Evaluation of Wettability at Interface between Molten Slag and Liquid Fe on Recovery of Metallic Fe from Lunar Regolith

Abstract

High-temperature H₂ reduction and melting experiments were conducted to extract metallic Fe from lunar regolith simulant. Differences in the recovery of metallic Fe with the addition of oxides were investigated in terms of the wettability at the interface between molten slag and liquid Fe. Ilmenite, albite, and Na₂O·xSiO₂ compounds were used as additive oxides. The effect of wettability on Fe recovery is discussed by evaluation of the contact angle obtained by calculations of surface tension and interfacial tension. The results confirmed that wettability is a major factor affecting coalescence of Fe particles in these slags.

1. Introduction

Physicochemical properties (viscosity, surface tension, wettability, etc.) of high-temperature liquids are very important factors in metallurgical processes. This knowledge has been accumulated over a long period with development of the metallurgical industry. The physical properties of slag vary greatly, depending on the composition. The main components of slag typically handled in the metallurgical industry are SiO₂, CaO, Al₂O₃, and MgO. These are the basic chemical components of Earth’s crust, and exist in the form of minerals within various rocks. These minerals can also be found on extraterrestrial planets. In particular, the Moon, which was the first target for mankind’s entry into space and is the site for construction of a manned base in the future, is known to be of similar composition to the crust of Earth.

Table 1 shows the chemical compositions of lunar regolith,¹⁾ terrestrial volcanic rocks,²⁾ and typical steel industry slags³⁾ originating from blast furnace (BF), basic oxygen furnace (BOF), and electric arc furnace (EAF) processes. As shown in Table 1, lunar regolith is generally distributed in two different regions: Mare and Highland regions. Volcanic rock is formed by the cooling of magma ejected on the surface. Similarities between the components of Earth, the Moon, and slag suggest the possibility that the metallurgical knowledge of Earth can be applied to the development of lunar resources. Therefore, accumulating information on various physical properties of slag, volcanic rock, and magma can be used for future lunar resource development. The atmospheric pressure is very low, ~10⁻¹⁵ atm, and fossil fuels are not present on the Moon. In addition, the Moon’s gravity is one-sixth of that of Earth, so it is difficult to separate metals from molten slag by gravity. Therefore, the design of new processes considering the Moon’s environment is required.

Table 1. Comparison of chemical compositions of lunar regolith, terrestrial volcanic rocks, and typical steel industry slags.

mass%		SiO2	CaO	Al2O3	MgO	FeO	TiO2	Na2O	Fe2O3	Bal.
Lunar regolith1)	Mare	45.4	11.8	14.9	9.2	14.1	3.9	0.6	–	–
	Highland	45.5	15.9	24.0	7.5	5.9	0.6	0.6	–	–
Volcanic rock2)	Basalt	50.1	9.7	16.0	7.0	7.5	1.9	3.0	3.9	0.9
	Andesite	56.9	6.9	17.2	3.4	4.3	0.9	3.5	3.3	3.6
	Rhyolite	74.0	1.2	13.5	0.4	1.2	0.3	3.6	1.5	4.3
Steel industry slag3)	BF	34.0	42.0	13.0	7.4	0.4	Other oxides
	BOF	11.0	46.0	2.0	6.5	17.4
	EAF	12–19	23–55	7–17	5–7	0.3–30

It has been reported that water ice exists at the poles of the Moon.⁴⁾ Hydrogen (H₂) could be obtained through electrolysis of water ice. Gibson et al.⁵⁾ experimentally demonstrated the production of oxygen from lunar basalt by H₂. Sargeant et al.⁶⁾ reported that water can be produced by reducing iron oxide minerals in lunar regolith to H₂. In addition, several methods^{7,8,9,10,11,12,13,14)} have been proposed to extract metals or oxygen from molten slag using electrochemical processes.

We applied a pyrometallurgical process to utilize lunar resources based on the similarities of slag, volcanic rock, and lunar regolith. In our previous study,¹⁵⁾ we successfully extracted metallic iron (Fe) from regolith simulant at low oxygen partial pressure using H₂. We observed that liquid Fe particles reduced from the regolith simulant were dispersed in the molten slag, and a bulk Fe alloy was recovered after coalescence of these particles. Lunar mare basalts are rich in ilmenite (FeTiO₃); thus, a large amount of ilmenite will increase the concentration of titanium dioxide (TiO₂) in the molten slag produced on reduction of this material. TiO₂ is known to lower the viscosity of molten silicate-based slag,¹⁶⁾ which is generally advantageous for metal recovery. However, our previous study¹⁵⁾ showed that recovery of the Fe alloy decreased with addition of TiO₂ in the slag, even though the viscosity of the molten slag decreased. We concluded that when the molten slag wetted the liquid Fe, a repulsive capillary force acted on the contact points between Fe particles in the slag,^15,17) making it difficult for the fine liquid Fe particles to coalesce.

In this follow-up study, we investigated the effect of the wettability between molten slag and liquid Fe on the coalescence of Fe particles by addition of various oxides when recovering metallic Fe from lunar regolith simulant. In particular, as a part of the realization of lunar metallurgy, we focused on the change in Fe recovery on addition of ilmenite, an abundant mineral of the mare region, and albite (NaAlSi₃O₈), a common mineral of the highland region on the Moon.^1,15)

2. Experimental

2.1. Sample Preparation

The lunar regolith simulant was the same as that used in our previous study.¹⁵⁾ The regolith simulant was crushed to less than 125 μm, dried at 473 K for 24 h to remove moisture, and then uniformly mixed with various oxides: ilmenite, albite, and Na₂O·xSiO₂ compounds. Table 2 shows the chemical compositions for the experimental conditions before and after mixing the regolith simulant with oxides. High-purity ilmenite powder (99.8%; Alfa Aesar Co., Inc.) was used in the experiments. The mineral mixture corresponding to Na₂O·1.74Al₂O₃·11.25SiO₂ was used as albite in this study. For the Na₂O·xSiO₂ compounds, two types of samples were prepared: Na₂O·4SiO₂ and Na₂O·2SiO₂. Na₂O·4SiO₂ was prepared by pre-melting after mixing Na₂CO₃ and SiO₂ powder; Na₂O·2SiO₂ was prepared by calcining sodium silicate powder (Na₂O·2SiO₂·xH₂O) at 773 K for 24 h. In this paper, Na₂O·4SiO₂ and Na₂O·2SiO₂ are respectively referred to as 1N·4S and 1N·2S for convenience.

Table 2. Chemical compositions of slag components for different experimental conditions.

Component (mass%)	No.	Addition	SiO2	CaO	Al2O3	MgO	FeO	Fe2O3	TiO2	Na2O	Bal.
Regolith simulant	A0	–	49.60	9.45	16.90	5.62	6.13	6.53	1.53	2.61	1.63
TiO2 (Rutile)*	A1	+50%TiO2	49.21	9.38	16.77	5.58	6.08	6.48	2.31	2.59	1.62
	A2	+100%TiO2	48.82	9.30	16.63	5.53	6.03	6.43	3.08	2.57	1.60
	A3	+150%TiO2	48.44	9.23	16.50	5.49	5.99	6.38	3.84	2.55	1.59
	A4	+200%TiO2	48.06	9.16	16.38	5.45	5.94	6.33	4.58	2.53	1.58
Ilmenite	B1	+50%TiO2	48.90	9.32	16.66	5.54	6.71	6.44	2.25	2.57	1.61
	B2	+100%TiO2	48.23	9.19	16.43	5.46	7.27	6.35	2.95	2.54	1.58
	B3	+150%TiO2	47.57	9.06	16.21	5.39	7.82	6.26	3.63	2.50	1.56
	B4	+200%TiO2	46.93	8.94	15.99	5.32	8.35	6.18	4.29	2.47	1.54
Albite	C1	+2%SiO2	49.95	9.31	16.94	5.54	6.04	6.44	1.51	2.67	1.61
	C2	+4%SiO2	50.29	9.18	16.97	5.46	5.96	6.35	1.49	2.73	1.58
	C3	+6%SiO2	50.61	9.05	17.00	5.38	5.87	6.26	1.47	2.78	1.56
	C4	+8%SiO2	50.93	8.93	17.04	5.31	5.79	6.17	1.45	2.84	1.54
	C5	+10%SiO2	51.25	8.81	17.07	5.24	5.71	6.09	1.43	2.89	1.52
Na2O·4SiO2	D1	+15%Na2O	50.18	9.27	16.58	5.51	6.01	6.41	1.50	2.93	1.60
	D2	+30%Na2O	50.73	9.10	16.28	5.41	5.90	6.29	1.47	3.24	1.57
	D3	+45%Na2O	51.27	8.94	15.98	5.31	5.80	6.17	1.45	3.54	1.54
	D4	+60%Na2O	51.79	8.78	15.70	5.22	5.69	6.06	1.42	3.83	1.51
Na2O·2SiO2	E1	+25%Na2O	49.91	9.27	16.58	5.51	6.01	6.41	1.50	3.20	1.60
	E2	+50%Na2O	50.20	9.10	16.28	5.41	5.90	6.29	1.47	3.77	1.57
	E3	+75%Na2O	50.49	8.94	15.98	5.31	5.80	6.17	1.45	4.32	1.54
	E4	+100%Na2O	50.77	8.78	15.70	5.22	5.69	6.06	1.42	4.85	1.51

*  Previous work.¹⁵⁾

2.2. Experimental Procedure

Figure 1 shows the experimental process designed from thermodynamic prediction by FactSage in our previous study.¹⁵⁾ The experimental process was divided into two steps, as shown in Fig. 1. Step 1 was a reduction process, in which regolith simulant particles less than 125 μm in diameter were reduced to fine Fe particles by H₂ gas. The extent of reduction of Fe oxide in regolith simulant under the conditions of this experiment was approximately 38.3%; here, the extent of reduction is expressed as a percentage of the weight loss by measuring the weight of the sample before and after the reduction experiment. The amount of oxide added was very small compared with the amount of regolith simulant and was uniformly mixed with the simulant; therefore, we assumed comparable reduction for all samples. Step 2 was a melting process in which regolith simulant and reduced Fe particles were melted, and the liquid Fe particles dispersed in the molten slag coalesced with each other.

Fig. 1. Conceptual flowsheet of experimental process steps.

The experimental equipment was as previously described.¹⁵⁾ Approximately 5 g of sample was heated to 1273 K in an alumina crucible with Ar gas at a flow rate of 100 mL/min. At 1273 K, the sample was reduced with 100 mL/min of Ar–20%H₂ for 2 h (Step 1). The sample was then heated to 1873 K and held for 1 h to melt it (Step 2). After melting, the sample was cooled to room temperature and the crucible was crushed to recover the Fe alloy. In this study, the recovery is defined by Eq. (1):

  

$$\text{Recovery}\mathrm{\hspace{0.17em} } \text{(\%)}=\frac{\text{Recovered}\mathrm{\hspace{0.17em} } \text{bulk}\mathrm{\hspace{0.17em} } \text{Fe}\mathrm{\hspace{0.17em} } \text{alloy}\mathrm{\hspace{0.17em} } \text{(g)}}{\text{Total}\mathrm{\hspace{0.17em} } \text{Fe}\mathrm{\hspace{0.17em} } \text{in}\mathrm{\hspace{0.17em} } \text{original}\mathrm{\hspace{0.17em} } \text{sample}\mathrm{\hspace{0.17em} } (\text{g})}\times 100$$(1)

The recovered metallic Fe sample contained trace elements; thus, it is referred to as the “Fe alloy”. However, the quantities of elements other than Fe were very small;¹⁵⁾ hence, we assumed the alloy to be pure Fe in calculation of the recovery. Furthermore, we only considered the bulk Fe alloy in the recovery calculation and neglected the fine Fe particles dispersed in slag phase.¹⁵⁾ In the case of ilmenite addition, Fe in the ilmenite was also considered in the original sample in Eq. (1).

3. Results and Discussion

3.1. Effect of Additive Oxides on Recovery of Fe Alloy

a. Reduction Behavior of Regolith Simulant by Hydrogen

Figure 2 shows a cross-section of a sample recovered after reduction–melting of regolith simulant without the addition of oxides. Completely melted slag and spherical Fe alloy settled on the bottom of the crucible, as shown in Fig. 2(a). The bulk Fe alloy in Fig. 2(a) was used for the recovery calculation. Fine Fe particles that were not recovered remained in the slag. Their diameter generally ranged from approximately several μm to 10 μm, as shown in Fig. 2(b). The terminal velocity of the fine Fe particles was calculated in the previous study:¹⁵⁾ that of a 10 μm diameter particle was about 0.24 mm/h in the molten slag, according to Stokes’ law for particles falling through a stationary liquid. Considering this sedimentation under the gravity conditions of the Moon, it is important to utilize physical properties to enhance coalescence of such fine particles in the molten slag.

Fig. 2. Appearance of lunar regolith simulant sample after 2 h of reduction at 1273 K and 1 h of melting at 1873 K. (a) Slag and Fe alloy. (b) Scanning electron microscopy image of cross-section of area in yellow box in (a) showing fine Fe particles (white dots) in the slag. (Online version in color.)

b. Effect of Addition of Ilmenite to Regolith Simulant

Figure 3 shows the variation in recovery of Fe alloy and viscosity of the molten slag with the addition of oxides. The viscosity of molten slag was calculated by FactSage 8.2 from the composition at 1873 K at an oxygen partial pressure of 10⁻¹⁵ atm for each experimental condition. Recovery of Fe alloy decreased with the addition of ilmenite, as shown in Fig. 3(a); viscosity of the molten slag similarly decreased. In general, it is predicted that a low slag viscosity promotes sedimentation and coalescence of Fe particles, i.e., high recovery, due to the enhanced mass transfer. In contrast, the relationship between Fe recovery and viscosity of the molten slag in Fig. 3(a) is not in agreement with such a trend, as reported in our previous study¹⁵⁾ with addition of TiO₂.

Fig. 3. Variation of recovery of Fe alloy and viscosity of molten slag with amounts of (a) ilmenite, (b) albite, (c) Na₂O·4SiO₂, and (d) Na₂O·2SiO₂ added to regolith simulant after 2 h of reduction at 1273 K and 1 h of melting at 1873 K.

c. Effect of Addition of Albite to Regolith Simulant

Figure 3(b) shows the variation of Fe alloy recovery and viscosity of the molten slag with the addition of albite. As the albite addition increased, the recovery of Fe alloy remained virtually constant and there was a linear increase of slag viscosity. From the viewpoint of sedimentation and coalescence of Fe particles by considering the viscosity of molten slag, the relationship shown in Fig. 3(b) is not reasonable.

d. Effect of Addition of Na₂O·xSiO₂ Compounds to Regolith Simulant

Figures 3(c) and 3(d) show the analogous data with the addition of 1N·4S and 1N·2S, respectively. These results show that both the Fe recovery and viscosity increased with increasing addition of these compounds. As mentioned in Sections 3.1b and c, this tendency is not explained by the trend of viscosity of molten slag with addition of Na₂O·xSiO₂ compounds.

Figure 4 compares the combined results of the variations in Fe recovery with slag viscosity in the present work with previous results¹⁵⁾ for TiO₂. Considering that a low viscosity of molten slag is advantageous when recovering metal particles by gravity separation, the recovery behavior shown in Fig. 4 cannot be explained by the variation in viscosity. This means that a more influential factor affects the recovery of Fe particles.

Fig. 4. Comparison of all results of variations in Fe recovery with slag viscosity. *Previous work.¹⁵⁾ (Online version in color.)

As previously discussed,¹⁵⁾ recovery depends on coalescence of the liquid Fe particles, which is affected by the wettability between the molten slag and liquid Fe. The effect of wettability between molten slag and liquid Fe on Fe recovery was therefore systematically evaluated based on these results for addition of ilmenite, albite, and Na₂O·xSiO₂ compounds, and prior results¹⁵⁾ for TiO₂. The calculated contact angle between molten slag and liquid Fe, described in Section 3.2, was used as a quantitative indication of wettability.

3.2. Wettability Evaluation

The wettability of different oxides on liquid Fe, i.e., the contact angle between molten slag and liquid Fe, was evaluated by Neumann’s relation.¹⁸⁾ Figure 5 shows the balance of the surface tension of liquid Fe (σ_Fe), surface tension of the molten slag (σ_slag), and interfacial tension between the two phases (σ_Fe/slag) at the triple point. θ is the contact angle between the molten slag and liquid Fe, and α is the apparent contact angle. Based on Neumann’s relation, the following equation is derived:

  

$${[{\sigma }_{\text{Fe}/\text{slag}}]}^2={[{\sigma }_{\text{Fe}}]}^2+{[{\sigma }_{\text{slag}}]}^2-2{\sigma }_{\text{Fe}}\cdot {\sigma }_{\text{slag}}\cdot cos\alpha$$(2)

Additionally, Eq. (3) is derived from the balance of forces in the vertical direction:

  

$${\sigma }_{\text{Fe}/\text{slag}}\cdot sin(\theta -\alpha )={\sigma }_{\text{slag}}\cdot sin\alpha$$(3)

Fig. 5. Schematic diagram of droplet of molten slag on surface of liquid Fe, indicating the balance of forces at the triple point.

Once the values of σ_Fe/slag, σ_Fe, and σ_slag are determined, the contact angle can be calculated from Eqs. (2) and (3). The experimental conditions selected in Table 2 for application to the calculation are as follows: Regolith simulant (A0), + 200%TiO₂ (A4), + 200%TiO₂ of ilmenite (B4), + 10%SiO₂ of albite (C5), + 60%Na₂O of 1N·4S (D4), and + 100%Na₂O of 1N·2S (E4). Table 3 shows the chemical compositions of the slags recovered for each of these conditions (A0, A4, B4, C5, D4, E4) after reduction–melting, as determined by scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDX).

Table 3. Chemical compositions of slags collected after melting experiments obtained by scanning electron microscopy with energy-dispersive X-ray spectroscopy and equilibrium oxygen contents of liquid Fe for different experimental compositions.

No.	Slag composition							[mass%O]*
	SiO2	CaO	Al2O3	MgO	Na2O	FeO	TiO2
R. S (A0)	47.64	11.11	21.04	5.85	3.27	9.08	2.02	2.30×10–2
TiO2 (A4)	47.10	10.41	18.62	5.56	2.12	9.71	6.47	2.20×10–2
Ilmenite (B4)	46.10	11.53	17.96	5.08	2.71	11.69	4.93	2.98×10–2
Albite (C5)	50.89	8.84	21.06	6.10	4.18	7.39	1.53	1.79×10–2
1N·4S (D4)	51.30	9.46	21.01	5.24	5.14	6.03	1.82	1.58×10–2
1N·2S (E4)	50.87	8.76	21.70	5.19	6.25	5.67	1.55	1.65×10–2

*  Oxygen content [mass%O] in liquid Fe predicted by FactSage.

3.3. Evaluation of Surface Tension of Liquid Fe

The surface tension of liquid Fe is strongly affected by oxygen.¹⁸⁾ The presence of FeO in molten slag leads to an increase in the oxygen content in liquid Fe.¹⁹⁾ Regolith simulant contains Fe oxide; thus, the oxygen contents in the liquid Fe should be considered. We used Eq. (4), proposed by Ogino et al.,²⁰⁾ to calculate the surface tension of liquid Fe:

  

$${\sigma }_{\text{Fe}}=1\mathrm{\hspace{0.17em} }910-825log\left(1+210[\text{mass\%O}]\right)(\text{mN}/\text{m})$$(4)

The oxygen content [mass%O] in liquid Fe on addition of oxide was estimated from the following relationship:

  

$${\text{Fe}}_{(\text{l})}+\text{O[mass\%]}={\text{FeO}}_{(\text{l})}$$(5)

Activity of FeO was predicted from the slag composition by FactSage calculation. The oxygen content [mass%O] in liquid Fe for each experimental condition, which was obtained by FactSage calculation and Eq. (5), is presented in Table 3. The surface tension (σ_Fe) of liquid Fe was calculated for each condition using these values in Eq. (4).

3.4. Evaluation of Surface Tension of Molten Slag

The model developed by Tanaka et al.,²¹⁾ based on the Butler’s equation²²⁾ for evaluation of surface tension of ionic mixtures, was applied to the seven-component SiO₂–CaO–Al₂O₃–MgO–Na₂O–FeO–TiO₂ system. The surface tension of the molten slag was calculated from Eq. (6):

  

$$\sigma ={\sigma }_i^{\text{Pure}}+\frac{RT}{A_i}\text{ln}\frac{M_i^{\text{Surf}}}{M_i^{\text{Bulk}}}$$(6)

where

  

$$\begin{array}{l}{M}_i^{\text{P}}=\\ \frac{\frac{R_{\mathrm{A}}}{R_{\mathrm{X}}}\cdot N_i^{\mathrm{P}}}{\frac{R_{\mathrm{S}{\mathrm{i}}^{4+}}}{R_{\mathrm{S}\mathrm{i}{\mathrm{O}}_4^{4-}}}\cdot N_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}^{\mathrm{P}}+\frac{R_{\mathrm{C}{\mathrm{a}}^{2+}}}{R_{{\mathrm{O}}^{2-}}}\cdot N_{\mathrm{C}\mathrm{a}\mathrm{O}}^{\mathrm{P}}+\frac{R_{\mathrm{A}{\mathrm{l}}^{3+}}}{R_{{\mathrm{O}}^{2-}}}\cdot N_{\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3}^{\mathrm{P}}+\frac{R_{\mathrm{M}{\mathrm{g}}^{2+}}}{R_{{\mathrm{O}}^{2-}}}\cdot N_{\mathrm{M}\mathrm{g}\mathrm{O}}^{\mathrm{P}}+\frac{R_{\mathrm{N}{\mathrm{a}}^{+}}}{R_{{\mathrm{O}}^{2-}}}\cdot N_{\mathrm{N}{\mathrm{a}}_2\mathrm{O}}^{\mathrm{P}}+\frac{R_{\mathrm{F}{\mathrm{e}}^{2+}}}{R_{{\mathrm{O}}^{2-}}}\cdot N_{\mathrm{F}\mathrm{e}\mathrm{O}}^{\mathrm{P}}+\frac{R_{\mathrm{T}{\mathrm{i}}^{4+}}}{R_{{\mathrm{O}}^{2-}}}\cdot N_{\mathrm{T}\mathrm{i}{\mathrm{O}}_2}^{\mathrm{P}}}\end{array}$$(7)

Subscript i refers to the following components: SiO₂, CaO, Al₂O₃, MgO, Na₂O, FeO, or TiO₂. Subscripts A and X refer to the cations and anions of component i, respectively. Superscripts “Surf” and “Bulk” indicate the surface and bulk, respectively. R is the gas constant, T is the absolute temperature, and ${\sigma }_i^{\text{Pure}}$ is the surface tension of pure molten component i, which is treated as a model parameter. $A_i=N_0^{1/3}\cdot V_i^{2/3}$ corresponds to the molar surface area in a monolayer of pure molten component i (N₀: Avogadro’s number, V_i: molar volume of pure molten component i). $N_i^{\mathrm{P}}$ is the mole fraction of component i in phase P (P = Surf or Bulk). R_A is the radius of the cation, and R_X is the radius of the anion; for example, in the case of the SiO₂–CaO–Al₂O₃–MgO–Na₂O–FeO–TiO₂ system:

  

$$R_{\text{A}}=R_{{\text{Si}}^{4+}},\mathrm{\hspace{0.17em} }{R}_{{\text{Ca}}^{2+}},\mathrm{\hspace{0.17em} }{R}_{{\text{Al}}^{3+}},\mathrm{\hspace{0.17em} }{R}_{{\text{Mg}}^{2+}},\mathrm{\hspace{0.17em} }{R}_{{\text{Na}}^{+}},\mathrm{\hspace{0.17em} }{R}_{{\text{Fe}}^{2+}},\mathrm{\hspace{0.17em} }{R}_{{\text{Ti}}^{4+}}$$(8)

  

$$R_{\text{X}}=R_{{\text{SiO}}_4^{4-}},\mathrm{\hspace{0.17em} }{R}_{O^{2-}}$$(9)

where ${\text{SiO}}_4^{4-}$ is considered to be the minimum anionic unit in SiO₂, and the value of $R_{{\text{Si}}^{4+}}/R_{{\text{SiO}}_4^{4-}}$ was empirically determined to be 0.5.^21,23,24,25) This model can be widely applied to a variety of molten slags because it is based only on the surface tension, molar volume, and ionic radii of the pure components in the system.^{21,23,24,25,26,27,28,29,30)}

Data for the ionic radii were obtained from Shannon³¹⁾ and Ikemiya et al.,³²⁾ and the molar volumes of the pure oxides recommended by Mills and Keene³³⁾ were used. These values are listed in Tables 4 and 5, respectively. The temperature dependence of the surface tension for pure SiO₂ was taken from the NIST database for the calculations in this study.³⁴⁾ The temperature dependences of surface tensions for pure CaO, Al₂O₃, MgO, FeO, and Na₂O, as evaluated in previous studies^23,24,25) by our co-authors, were used; that for pure TiO₂ was obtained by fitting data from literature.³⁵⁾ The equations for determining the temperature dependences of surface tension are listed in Table 6.^{23,24,25,34,35)} The surface tension (σ_slag) of the molten slag was calculated for each experimental condition using Eq. (6).

Table 4. Ionic radii of cations and oxygen ion.^31,32)

Ion	Radius (10–1 nm)
Si4+	0.42
Ca2+	0.99
Al3+	0.51
Mg2+	0.66
Na+	0.97
Fe2+	0.74
Ti4+	0.61
O2–	1.44

Table 5. Molar volumes of pure components.³³⁾

Oxide	Temperature (K) dependence of molar volume (m3/mol)
SiO2	27.516{1+1·10–4 (T − 1773)}·10–6
CaO	20.7{1+1·10–4 (T − 1773)}·10–6
Al2O3	28.3{1+1·10–4 (T − 1773)}·10–6
MgO	16.1{1+1·10–4 (T − 1773)}·10–6
Na2O	33.0{1+1·10–4 (T − 1773)}·10–6
FeO	15.8{1+1·10–4 (T − 1773)}·10–6
TiO2	24.0{1+1·10–4 (T − 1773)}·10–6

Table 6. Temperature dependence of surface tension of pure components.^{23,24,25,34,35)}

Oxide	Temperature (K) dependence of surface tension (mN/m)
SiO2	243.2 + 0.031·T
CaO	791 − 0.0935·T
Al2O3	1024 − 0.177·T
MgO	1770 − 0.636·T
Na2O	438 − 0.116·T
FeO	504 + 0.0984·T
TiO2	724.51− 0.174·T

3.5. Evaluation of Interfacial Tension between Molten Slag and Liquid Fe

The equation developed by Girifalco and Good³⁶⁾ was applied to the molten slag–liquid Fe system for evaluation of interfacial tension (σ_Fe/slag). These authors introduced a characteristic of the system (Φ), defined as the corresponding ratio of adhesion and cohesive energies for the two immiscible liquids, for the estimation of interfacial tension:

  

$${\sigma }_{\text{Fe}/\text{slag}}={\sigma }_{\text{Fe}}+{\sigma }_{\text{slag}}-2\mathrm{\Phi }{({\sigma }_{\text{Fe}}\cdot {\sigma }_{\text{slag}})}^{0.5}$$(10)

Experimental data were collected from the literature^{37,38,39,40,41)} for calculation of Φ for the seven-component molten slag, as given in Table 7. Considering the chemical composition of the regolith simulant, systems containing one of FeO, TiO₂, or Na₂O in the molten slag and containing oxygen or sulfur in the liquid Fe were included. Equation (11) was developed here for calculation of Φ for the seven-component molten slag by regression analysis of the values obtained from the data in Table 7:

  

$$\begin{array}{l}\mathrm{\Phi }=0.002904({\text{\%SiO}}_2)+0.006573(\text{\%CaO})\\ \hspace{1em}+0.001325({\text{\%Al}}_2{\text{O}}_3)+0.005500(\text{\%MgO})\\ \hspace{1em}+0.007164({\text{\%Na}}_2\text{O})+0.013557(\text{\%FeO})\\ \hspace{1em}+0.005897({\text{\%TiO}}_2)\end{array}$$(11)

The value of Φ obtained by Eq. (11) was applied to the following relation proposed by Cramb and Jimbo¹⁸⁾ to consider the effect of oxygen on FeO in molten slag:

  

$${\mathrm{\Phi }}_{(2)}={\mathrm{\Phi }}_{(1)}+\frac{(0.82-{\mathrm{\Phi }}_{(1)})\cdot (\text{\%FeO})}{100}$$(12)

where Φ₍₂₎ is the Φ value of the system after addition of FeO, and Φ₍₁₎ is the Φ value calculated by regression. The accuracy and applicability of Eq. (12) were validated by comparing the experimentally measured and calculated values. Figure 6 shows a comparison between the measured and calculated interfacial tensions, indicating the good agreement. The interfacial tension (σ_Fe/slag) was then calculated for each selected condition (A0, A4, B4, C5, D4, E4) using Φ₍₂₎ and Eq. (10).

Table 7. Systems and temperatures used for evaluation of interaction coefficient Φ.

System	Temperature (K)	Ref.
SiO2–CaO–FeO	1873	37, 38
SiO2–CaO–Al2O3–FeO	1853, 1873	37, 39, 40
SiO2–CaO–Al2O3–Na2O	1873	37
SiO2–CaO–Al2O3–FeO–Na2O	1873	37
SiO2–CaO–Al2O3–MgO–FeO	1873	39
SiO2–CaO–Al2O3–MgO–TiO2	1873	41

Fig. 6. Comparison of measured interfacial tensions with values calculated by Eq. (10). (Online version in color.)

3.6. Relationship between Wettability and Recovery

Table 8 shows all calculated values of surface tension (σ_Fe, σ_slag), interfacial tension (σ_Fe/slag), apparent contact angle (α), and contact angle (θ) for each experimental condition. The effect of interfacial tension between molten slag and liquid Fe on the recovery of Fe alloy was first investigated. It was reported that an increase in interfacial tension between two liquid phases in a liquid–liquid system facilitates coalescence of dispersed droplets in the liquid due to minimization of interfacial energy.⁴²⁾ In other words, when the interfacial tension between molten slag and liquid Fe increases, coalescence of Fe particles becomes easier, which increases the recovery of Fe alloy. Figure 7(a) shows the variation in average recovery with respect to interfacial tension for the selected experimental conditions. Although there appears to be a weak positive correlation, a distinct correlation cannot be identified owing to the wide scatter.

Table 8. Calculated wettability parameters for different experimental compositions.

No.	σFe	σslag	σFe/slag	α	θ
R. S (A0)	1278	374	1009	37.81	50.96
TiO2 (A4)	1291	377	996	32.89	44.75
Ilmenite (B4)	1200	379	892	29.95	42.20
Albite (C5)	1351	362	1102	40.56	52.89
1N·4S (D4)	1386	356	1148	42.43	54.52
1N·2S (E4)	1373	352	1145	43.59	55.82

*σ (mN/m), α (°), θ (°)

Fig. 7. Variation of average Fe recovery from regolith simulant as a function of (a) interfacial tension and (b) contact angle.

Figure 7(b) shows the variation in average recovery with contact angle (θ). There is a strong positive correlation between the contact angle and recovery. This result means that a high contact angle, i.e., poorer wettability, facilitates recovery of Fe, i.e., coalescence of Fe particles. The mechanism of the effect of wettability on the coalescence of Fe particles is proposed as follows. When the molten slag wets Fe particles, the slag tends to penetrate the contact point between the particles by capillary action. As the Fe particles approach each other, a repulsive force is generated at this contact point.^15,17) In other words, molten slag interferes with contact between the particles, making it difficult for them to coalesce. As the contact angle increases, i.e., the wettability deteriorates, the repulsive force at the point of contact between two particles decreases, resulting in an increase in recovery. Therefore, it is believed that the measured recovery changed because the wettability changed depending on the added oxide, which affected coalescence of the particles in the slag. These results indicate that wettability has a more dominant effect on the recovery of Fe than other factors under our experimental conditions.

4. Conclusions

High-temperature H₂ reduction and melting experiments were performed to extract and recover metallic Fe from lunar regolith simulant with the addition of various oxides. The effect of wettability between molten slag and liquid Fe on variation in Fe recovery is discussed based on their calculated contact angle. The following findings were obtained.

(1) Recovery of the Fe alloy decreased with the addition of ilmenite, did not change with albite, and increased with Na₂O·xSiO₂ compounds. This recovery trend is not explained by the viscosities of the respective molten slags.

(2) Recovery of the Fe alloy was strongly positively correlated with the contact angle between the molten slag and liquid Fe. It is concluded that wettability is a dominant factor for the recovery of Fe particles in these slags.

Acknowledgements

This work was supported by JST SPRING, Japan Grant Number JPMJSP2138.

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