Droplet Motion on Non-smooth Solid Surface

Abstract

Liquid dripping in a packed bed of coke in a blast furnace decreases the gas permeability and production stability. Enhancing the liquid flow is desirable to increase the productivity of the blast furnace process. The wettability between the liquid and coke affects the dripping behavior. In present study, the contact angle of a moving droplet on a non-smooth solid surface was investigated considering dripping slag and pig iron droplets in a packed bed of coke. The advancing and receding contact angles of water and mercury on a substrate were measured at room temperature while controlling the wettability and roughness. The angles between the cut surface of the coke and water or mercury were also measured. The roughness of the solid surface affected the movement of the adhering droplets, but the effect of the roughness was significantly altered by the wettability. It was found that the resistance to movement of the liquid increased and decreased under good and poor wettability conditions, respectively. Because the wettability of the liquid phase in the blast furnace changed depending on the temperature and composition of molten slag or iron, the force on a liquid droplet from the coke surface changed depending on the position and composition of the hot metal and molten slag in the coke bed.

1. Introduction

The molten slag and liquid iron formed from iron ore descend and the gas injected from tuyeres flows upward through the coke bed of a blast furnace. The liquid phase in the packed bed decreases the gas permeability and affects the stability and productivity of the blast furnace process. The pressure loss in a packed bed was reported by Ergun,¹⁾ and could be derived from the particle size and void fraction. The liquid in a packed bed decreases its void fraction and permeability and is easily held up by an upward force from the gas. When a large amount of liquid accumulates in a coke bed, flooding occurs, and the gas permeability is significantly decreased. It has been found that the structure and moving behavior of the packed bed, and the physical properties of the liquid affect the hold-up of liquid in the packed.²⁾ A formula to predict the hold-up and flow resistance based on the physical properties of the liquid and the structure of the packed bed was previously proposed.^3,4) The motion and hold-up of the liquid on solid surfaces are affected by the wettability, contact area, void fraction, particle shape, and particle size of the packed bed. The wettability is evaluated using the contact angle, which is determined by the system for the gas, liquid, and solid. The contact angle θ for the gas–liquid–solid system on a smooth and flat plane is represented by the formula of Young, as follows:   

$${\sigma }_{gs}={\sigma }_{gl}cos\theta +{\sigma }_{ls}$$(1)

where σ_ls, σ_gl, and σ_gs [N/m] denote the interfacial energies between the liquid and solid, gas and liquid, and gas and solid, respectively. With poor wettability, contact angle θ has a value of 90° or more, and adhesion wetting by droplets can be observed. With good wettability, the angle is less than 90° and immersional wetting is observed. Under a good wettability condition, liquid is held up around the contact point between packed materials.^5,6) On the other hand, under a poor wettability condition, a capillary force holds up the liquid at a narrow neck of the packed bed.^7,8) The hold-up of the liquid is influenced by the contact angle, surface tension, and packed layer structure, as described above. The wettability between carbon and slag in a blast furnace was thoroughly described by Mukai et al.⁹⁾ and Barrett et al.¹⁰⁾ Measurements of the contact angle between the coke and liquid have been conducted in recent years considering the influence of ash.^11,12) The contact angle between pig iron and coke is 60–130°.¹³⁾ In addition, this angle changes with a change in the carbon or sulfur concentration in the iron. The contact angle between the carbon and slag of the CaO–SiO₂–Al₂O₃ system is 20°–160°,²⁾ which is a wide range. The addition of Fe₂O₃ to the slag system causes a reaction with coke and significantly decreases the contact angle. In addition to the influence of the ash or impurity of the coke, the wettability change depends on the shape and texture of the coke surface and the reaction between the liquid and coke. The coke surface is not smooth but contains pores and unevenness. An expression of the contact angle of the liquid on a non-smooth solid surface was derived by Wenzel and Cassie. When a liquid droplet contacts a non-smooth solid, the relationship between the interfacial energies is represented¹⁴⁾ as follows:   

$$r({\sigma }_{gs}-{\sigma }_{ls})={\sigma }_{gl}cos\theta$$(2)

where r [–] is the actual surface/geometric surface ratio and increases with an increase in the surface roughness. If the contact angle on a flat substrate is less than or greater than 90°, the contact angle become less than or greater than that on a rough surface, respectively.

Further, when the liquid does not penetrate into the pores of the solid surface, the non-contact and contact surfaces are simultaneously present. The contact angle is represented¹⁵⁾ as follows:   

$$cos\theta =a_{1}cos{\theta }_1-a_2$$(3)

where a₁, a₂ [–], andθ₁ denote the ratio of the contact area, ratio of the non-contact area, and contact angle on a flat substrate, respectively. The contact angle increases with an increase in the ratio of the non-contact area. As shown in Fig. 1, Droplets moving on a solid receive a force from the contact surface, and the advancing and receding contact angles (b) deviate from the equilibrium contact angle (a). The angle of tilt needed for a drop to slide on a surface was derived by Frumidge.¹⁶⁾   

$$A\rho gsin\alpha ={\gamma }_{gl}(cos{\theta }_R-cos{\theta }_A)$$(4)

where θ_R and θ_A are the receding and advancing contact angles, and these are smaller and larger than the equilibrium contact angle, respectively. In addition, A [m²], ρ [kg/m³], g [N/kg], α, and γ_gl [N/m] denote the shape of the contact area, density of the liquid, gravity force, the angle of tilt needed for sliding, and surface tension, respectively.

Fig. 1.

Relationship between angle of tilt of substrate and the equilibrium, advancing and receding contact angles.

The hold-up of the liquid flowing into the narrow neck of a coke bed depends on the advancing contact angle.¹⁷⁾ Therefore, in order to estimate the amount of hold-up in the coke bed, it is necessary to consider the contact phenomena of a moving droplet on a non-smooth surface. In the present study, the change in the dynamic contact angle of a droplet on a non-smooth surface was investigated to determine the movement of molten iron and slag on the coke in a blast furnace. The advancing and receding contact angles of a water droplet on a substrate with controlled wettability and roughness and a mercury droplet on a cross section obtained by cutting the coke were measured at room temperature.

2. Experimental Procedure

2.1. Samples

To measure the advancing and receding contact angles at room temperature, ion-exchanged distilled water and reagent grade mercury were employed as specimens. The physical properties and contact angles with carbon of water,¹⁸⁾ mercury,¹⁹⁾ molten iron,²⁰⁾ and the CaO–SiO₂–Al₂O₃ system²¹⁾ are listed in Table 1. The surface tensions of the mercury and slag are comparable, but that of water is small, and the Fe–C system shows a large value.

Table 1. Physical property of specimen and liquid in the blast furnace.

System	Contact angle with carbon [degree]	Surface tension [mN/m]
H2O	108	72.25 (302 K)18)
Hg	150	465 (297 K)19)
Fe–C	60–13013)	1500–1900 (1823–1873 K)20)
CaO–SiO2–Al2O3	40–16021)	400–480 (1673–1873 K)10)

Seven kinds of substrates were prepared, including 100×32×3 mm³ aluminum hair-line plates finished with #80, #180, and #320 emery papers, and mirror polished using #10000 diamond paste. The aluminum plates were then dried for 6 h at 60°C in air. A cross section of the blast furnace coke was prepared using a fine cutter. The aluminum plates, a 100×25×2.5 mm³ glass-like carbon substrate with a porosity of 1%–3%, a 60×60×20 mm³ graphite block, and the cross section of coke were used as substrate specimens.

The roughness of the substrate surface was evaluated using a confocal laser microscope. The average roughness (Ra) in the direction perpendicular to the hair-line processing of the aluminum plate and the average length of the curve of roughness (RSm) were measured. The Ra values for the samples hair lined using the #80, #180, and #320 emery papers, the mirror polishing, the graphite block and the glass-like carbon were 28.3, 18.2, 15.9, 4.6, 13.5, 2.6 μm, respectively. Their RSm values were 18.8, 19.5, 24.5, 17.7, 18.7, 14.7 μm, respectively. The roughness decreased with a decrease in the particle size of the abrasive. A sample of coke is shown in Fig. 2. There are relatively smooth (a) and rough (b) areas on the cross section. The Ra values of the flat and rough areas are 61.8 and 557.98 μm, respectively. Pores can be seen in the rough area, and pore and surface portions can be distinguished. The texture of the surface portion was similar to that of the smooth area. However, because the depth of the pore portion was too deep to be measured, an evaluation of the roughness of the surface with pores using the microscope found the apparent measured value.

Fig. 2.

Texture of coke surface. (a) flat (b) rough.

In a preliminary experiment, the static contact angles of water on the substrates were measured using the sessile drop method. The contact angle of water on aluminum with a mirror finish was about 80°, and it was wettable. A non-wettable substrate with a contact angle of about 100° was prepared using a water repellent for the aluminum plate. Other hair-line finished aluminum plates and coke cross sections were prepared using the water-repellent treatment. A fluorine-based water-repellent material was applied for the treatment, and the substrates were dried and held for 6 h in air at 60°C.

2.2. Experimental Procedure

The advancing and receding contact angles were measured using an added and remove volume method. A schematic of the experimental apparatus is shown in Fig. 3. A substrate was placed horizontally, and a 2.5-ml syringe was fixed above it. Syringes with and without a hollow needle with an outer diameter of 0.50 mm were used in the experiments with water and mercury, respectively. In order to measure the stable contact angles during advancing and receding, the expansion and contraction of the droplets were carried out slowly. When liquid is added or removed slowly, the dynamic advancing receding contact angles are almost equal to the static advancing and receding contact angles, respectively. In the experiments with water, 0.2 ml of water was injected onto the substrate over a period of 15 s at a constant flow rate, and then aspirated over a period of 15 s after the droplet stabilized. In the experiments with mercury, 0.2 ml was injected onto the substrate over a period of 20 s, and then aspirated over a period of 20 s at a constant flow rate. The shapes of the droplet during its extension and contraction were captured as a high resolution video using a camera mounted in a horizontal position. In order to clarify the outline of the droplet, LED lights were placed behind the droplet.

Fig. 3.

Schematic of experimental apparatus.

2.3. Method for Analyzing Contact Angle from Photos

Six or twelve still images of the water or mercury droplet during expansion and contraction were obtained from the movie, respectively. The width of the droplet image was about 1000 pixels at the maximum. The contact angle was measured from the image. The position of the triple point and two positions on the contour of the droplet about 10 and 20 pixels away from the triple point were read, and a circle passing through these three points was drawn. Then, the angle between the substrate and the tangent to this circle was determined. The contact angle reading error using this method was less than 4°. The means and standard deviations of the contact angles of contraction and expansion were calculated.

3. Dynamic Contact Angle of Water

3.1. Experimental Result

The shape of a sample in the experiment is shown in Figs. 4 and 5. Water or mercury was injected and aspirated on a water-repellent aluminum plate or a glass like carbon, respectively. A hair-line finish was applied using #180 emery paper in the orthogonal direction of the photo. The dark colored vertical line and lower part are the needle and substrate, respectively. In Figs. 4 and 5, (a)–(c) and (d)–(f) represent expanding and contracting samples and show the contact angles during advancing and receding, respectively. The influence of the tip of needle or syringe on the contact angle could be ignored. The contact angles of (a)–(c) are larger than those of (d)–(f). The position of the triple point repeatedly moved and stopped. Therefore, the dynamic contact angle varied according to the time that the image was taken. The standard deviation indicates the scale of the variation in the contact angle.

Fig. 4.

Shape of water drop on substrate in experiment.

Fig. 5.

Shape of mercury drop on substrate in experiment.

The receding contact angle decreased with a decrease in the diameter of a droplet to less than 3 mm. Volume of liquid do not affect on the contact angle in the principle. However, in a small droplet, the line energy at the triple point became relatively large for the interface energy,²²⁾ and the contact angle might have been affected by the energy of the coexisting gas–liquid–solid triple line. Thus, only the images of droplets with diameters greater than 3 mm were used for the analysis.

The contact angle of water on the aluminum substrate is shown in Fig. 6. The solid and open circles show the advancing and receding contact angles, respectively. The horizontal axis shows the direction and substrate. In horizontal axis, Pol., #320, #180 and #80 denote substrate mirror polished, and finished with #320, #180, and #80, respectively. The results for the movement of the triple point parallel and orthogonal to the hair lines are denoted as p and o, respectively. The error bars indicate the standard deviation. The contact angle of water on the mirror-finished aluminum substrate in air at room temperature was about 80°.

Fig. 6.

Advancing and receding contact angles of water on aluminum substrates.

The advancing and receding contact angles were 97° and 43° on the mirror-finished aluminum plate, respectively. The contact angle of a static droplet was smaller than 90°, and it was wettable. However, it became non-wettable with the advancing contact angle.

The advancing and receding contact angles on the hair-line finished substrate were smaller than on those of the mirror-finished substrate. In the measurement of the receding contact angle, the wetted surface area of the droplet did not decrease. The contact angle continued to decrease until it became 0°. The advancing contact angle was affected by the roughness of the substrate; that in the direction across the asperity (o) was larger than that parallel (p) to the asperity. The contact angle decreased with an increase in the roughness.

The results of the contact angle measurements for water droplets on the water repellent substrates are shown in Fig. 7. The flat part of a coke surface (Fig. 2(a)) was employed as the coke substrate. The contact angles parallel and perpendicular to the hair lines were analyzed. The advancing contact angle in a direction parallel to the hair lines was almost the same as that for the mirror-finished substrate. On the other hand, when advancing in a perpendicular direction, the contact angle increased with an increase in the roughness of the substrate. The contact angle on the coke was almost the same as that on the #80 substrate, whereas the standard deviation for the coke surface was larger than that for the substrate finished with the #80 emery paper. When making contact in the parallel direction, there was no difference in the receding contact angles for the substrates with the hair-line finish and mirror finish. The receding contact angle in the orthogonal direction was about 10° smaller than that in the parallel direction. Because air was entrapped on the interface, the receding contact angle on coke was smaller than that on the mirror-finished substrate, and the standard deviation of the angle was larger than that under other conditions.

Fig. 7.

Advancing and receding contact angles of water on water-repellent aluminum substrates.

3.2. Discussion

For the contact of a droplet with a wettable solid surface with asperity, the relationship between the contact angle and surface roughness was derived as shown in Eq. (2). If a droplet was static on a solid surface, its contact area increased with an increase in the surface roughness. Therefore, the absolute value of cos θ increased with an increase in the influence of the surface roughness. Further, if the gas phase was present between the droplet and substrate, the contact angle could be expressed as Eq. (3). In this case, the contact angle monotonically increased with an increase in the roughness.

According to Figs. 6 and 7, when the triple point crosses the asperity on a water-repellent substrate, the advancing contact angle increases. Meanwhile, on the other substrate, the contact angle decreases with increasing roughness. In this case, the adaptation of Eq. (2) would be more appropriate than that of Eq. (3).

In Fig. 6, the advancing contact angle on the mirror-finished aluminum is greater than 90°. On the other hand, the angle of the substrate with a hair-line finish is less than 90°, and the sign of cos θ is reversed. According to Eq. (2), the absolute value of cos θ increases with an increase in the roughness. Therefore, it is not reasonable to evaluate the effect of the roughness on the advancing contact angle using Eq. (2). Because the static contact angle is less than 90°, the advancing contact angle is decreased by the surface roughness, and then increased by the motion of the triple point. Further, if the triple point moves across the asperity, the contact angle is clearly increased. In the retreat of the triple point, the drag force from the substrate is greater than the force to move the triple point from the surface tension of the liquid surface. Therefore, the triple point did not move, and thus the contact angle decreased to 0°. Even in systems with an equilibrium contact angle of around 90°, there is a possibility that a liquid film will remain on a solid surface by the movement of droplets, which will wet a solid packed bed.

The relationship between the critical contact angle of the droplet and the advancing contact and receding contact angles is derived from Eq. (4).   

$$\frac{A\rho g}{{\gamma }_{gl}}sin\alpha =cos{\theta }_R-cos{\theta }_A$$(5)

Here, sin α is the critical angle related to the sliding angle. Assuming that the force on a droplet during its advance and retreat is F,   

$$2F={\gamma }_{gl}(cos{\theta }_R-cos{\theta }_A)$$(6)

where F includes the forces from the irregularities of surface atoms, asperity of the surface, and pores.

The cosθ_R–cosθ_A values of the contact angles of water on the aluminum substrates are shown in Fig. 8. The solid and open circles denote the results under wetting and non-wetting conditions, respectively. The vertical axis represents 2F/γ_gl, which is influenced by the width of the contact area. Therefore, the force cannot be directly compared in a precise sense. In comparison to the F received from the smooth surface, the change in F due to surface roughness can be seen to be relatively small. Under both wetting and non-wetting conditions, compared to its behavior on the mirror finish, the droplet easily falls in the hair-line direction, but it is difficult for it to fall in the orthogonal direction. Compared to the F value of the mirror-finished substrate, the F value in hair-line direction is smaller, and that in the orthogonal direction is larger. In addition, the sliding angle is reduced by an increase in the surface roughness. The change in F based on the direction indicates that the force is needed to move beyond the asperity. There are relatively large pores and asperity on the surface of coke. However, the F value for the coke was similar to that for the #80 hair-line finished substrate. The contact condition for the liquid on coke was different from that on the aluminum substrate. The surface roughness increased the drag force on the triple point, whereas the non-contact area caused by the pores decreased the drag force.

Fig. 8.

Difference between advancing and receding contact angle of water on substrates.

4. Contact Behavior of Mercury on Substrate of Carbon

The advancing and receding contact angles of mercury on a glassy carbon, carbon block, and cross section of coke were measured. The experimental results are shown in Fig. 9. The error bars indicate the standard deviation. The contact angles of mercury on the carbon substrate and cross section of coke are larger than that on the glassy carbon. The advancing and receding contact angles measured for mercury were greater than 140° and 120°, respectively. These were the result of adhesion wetting. In the case of the adhesion wetting, the contact angle increases due to both an increase in the surface roughness (Eq. (2)) and a decrease in the contact area (Eq. (3)). Meanwhile, the advancing contact angle had the maximum value on the carbon substrate, which was apparently smooth. The force needed to move the triple point from the surface was the largest on the glassy carbon, which was the smoothest substrate. This indicated that the influence of the decreasing contact area was larger than that of the increasing resistance from the contact area.

Fig. 9.

Advancing and receding contact angles of mercury.

Figure 10 shows the cosθ_R − cosθ_A results for mercury on the carbon substrate. The force needed to move the droplet on the glass-like carbon was the largest, and this force apparently decreased with an increase in the surface roughness. As shown in Eq. (6), the decrease in this value indicates a decrease in the force needed to move the triple point. This phenomenon was different from the behavior of water on the aluminum substrate. This was due to the difference in the contact angle, which was around or significantly greater than 90°.

Fig. 10.

Difference between advancing and receding contact angles of mercury on carbon or coke.

As shown in Fig. 9, the contact angle has a maximum value on the carbon substrate. However, regardless of this tendency, a decrease in the surface roughness apparently increases the force required to move the triple point. As expressed in Eq. (3), the area of the non-contact interface between the liquid and substrate will be increased by an increase in roughness. Thus, the tendencies for water and mercury were that their contact areas with a substrate were increased and decreased with an increase in the roughness of the substrate, respectively.

5. Behavior of Droplets on Coke in Blast Furnace

In the present study, the influence of the surface roughness of a substrate on the dynamic contact angle of a droplet on it was investigated at room temperature. Here, the liquid motion in a coke packed bed of a blast furnace is discussed. The main component of coke is carbon. The contact properties of carbon and molten slag or liquid iron were well summarized by Hayashi et al.²⁾ The surface tensions of the molten Fe–C system²³⁾ and the molten slag are changed by variation of the composition of liquid phase, however, the change in the contact angle due to the reaction between the liquid and coke is more larger. The contact angle between the molten CaO–SiO₂–Al₂O₃ system, which provides the basicity of the ironmaking slag and graphite is around 160°.²¹⁾ Generally, a chemical reaction at the interface decreases the contact angle. Therefore, the addition of FeO or Fe₂O₃ causes a reduction reaction and decreases the contact angle of molten slag. The contact angle between the molten Fe–C system and graphite increases with an increasing carbon content, with values of 60° and 130° with 0% and 5% C, respectively.¹³⁾ Molten iron and slag drip from the lower side of the cohesive zone in the blast furnace. During dripping in the coke bed, the concentration of FeO in the slag decreases by a reduction reaction, and the concentration of carbon in the iron increases by a reaction with coke. Because the slag at an upper position of the dripping zone includes FeO, the wettability of the slag would be good. In addition, the C concentration in the iron at an upper position is low. Therefore, the wettability of the iron with the coke bed would be good. However, after the reaction, the wettability of both the slag and iron would become poor. Under wetting and non-wetting conditions, the roughness of the coke surface inhibits and enhances the movement of a droplet, respectively. The effect of the coke surface on the liquid flow changes with the variation of the reaction ratio of the liquid.

As shown in Eqs. (5) and (6), the surface tension also affects the contact angle. The surface tensions of slag and iron decrease with a decrease in the FeO concentration and an increase in the carbon concentration, respectively. The effect of the surface roughness on the wettability of a liquid would decrease in the lower part of the coke packed bed. The descent of the liquid is mainly limited by the static hold-up in a coke packed bed. This static hold-up occurs at a narrow neck of the packed bed. There are two types of static hold-ups, namely wetting hold-up and non-wetting hold-up.¹⁷⁾ At the upper and lower parts of the dripping zone, the wettabilities of the slag and iron are responsible for the wetting and non-wetting hold-ups, respectively. Therefore, the surface roughness would increase the static hold-up in both the upper and lower potions of the dripping zone.

6. Conclusions

In order to analyze the motion of molten slag and iron on the surface of coke in a blast furnace, the change in the dynamic contact angle of a droplet on a non-smooth surface was investigated. The advancing and receding contact angles of water and mercury droplets on substrates with controlled wettabilities and roughnesses were measured at room temperature, and the following conclusions were obtained.

(1) If the contact angle was less than or around 90°, the drag force on the triple point for the substrate was increased by an increase in roughness of the solid surface, and the mobility of the droplet was reduced.

(2) If the wetting angle was significantly greater than 90°, the contact area of the interface between the solid and liquid was reduced by an increase in surface roughness, and thus the drag force on the triple point was lowered.

(3) The wettabilities of the molten slag and iron varied with the progress of a reduction reaction in the blast furnace. At the upper part of the dripping zone, the wettability was increased by an increase in surface roughness of the coke. Meanwhile, at the lower part, the wettability was decreased.

(4) Because the wettabilities of slag and iron change within the coke bed, wetting hold-up and non-wetting hold-up are likely to be increased by the roughness of the coke surface in the upper and lower parts of the dripping zone, respectively.

Acknowledgement

Present research was carried out with ISIJ Research Promotion Grant. Some of the authors express sincere thanks for the support.

References

• 1)   S.  Ergun: Chem. Eng. Prog., 48 (1952), 89.
• 2)   M.  Hayashi,  S.  Sukenaga,  K.  Ohno,  S.  Ueda,  K.  Sunahara and  N.  Saito: Tetsu-to-Hagané, 100 (2014), 211.
• 3)   T.  Fukutake and  V.  Rajakumar: Trans. Iron Steel Inst. Jpn., 22 (1982), 355.
• 4)   T.  Sugiyama, T. nakagawa, H. Sibaike and Y. Oda: Tetsu-to-Hagané, 73 (1987), 2044.
• 5)   Y.  Endo,  Y.  Kosaka and  M.  Ishii: Kagaku Kogaku Ronbunshu, 19 (1993), 1128.
• 6)   S.  Kikuchi,  T.  Kon,  S.  Ueda,  S.  Natsui and  R.  Inoue: ISIJ Int., 54 (2014), 1244.
• 7)   K.  Saito,  K.  Ohno,  T.  Miki,  Y.  Sasaki and  M.  Hino: ISIJ Int., 46 (2006), 1783.
• 8)   H. L.  George,  B. J.  Monaghan,  R. J.  Longbottom,  S. J.  Chew and  P. R.  Austin: ISIJ Int., 53 (2013), 1172.
• 9)   K.  Mukai and  T.  Ishikawa: J. Jpn. Inst. Met., 45 (1981), 147.
• 10)   L. R.  Barrett and  A. G.  Thomas: J. Soc. Glass Tech., 43 (1959), 179.
• 11)   K.  Ohno,  T.  Maeda,  K.  Kunitomo,  T.  Miyake and  S. Tsurumaru: CAMP-ISIJ, 27 (2014), 16, CD-ROM.
• 12)   S.  Sukenaga,  H.  Shibata,  T.  Fuchigami,  K.  Yasutake,  S.  Rine,  N.  Satito and  K.  Nakashima: CAMP-ISIJ, 27 (2014), 19, CD-ROM.
• 13)   M.  Humenik,  D. W.  Hall and  R. L.  Van Alsten: Met. Prog., 81 (1962), 101.
• 14)   R. N.  Wenzel: J. Phys. Colloid Chem., 53 (1949), 1466.
• 15)   A. B. D.  Cassie: Discuss. Faraday Soc., 3 (1948), 11.
• 16)   C. G. L.  Furmidge: J. Colloid Sci., 17 (1962), 309.
• 17)   T.  Kon,  S.  Natsui,  S.  Ueda and  H.  Nogami: ISIJ Int., 55 (2015), 1284.
• 18)  Iwanami Rikagakujiten, 4th ed., Iwanami Shoten, Tokyo, (1987), 1264.
• 19)  Kinzoku Data Book, Maruzen, Tokyo, (1974), 15.
• 20)   B. J.  Keene: Int. Mater. Rev., 33 (1988), 1.
• 21)   H.  Ohgusu,  Y.  Sassa,  Y.  Tomita,  K.  Tanaka and  M.  Hasegawa: Tetsu-to-Hagané, 78 (1992), 1164.
• 22)   S.  Ueda,  H.  Shi,  X.  Jiang,  H.  Shibata and  A. W.  Cramb: Metall. Mater. Trans. B, 34B (2003), 503.
• 23)   K.  Morohoshi,  M.  Uchikoshi,  M.  Isshiki and  H.  Fukuyama: ISIJ Int., 53 (2013), 1315.