenite particles was clean. However, Figure 6c,d show that aggregation occurred not only between fine forsterite (−19 μm) and coarse ilmenite but also between fine forsterite itself. The ilmenite surface adhered to fine forsterite, and there were also aggregates of fine forsterite present. This is consistent with the results of the flotation experiment and the particle size measurement.

3.6. DLVO Theoretical Calculation

With the zeta potential and mineral surface energy parameters, the interaction potential energy profiles between forsterite and ilmenite particles can be calculated according to Equations (2)–(11); the calculation results are shown in Figure 7. The volume-average radius of ilmenite in the −151 + 74 μm range was 56.18 μm, while the volume-average radius of −19 μm forsterite was 4.98 μm. Additionally, the volume-average radii of the −45 + 25 and −25 + 19 μm forsterite were 17.5 μm and 11 μm, respectively. The Hamaker constant for water (A₃₃) is 3.7 × 10⁻²⁰ J, while the values for ilmenite and forsterite are presented in Table 3. Utilizing Equation (4), A₁₃₂ was calculated to be 4.20 × 10⁻²⁰ J. The van der Waals interaction energy, V_w, could subsequently be determined. The electrolyte concentration in the flotation process was uniformly 10⁻³ M; then, $\mathrm{\kappa }=0.104 {\mathrm{nm}}^{-1}$ was calculated from Equation (10). According to Figure 5, under the condition of pH 7, the zeta potentials of ilmenite and forsterite were −25.62 mV and −28.44 mV without NaOL and −58.46 mV and −49.39 mV with NaOL (3 × 10⁻⁴ M), respectively. The electrostatic interaction energy, V_E, could be calculated based on these values. Using the data from Table 3 and the surface energy parameters of water (${\gamma }_{\mathrm{S}}^{-}$ = ${\gamma }_{\mathrm{S}}^{+}$ = 25.5 mJ·m⁻²), the polar interface interaction energy constant, $V_{\mathrm{H}}^0$, was computed. V_H was also calculated. The total interaction potential energy, $V_{\mathrm{T}}^{\mathrm{ED}}$, was obtained by summing V_w, V_E, and V_H.

Figure 7a–c show the interaction potential energy profiles of DLVO and E-DLVO between coarse ilmenite (−151 + 74 μm) and forsterite particles of various particle sizes. At pH 7 and a NaOL concentration of 3 × 10⁻⁴ M, an energy barrier was observed in the interaction potential energy between coarse ilmenite (−151 + 74 μm) and forsterite particles of sizes −45 + 25 μm, −25 + 19 μm, and −19 μm, with energy barrier values of 11.94 × 10³ kT, 8.23 × 10³ kT, and 4.09 × 10³ kT, respectively. The strength of the barrier diminished as the size of forsterite decreased, suggesting that fine forsterite (−19 μm) might more easily overcome the barrier and aggregate with coarse ilmenite during flotation agitation. Thus, the content of conventional-sized forsterite (−45 + 25, −25 + 19 μm) has no effect on the floatability of ilmenite, whereas the fine forsterite (−19 μm) will gradually affect the floatability of coarse ilmenite with the increasing content.

Figure 7d presents the interaction potential energy profiles of DLVO and E-DLVO for fine forsterite (−19 μm). The energy barrier between fine forsterite was calculated at 0.51 × 10³ kT, which is lower compared to the barriers calculated between ilmenite and forsterite. This indicates that fine forsterite tends to aggregate more readily, another significant factor contributing to the lower recovery of ilmenite. Fine forsterite will aggregate with each other to form agglomerates of fine forsterite particles. This agglomerate still retains stronger micro-forces between the fine forsterite and ilmenite compared to the conventional-sized forsterite (−45 + 25, −25 + 19 μm), because the surface of the agglomerate is still ultrafine forsterite. As a result, these agglomerates adhere to ilmenite particles, leading to more forsterite entering the concentrate and resulting in reduced ilmenite recovery.

4. Conclusions

In this study, according to the significant changes in the properties of magmatic ilmenite ore, forsterite with increasing content in the ore was selected as the gangue mineral, and a mineral flotation experiment was carried out. The interaction phenomenon between forsterite and ilmenite particles with different particle sizes was discussed, and the underlying interaction mechanism was explained by applying E-DLVO theory. The results show the following:

• The content of conventional-sized forsterite (−45 + 25, −25 + 19 μm) has little effect on the floatability of ilmenite in a neutral environment. However, the ilmenite recovery decreases with an increase in the fine forsterite (−19 μm) content. In the mining industry, where the content of forsterite is gradually increasing, particular attention should be paid to variations in the content of fine forsterite (−19 μm) during the flotation production process.
• According to particle size measurements, scanning electron microscopy (SEM), and E-DLVO theoretical calculations, fine forsterite (−19 μm) directly covers the surface of coarse ilmenite (−151 + 74 μm) particles, preventing the ilmenite from being collected and reducing its floatability. On the other hand, aggregates of fine forsterite (−19 μm) enter the ilmenite concentrate together with the ilmenite, resulting in lower ilmenite recovery.

Further research should be conducted to explore the correlations between various particle sizes and contact angles, as well as to reduce the influence of fine particles on the flotation process, considering the potential limitations highlighted in this study.