OS3-2ISS搭載ELFによる高温融体界面張力計測（Interfacial Energy
プロジェクト）の進捗報告
Current States of Interfacial-Energy Project using Electrostatic
Levitation Furnace (ELF) in ISS
渡邉匡人 1,† ,佐藤令奈1 ，佐藤諒平1 ，石塚美里1 ，松下泰士 2 石川毅彦 3 小山千尋 3 織田裕久 3 , 伊藤剛3Masahito WATANABE 1 , Reina SATO 1 , Ryohei SATO 1 , Misato ISHIZUKA 1 , Taishi MATSUSHITA 2 ,Takehiko ISHIKAWA 3 , Chiro KOYAMA 3 , Hirohisa ODA 3 and Tsuyoshi ITO 3
1

学習院大学理学部, Department of Physics, Gakushuin University, Tokyo, Japan
Department of Materials and Manufacturing, Jönköping University, Jönköping, Sweden
3
宇宙航空研究開発機構, JAXA, Tsukuba, Japan∗ Correspondence: masahito.watanabe@gakushuin.ac.jp
2

1. Introduction
Interfacial tension measurements are required in steel industries, which include smelting, continuous
casting, and welding. In the continuous casting process, mold flux made of molten oxides covers steel meltin the casting pool. Here, the interfacial tension prevents the oxide from being pulled down into the steel
melt. In the welding process, the welding flux, made of an oxide, encloses the steel melt in order to preventthe melt from oxidizing and to control the shape of the welded part. For this control, the interfacial tension
between the welding flux and the steel melt plays an important role. The interfacial tension in these processes
is changed empirically by changes in the oxide composition. Therefore, in order to systematically be able
to control the interfacial tension between molten oxide and the steel melt, we need to obtain the values ofthis tension for many kinds of these media 1). However, oxide compositions were limited by the temperaturein previous measurements using a sessile drop with an X-ray radiograph 2) due to the difficulty in raising
the temperature above the melting point of iron with conventional methods using a container. Therefore, acontainer-less technique must be used to measure the temperature dependence of interfacial tension between
molten oxides and steel melts. As such, we planned to measure this interfacial tension using core-shell dropletswith an oscillating drop technique in microgravity 3). Under microgravity conditions, two immiscible liquids
form a core-shell droplet which is dominated by the surface and interfacial free energies. Then the interfacial
tension, which is the interfacial free energy per unit area, can be found. The surface tension is measured using
the drop oscillating technique from the eigenfrequencies of the surface oscillation of levitated liquid droplets.
To perform the measurement of interfacial tension between molten oxide and steel melts forming a core-shell
droplet, we selected the electrostatic levitation method to achieve the requirements needed for the measurement.
We were able to use the electrostatic levitation furnace (ELF) 4) installed in the KIBO module of the International
Space Station (ISS). In this report, we review the current status of our research using the ELF for finding theinterfacial tension between molten oxides and liquid Fe.
2. Surface oscillation of core-shell droplet
The surface oscillation of core-shell droplets was analytically investigated by Sufferen et al. 4) as follows
from the incompressible fluid motions using velocity potential ~v = −∇ ϕ. The pressure difference is supportedby the boundary stress and P denotes the pressure in the fluid of density ρ. The pressure difference across a
spherical boundary of radius R and interfacial tension σ is described by the Young-Laplace formula as ∆P =−(2σ)/R. On the assumption of small deviations of a boundary from the original sphere as r = R0 + R(θ, φ) in
the polar coordinate, we delivered from the Young-Laplace formula to the following equation,
ρ



∂2 ϕ
σ
∂ϕ
∂ 2 
−2+∇ϕ= 0 at r = R0 ,s∂r∂t2
R20 ∂r

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Figure 1. Three liquid systems for normal mode analysis of core-shell droplet.

where, ∇2s is the surface Laplacian. For core-shell droplets, from the existing two boundary conditions thesolutions of the eq.(1) for ϕ are in the three regions for shell, core and host(atomospher) as:hiϕ(r, t) = ∑ A(l, m; t)r l + B(l, m; t)r −(l −1) Ylm (θ, φ),(2)l,mϕi (r, t) = ∑ Ai (l, m; t)r l Ylm (θ, φ),(3)ϕo (r, t) = ∑ Ao (l, m; t)r −(l +1) Ylm (θ, φ).

(4)

l,m

l,m

where A and B are constant values, Ylm (θ, φ) is a spherical harmonic function with the normal mode index
integer l and m. If the condition that the normal component of velocity across each boundary is continuous−(2l +1)(2l +1)is imposed, we obtain Ai = A − [(l + 1)/l ] BRi
and Bo = B − [l/(l + 1)] Ri. The conditions forexisting these velocity potentials simultaneously are obtained from the eigenvalue equation, and then we obtaineigenfrequencies of the normal mode of surface oscillation of core-shell droplet as,
τ81,
σ (1 + ∆ρi )τ 10 − 2/3∆ρi

 s 

mo τ 3mo τ 3
1 σmi
1 σmi
+
−
±
+ 1.
K± =
2 τ3
σ
4 τ3
σ

2
ω±
= ω02 K±

(5)
(6)

In eqs.(5) and (6), symbols are shown in Fig. 1 and follows,σ=pσo /σi , τ =p

Ro /Ri , ∆ρi =(l + 1)(ρi − ρo )l ( ρa − ρo ), ∆ρo =,
(2l + 1)ρo
(2l + 1)ρomi = (1 + ∆ρi )τ (2l +1) − ∆ρi τ −(2l +1) , mo = (1 + ∆ρo )τ (2l +1) − ∆ρo τ −(2l +1) .
If the eigenfrequencies ω+ and ω− can be obtained from measurements, the interfacial tension σi can be obtainedby transforming eq. (1) with l = 2 for the fundamental mode as follows

R3i R3o 5ρo 2
J2,
mi mo − 1 σo24
23
J = (1 + ∆ρi )τ 5 − ∆ρi τ −5 .
552 2
σi = ω−ω+(7)

From eq.(7), it can be seen that to obtain the interfacial tension value σi from the eigenfrequencies of thecore-shell droplet by two immiscible liquids, the density of core liquid ρi , the density of shell liquid ρo , andthe surface tension of shell liquid σo are required. For our target research to obtain the interfacial tension, thecore liquid is liquid Fe and the shell liquid is molten oxides. Since the density of liquid Fe was reported muchnumber in previously, we can obtain it easily. On the other hand, for molten oxide, we can obtain its density by
ELF and also use the literature value but it is difficult to find the surface tension from literature at the same
compositions for the target oxides. Therefore, we have measured the molten oxide surface tension using theoscillating drop technique by ELF. However, it is difficult to obtain accurate surface tension of multi-component
molten oxides containing Fe even in ELF due to their electrification behavior. For this reason, we try to makea new equation to obtain the interfacial tension σi without the surface tension of molten oxide σo with anapproximation of eqs. (5) and (6). Details of the equation are described and discussed in late section 4.

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Figure 2. X-ray radiograph image of a core-shell sample by oxide (shell) and Fe (core), which is installed in ISS.

3. Preparation of core-shell sample by Fe and oxides
Core-shell samples made by liquid Fe and molten oxides for oscillating drop experiments in ELF wereprepared as follows. First, the oxide sample powder was dried and weighed after removing water, and thenprovisionally sintered by a CO2 laser. The sample was melted by a CO2 laser on a water-cooled copper platewith a conical hole, and during the cooling process, spherical iron was dropped into the oxide and completely
solidified in the spherical oxide. The solidified samples were checked by X-ray radiography for the presence of
air bubbles, and those without bubbles were selected for installation on the ISS. From numerical simulations 6),
surface oscillations can be clearly observed when the radius ratio of core to shell is 1.3. We made core-shellsamples by adjusting the radius ratio of 1.3 by the volume estimating from their masses. An X-ray radiographimage of a core-shell sample prior to the ISS installation is shown in Fig. 2. For the first tried observation of
surface oscillation observation of core-shell droplets by molten oxide and Fe melt, we used oxide compositionsas SiO2 :CaO:Mn3 O4 :TiO2 :Fe2 O3 =25:7:20:18:30 mass%, which is the flux material model composition used in thewelding process (named as Flux9). In this sample, the core is aligned with the center of the shell, but in somecases, the centers of the core and shell were not aligned.
4. Oscillating drop experiments using ELF in ISS
Using the ELF 4) (Fig. 3) installed in the ISS, core-shell droplets were formed by heating and melting a
core-shell sample made of a flux material model composition (Flux9) oxide in the welding process using asemiconductor laser with a wavelength of 980 nm. After the core-shell droplet formation, an alternating electricfield was applied between the electrodes to excite the surface oscillation of the droplet and the time variationof the droplet shape was measured by the shadow sensing method 7) and the time variation of the surface
oscillation amplitude was obtained.
The density of the oxide melt was obtained by levitating a single oxide melt at ELF and measuring thedroplet shape using backlight optics to obtain the volume, then calculating the temperature variation of thedensity from the mass of the returned sample on the ground to obtain the density at the temperature when
the surface vibration of the core-shell droplet was measured. The sample temperature was determined as theapparent temperature using a single-color pyrometer with a wavelength of 1.6 µm by emissivity set to 1. Since
the surface of the core-shell droplet is covered with molten oxide, we need the emissivity of the molten oxidein the shell phase to measure the droplet temperature using a pyrometer. The normal spectral emissivity ofthe molten oxides (Flux9) used in the present experiment was then obtained by the following procedure 8) andused to determine the core-shell droplet temperature in the present drop oscillating experiments.
First, the normal spectral emissivity of the molten Flux9 was determined in a simultaneous levitation
experiment of Fe and Flux9 using the electromagnetic levitation method 8). Since the Fe melting point (Tm =1535 ◦ C 9)) and the normal spectral emissivity of liquid Fe (ε Fe = 0.327 10,11)) are known, the radiance at the Fe
melting point RFe was determined to match that of the black body Rb . Since the normal spectral emissivity of
Fe is known, a correction constant Cs is calculated so that the radiance RFe at the Fe melting point is equal to theblackbody radiance Rb , and the temperature of molten Fe is determined from the emissivity at the wavelengthof 1.6 µm.

Cs RFe ( Tm ) = ε Fe Rb ( Tm ) = ε Fe

C1
1


.
λ50 exp C2 − 1

(8)

λ0 Tm

where C1 = 2πhc2 the first constant of radiation, C2 = hc = kB the second constant of radiation, where h: Planck
constant, c: the speed of light, kB : Boltzmann constant.

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Figure 3. Schematic diagram of ELF installed in ISS.

The normal spectral emissivity of Flux9 was determined to be ε ox = 0.76 ± 0.01 12) from the ratio ε ox =ε Fe ( Rox /RFe ) to the emissivity of the molten oxide at the same temperature, Rox ( T ), which was determinedfrom the temperature of the molten Fe part using the correction constants. Using this ε ox and the radianceRox converted from the measured temperature as the ELF instrumental constant CsEL and emissivity of 1, thefollowing eq.(9) was used to determine the temperature TEL for the surface oscillation of the core-shell droplet
at the ELF.
TEL =

C2
λ0

1
C1 ε ox+1ln
λ50 CsEL Rox

!.

(9)

5. Surface oscillation analysis of core-shell droplet by liquid Fe and molten oxides
Surface oscillation of core-shell droplets was measured by applying an alternating electric field to core-shell
droplets levitated in the ELF with applying frequencies from 130Hz to 145Hz. During the measurements, thedroplet temperature was 1920K which was corrected using the Flux9 emissivity of 0.76 ± 0.01. The amplitude of
the surface oscillation increased near the resonance frequency of the eigenfrequency of the surface oscillation.The
Fourier transform of the time variation of the surface oscillation amplitude in the free oscillation region after theAC electric field reduced is shown in Fig. 4 that the amplitude increased at two frequencies (ω− = 76Hz, ω+ =153Hz). This is consistent with the analytical results that the surface oscillation of core-shell droplets oscillates
at two frequencies, and is the first demonstration that the surface of core-shell drop oscillates at two frequencies
in core-shell droplets by immiscible liquids with very different densities. Using these two frequencies, we canobtain the interfacial tension from eq.(7). However, we did not obtain the surface tension of molten oxides of
Flux9. Therefore, we make an approximation for K± in eq.(6) with the assumption that the surface tension ofmolten oxide σo is larger than the interfacial tension between liquid Fe and molten oxide σi . This assumption iscaused by the core-shell drop formation by these two liquids. For the assumption, we find σmi /τ 3 > mo τ 3 /σand also that K± is simplified ? ). On the assumtion, ω+ and ω− are described as follows;5
3 τ6 2ω+= ωo 1 − ∆ρi τ −10 , ω− = ωo 2 1 − τ −10 ,
3
5σ

(10)

where, ωo is ωo2 = 8σo2 /(ρo R3o )which corresponds to the Rayleigh frequency of eigenfrequency of the normal
mode of single-liquid surface oscillation by molten oxides. On the basis of the features of eigenfrequencies of
surface oscillation of core-shell droplet, thus ω− only includes σ, and then we find that the interfacial tension σiis described only by ω− as following;
σi = ω−5ρo Ro1.
624 τ (1 − τ −10 )(11)

To obtain σi using eq.(11), we need ρo of molten oxide density,Ro of radius of molten oxide and τ including
Ri of liquid Fe radius. We can obtain these values from the inside observation of the core-shell droplet by for
instance an X-ray radiograph technique.
We perform only on the ground the X-ray radiograph observation for the solidified sample processedby ELF in ISS, therefore we must estimate the radius of core and shell parts during levitation in ELF. Duringcore-shell droplet levitation using ELF, we obtained the shadow image of the molten core-shell droplet and its
temperature.
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Figure 4. Power spectral density of surface oscillation frequencies of core-shell droplet obtained by FFT analysis of thesurface oscillation data by ELF.

The mass of core-shell dorp processed by ELF can be known when the solidified sample returns to thes . From these results, we can estimate ρ , R and R because the density of Fe is known well inground as Mtoooi
solid and liquid states with temperature dependence. If we are able to perform the inside observation of thes , Rs and Rs ,solidified sample processed by ELF and to obtain both radius core and shell Rsi and Rso . Using Mtooiwe can obtain the density of molten oxide ρo during levitated by ELF as,ρo =s − ρs V s
Mto
Fe Fe
s
(4π/3) R3o − ρsFe ρLFe VFe

s
, VFe
=

4π s 3
R .
3 Fe

(12)

From these procedures, we can calculate the interfacial tension from eq.(12) without new measurements
of molten oxide surface tension and density. In the presentation, experimental results will be applied to theprocedure and the obtained interfacial tension value will be discussed with the previous literature values.
6. Conculsion
Using the ELF on the ISS, we successfully measured the surface oscillation of core-shell droplets of liquid
Fe and molten oxide using the drop oscillating technique. On the ground, it is difficult to form core-shell
droplets due to the large density difference between liquid Fe and molten oxide, but core-shell droplets weresuccessfully formed in a microgravity environment without the density difference. The surface oscillation of thecore-shell droplet was excited, and it was found that the surface oscillation occurred at two different frequencies
even in liquids with large density differences. The interfacial tension will be calculated using the two surface
oscillation frequencies with a new equation of the interfacial tension with approximations. The new equation of
the interfacial tension does not include molten oxide surface tension and density, therefore, we do not need themeasurement of the thermophysical properties of molten oxide. In the presentation, we discussed about detailsof the procedure for obtaining the interfacial tension values from the data of experiments by ELF. In the future,
we will conduct measurements using oxide melts with systematically varied compositions to develop a modelfor the interfacial tension between oxide melts and molten iron.
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c 2021 by the authors.
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