Falling Angle of Fe-C-Based Alloy Droplet on Coke and Graphite

The hold-up of molten pig iron and slag melt in the coke packed bed of blast furnace (BF) causes a decrease of void between coke lumps and inhibits gas permeability. Smooth dripping of those liquids in the coke bed is desirable to keep the productivity of BF. Herein, the conditions for smooth ﬂ owing of molten iron on coke surface are calri ﬁ ed, and the falling angles of Fe-C and actual pig iron droplets on coke and graphite are measured at high temperature. It is found that Fe-C droplet easily slids down on coke because of small falling angle, and the falling angle of actual pig iron is even smaller, while those droplets adhere to a graphite substrate. The carbon in iron has only a small effect on the static contact angle with coke, but has a great in ﬂ uence on the falling angle. From the viewpoint of the roughness of coke surface, the variation of static contact angle and falling angle is discussed.


Introduction
The blast furnace (BF) process produces pig iron, slag, and BF gas through the reactions among iron ore, reducing agents, and high-temperature gas.Since the gas permeability inside BF directly affects the productivity and operational stability of BF, lump cokes and sintered ore are charged in alternating layers from the BF top to maintain the gas flow.A coke bed is formed between the cohesive zone and the dead man in the lower part of BF, and molten pig iron and molten slag generated in the cohesive zone flow down the coke bed.Contrary to these liquids, hot air blown from the tuyeres rises through gaps in the coke bed.When a liquid stagnation in the coke bed, which is called "liquid hold-up", occurs, the gas permeability will be reduced.Therefore, smooth dripping of liquids is required.
Many studies have been conducted on the liquid hold-up in the packed bed, which simulates the coke bed in BF.There are two types of liquid hold-up: the static hold-up and dynamic hold-up.The former relates to the stagnant liquid that does not flow in the gaps of the coke bed, and the latter concerns the liquid flowing through the gaps.[3] In those reports, it was said that the surface tension and the contact angle affected the hold-up.Kon et al. [4] reported based on numerical simulation that the viscosity had an influence on dynamic hold-up, while the wettability on static holdup in the coke bed layer.When the liquid had wettability with the packing layer, hold-up phenomena were observed near the contact points between solid particles due to liquid cross-linking. [5,6]When the liquid was not wettable, the hold-up occurred in dense coke layers due to the generation of capillary forces between coke lumps. [7,8]By summarizing these studies, it is concluded that liquid hold-up is affected by surface tension, wetting angle, and packed bed structure.
[13] In addition to the metal composition, the wetting angle is also affected by the irregularities of coke surface and the reaction between coke and liquid metal.
There have been many researches examining the hold-up mechanism in coke packed bed related to wetting angle and static wettability of iron melt onto smooth carbon material.[16] The relationship between droplet wettability and droplet mobility was studied in the field of surface science, [17][18][19][20][21][22][23][24] and the lotus effect caused by roughness of carbon has been the subject of many studies, while the droplet motion in coke packed bed layer composed of nonuniform and nonsmooth carbon surface has not been investigated.Feng et al. [25] said that the lotus effect and the rose petal effect can explain the wettability and fluidity of liquid on a material surface. [25]In both cases, water droplets do not wet the leaves and petals, but due to the difference in the surface microstructure, water droplets move easily on the former and not easily on the latter.This means that droplet mobility cannot be speculated only from the wetting angle.Kon et al. [26] attempted to clarify the phenomenon of slag dripping in a coke bed using numerical simulation.They examined based on the slag properties such as wettability with coke surface tension, density, and viscosity, but it is considered to be desirable to add the dynamic wettability to the factor.
The wettability between slag and coke varies with the change in interfacial energy due to chemical reactions at the contact interface.When the slag containing FeO or the molten iron unsaturated with carbon contacted with coke, FeO reduction or iron carburization proceeded and the wettability between coke and slag or iron improved. [27]However, the mechanism by which this interfacial reaction affects the mobility of liquid in contact with solid was not discussed.It is expected that accumulating knowledge on dynamic wettability will improve the better understanding of mass transfer and chemical reactions in the BF packed bed.For this purpose, the estimation method of the hold-up phenomena in BF coke bed layer should be developed by referring the wetting angle of pig iron, slag, and coke, which were previously measured and reported in relation to hightemperature processes. [27]n this study, the falling angles of Fe-C alloys and pig iron droplet on coke and graphite were measured at 1723 K to understand the dripping behavior of iron just after melting in the upper part of BF dripping zone, using the device equipped by our research group in previous research. [28]By investigating the effects of the carbon concentration in iron and coke surface condition on the falling angle of Fe-C melt, the relationship between static wettability and falling angle is discussed.

Sample Preparation
Carbon-saturated iron was prepared by melting electrolytic iron powder and graphite powder at 1673 K in Ar gas flow (200 mL min À1 ) using a graphite crucible and pouring the melt onto a stainless steel plate for rapid quenching.For the preparation of two types of Fe-C alloys with lower carbon concentrations, an appropriate portion of the carbon-saturated iron sample prepared above was melted with electrolytic iron powder in a dense MgO crucible and poured onto a stainless steel plate.Actual pig iron obtained by the conventional BF process was also used as a droplet sample, and a high-purity graphite plate and actual coke as substrates.
The carbon concentrations of the three Fe-C alloy samples were 5.10, 3.77, and 1.88 mass%, which are the average of three analyzed values for each Fe-C alloy using a combustion-infrared absorption method (HORIBA EMIA-920).The composition of the actual pig iron was 4.56 mass% C-0.51mass% Si-0.046 mass% S-0.18 mass% Mn-0.111 mass% P. Small chips of three Fe-C alloys and actual pig iron were crushed to less than 2 mm and supplied for the measurement of falling angle.
A coke substrate with dimensions of 35 Â 24 Â 4 mm was cut from the coke block used actually in BF process, and its surface in contact with alloy was polished using emery papers with #120 to #1000 (hereafter, called "untreated coke").To change the surface condition of the coke substrate by gasification reaction (hereafter, called "treated coke"), the substrates were heated at 1273 K for 2 h in CO-CO 2 gas flow (V CO /V CO2 = 1/1, 200 mL min À1 ).This atmosphere was employed to reproduce the redox atmosphere in the thermal reserve zone of BF.The physical properties of the coke and the change in coke surface after the gasification reaction have been reported by Kon et al. [14] and Ogyu et al. [16] They evaluated the surface roughness by using the arithmetic average of the roughness profile, Ra [μm], which was calculated according to JIS-B-0601.The value for Ra of the substrate used in this study was 0.7 μm for untreated coke and 2.0 μm for 2 h-treated coke.
A graphite piece (99 mass% C) was also cut into similar shape as coke substrate, and its surface was mirror polished using an emery paper with #4000.

Procedure
The horizontal resistance furnace shown in Figure 1 was used for measuring the falling angle of Fe-C alloys and pig iron at 1723 K.The metal sample placed on substrate can be inclined by rotating axially the mullite reaction tube under high-temperature conditions.
The coke or graphite substrate was placed on a porous alumina support plate, and small chips of Fe-C alloy or pig iron weighed to 0.76-0.85g were set on the substrate.The alumina plate with metal sample and substrate was slid from the low-temperature region to the hot zone of the furnace in about 5 s under a high-purity N 2 flow (200 mL min À1 ).After holding for 2-3 min until the metal sample melted into a droplet, the reaction tube was slowly rotated at a speed of less than 1 degree per second to tilt the metal droplet on the substrate.The falling angle at which the metal droplet slid down on the substrate was determined by the falling motion of the droplet taken by a video camera installed near the end of the reaction tube.

Falling Angle and Contact Angle of Fe-C and Pig Iron on Coke
The falling angles of three Fe-C melts and a molten pig iron (0.76-0.85 g) on coke were measured at 1723 K. Figure 2 shows the moment when the molten metal droplets began to slide down on the treated coke substrate.Figure 2a-c shows that the droplets of Fe-C melts with 1.88, 3.77, and 5.10 mass% C, respectively, and Figure 2d shows the molten pig iron.The tilt angle of substrate in those figures corresponds to falling angle.In Figure 2a,b,d, each droplet is sliding to the left, while that is sliding to the right in Figure 2c.In Figure 2c, the precipitates, which is considered to be oversaturated carbon, are found on the surface of the Fe-5.10 mass% C melt.The falling angles of droplets on the treated coke are listed in Table 1.In the case of Fe-3.77mass % C (Figure 2b), the sliding started when the substrate was tilted by over 6°, while Fe-1.89 mass% C droplet (Figure 2a) slid at smaller angle.For Fe-C alloys, the falling angle of Fe-3.77mass% C droplet (Figure 2b) is largest.In Figure 2d, the pig iron starts to move at an angle of about 2°, which is smaller than that of Fe-C alloys.The reason for those experimental findings will be described later.
Similar measurements were made for untreated coke.The results are also given in Table 1.The tendency that the falling angle of Fe-3.77mass% C droplet is the largest and the falling angle of pig iron is smaller than that of Fe-C alloy is the same as for treated coke.
The shape of samples on horizontal coke without gasification treatment are shown in Figure 3, where (a), (b), (c), and (d) are droplet of Fe-C melts with 1.88, 3.77, and 5.10 mass% C and pig-iron, respectively.The apparent static contact angles of molten metals to untreated graphite can be derived from those images.The results for untreated coke are shown in Table 1 along with those for treated coke.The static contact angles of all droplets on the two types of coke exceed 90°, indicating poor wettability of these droplets to coke.
Due to the individual variability of coke property, the measured falling angle is inevitably variable even for the same metal droplet, as shown in Table 1.Ogyu et al. [16] noted the nonuniformity of coke surface.Therefore, even when measuring on the same coke substrate, the falling angle is thought to vary depending on the location of the graphite surface on which the droplet is placed.To prevent carburization of the metal droplets and suspension of reaction products in the droplet due to prolonged retention time, measurements were performed within 30 s after droplet formation.No variation in the static contact angle was observed during falling angle measurement.
Figure 4 shows the relationship between the falling angles of metal droplets on cokes and the carbon concentration in the droplets.The results for Fe-C droplets on untreated and treated coke are represented by solid and open circles, respectively.Those for pig iron, which contains impurity elements other than carbon, on the untreated and treated cokes, are plotted by solid and open triangles, respectively.It is found from this figure that the falling angle of each droplet on the untreated coke is relatively  larger than that on the treated coke.Therefore, the gasification treatment tends to lower the falling angle.In addition, the falling angle of the Fe-C droplet with 3.77 mass% C tends to be the largest on both coke substrates, while that of pig iron is lower compared to Fe-C droplets.Humenik et al. [10] reported that the wetting angle of molten Fe-C alloy on carbon became smaller with lowering carbon concentration.Since the carburization reaction of the metal droplet on the carbon substrate is accelerated when the carbon concentration in the droplet is less than the saturation value, the wettability is expected to be improved with increasing the chemical driving force of the carburization reaction.However, it can be said from Table 1 that the Fe-1.88 mass% C droplet slides down more easily than the Fe-3.77mass% C sample.This experimental finding cannot be clearly explained by the wetting angle and the difference from saturated carbon concentration.Moreover, the direct correlation between the static contact angle and the falling angle is not found in Table 1.It will be discussed later.

Adhesion and Contact Angle of Fe-C Melts and Pig Iron on Graphite
Figure 5a-d shows the photos of the molten droplet of Fe-1.88 mass% C, Fe-3.77mass% C, Fe-5.10 mass% C, and pig iron, respectively, on graphite tilted at about 60°, which was the maximum inclination angle of the apparatus.It is found from Figure 5 that the droplets do not slide down even at 60°.This angle on graphite is significantly different compared to Figure 2, where all the falling angles on the coke substrate were less than 20°under all conditions.The effect of the substrate on the falling angle of each droplet is in the order of treated coke ≥ untreated coke >> graphite.
The apparent static contact angles of Fe-1.88, 3.77, and 5.10 mass% C liquid and molten pig iron with the graphite substrate are 62°, 68°, 96°, and 76°, respectively, are shown in Table 1.These values are close to the wetting angle of Fe-C alloys on carbon given by Humenik et al., [10] although no details were described on how they determined it.

Discussion
It is well known that the relationship between the contact angle θ and the interfacial tension of gas-liquid-solid system on a smooth substrate is expressed by Young's equation as follows where γ g/s , γ g/l , and γ l/s are the interfacial tension between gas and solid, gas and liquid, and liquid and solid, respectively.29] Keene [29] found by summarizing previous data that the γ g/l of  Fe-C melt tends to decrease with increasing carbon concentration in iron, whereas Lee et al. [11] reported that it increased with increasing carbon concentration in iron by the addition of sulfur.Chung and Cramb [13] examined the effect of C and S on the surface tension of iron and proposed that γ g/l of Fe-C-S melt is represented by Equation ( 2) and (3).
where T is the absolute temperature, K S is the adsorption coefficient of S in the molten iron alloy, and a [S] is the S activity in iron melt at infinite dilution.In this study, the value for a [S] was calculated from the S and C concentrations (mass%) in iron droplet and the first-order interaction parameters, [30] e S S and e S C , assuming no change in the sulfur concentration in iron droplet on contact with coke.From Equation ( 2) and ( 3), the minimum value for γ g/l at 1723 K was obtained at 3.82 mass% C regardless of the S concentration.Equation ( 4) is obtained by transforming Equation (1).
By substituting the γ g/l calculated from Equation ( 2) and ( 3), which are shown in Table 2, and the static contact angle θ listed in Table 1 into Equation ( 4), the difference Δ between solid-gas  and solid-liquid interfacial tensions can be estimated.At 1723 K, the Δ for Fe-1.88 mass% C, Fe-3.77mass% C, Fe-5.10 mass% C, and the pig iron (4.56 mass% C, 0.046 mass% S) melted on graphite are estimated as 994, 814, À240, and 62 [mN m À1 ], respectively.From Equation ( 4) for each Fe-C melt and molten pig iron, Equation ( 5)-( 7) are derived.
The wettability of Fe-C melts on coke (Figure 2) is inferior to that on graphite (Figure 5).The reason for this difference in wettability is presumed to be that, in addition to the difference in reactivity of coke and graphite to metal droplets, the contact properties of coke differ from those of graphite due to the irregularity or the presence of pores on coke surface.
The influence of coke surface topography is discussed here.For the contact angle of liquid to non-smooth solid surface, Wenzel [20] and Cassie [21] proposed some equations.When assuming that Fe-C melt does not penetrate into the pores on coke surface, Cassie's equation can be applied to the estimation of static contact angle of Fe-C melt on coke where the contact and noncontact surfaces are simultaneously present.The contact angle of liquid to solid, θ, is expressed by Equation ( 8) and ( 9). [15]sθ ¼ a 1 cosθ 1 -a 2 (8) where a 1 , a 2 , and θ 1 are contact area fraction, non-contact area fraction, and contact angle on a flat substrate, respectively.When evaluating the contact between solid and liquid, it is considered that the contact area fraction appears to be more intuitive than porosity because the porosity of coke is different between the surface and the interior.It can be said from Equation ( 8) and ( 9) that θ increases with increasing a 2 .
The static contact angles of Fe-1.88, 3.77, and 5.10 mass% C melts to graphite, θ 1 , are 62°, 68°, and 96°, respectively, and those on untreated coke, θ, are 145°, 143°, and 157°, respectively, as listed in Table 1.When the interfacial tension of molten metal to untreated coke is the same as that to graphite, the values for a 1 on untreated coke are calculated from Equation ( 8) and ( 9) to be 0.122, 0.151, and 0.087 for Fe-1.88,3.77, and 5.10 mass% C melts, respectively, and the values for a 2 on untreated coke are evaluated by Equation (9).Similarly, the values for a 1 and a 2 on the coke with gasification treatment are derived.Those results are summarized in Table 2.It is found that the contact area fraction a 1 is decreased by the gasification reaction of coke, and that of Fe-3.77mass% C is maximum on both coke substrates.
Figure 6 shows the relationships between the a 1 in Table 2 and the average falling angle in Table 1, where circles represent the results for Fe-C droplets and triangles for pig iron droplet, and open and solid marks correspond to the data on coke with and without gasification treatment, respectively.In the case of Fe-C droplets, the falling angle increases with the contact area fraction.From the experimental finding that the Fe-C droplet adhered to graphite in Figure 5, it is expected that the Fe-C droplet tends to adhere to the carbonaceous part of the coke.Since the adhesion force does not work on the noncontact area of the coke, the relationships shown in Figure 6 are considered to be reasonable.In addition, the gasification treatment of coke lowers the contact area fraction of coke to both Fe-C melts and molten pig iron in Figure 6.Although the difference in reactivity between coke and graphite was not taken into account in the evaluation of the contact area fraction on coke surface, the actual contact area fraction would be higher than the value derived above if the carbon portion of coke is less active with metal droplet.However, since the relative relationship between the reactivity and the contact area fraction on the same substrate is expected to remain approximately the same, the apparent change in contact angle is considered to be small.The lower contact area fraction on the coke treated by gasification in Table 2 is supported by Ogyu et al.'s report [16] that the gasification reaction changed the surface condition of coke.
The relationship between the contact area fraction on coke surface and the falling angle of molten pig iron shows a different trend from that of Fe-C melts in Figure 6.It is considered that the contact area and adhesion force of molten pig iron have a large effect on the falling angle.The contact area of molten pig iron is expected to be comparable to that of Fe-C melts because its static contact angle is not different significantly from that of Fe-C melts in Table 1, while the adhesion force of molten pig iron on coke may be reduced, since the surface tension of molten pig iron becomes smaller due to the influence of sulfur.It is suggested that the motion of molten pig iron on coke is affected more strongly by the interfacial tension between solid and liquid than the noncontact area fraction, because the interfacial tension is large.
For quantitative elucidation throughout the dropping zone in BF, the variation in surface tension, activities of alloying elements, and coke reactivity with temperature should be studied in detail.

Conclusions
The falling angles of Fe-C melts with 1.88, 3.77, and 5.10 mass% C and molten pig iron (4.56 mass% C) on coke and graphite were measured at 1723 K, and the effect of carbon concentration in those metal melts on the falling angle was discussed.From those results, the following conclusions were obtained.1) Fe-C and pig iron melts were not wettable on coke.2) There was no direct correlation between the carbon concentration in Fe-C melts and the falling angle, and the falling angle of Fe-3.77mass% C liquid was the largest.3) Since the Fe-C melt and molten pig iron adhered to graphite, their sliding phenomena were not observed.4) The falling angle of metal droplets tended to decrease with the contact area fraction at the solid-liquid interface.5) The variation in contact area fraction and the interfacial tension between solid and liquid affected the falling angle of metal droplets due to the surface topography of the reducing agent.

Figure 2 .
Figure 2. Photo of molten metal as it begins to fall from a coke substrate with gasification treatment.a) Fe-1.88%C, b) Fe-3.77%C, c) Fe-5.10%C and d) pig-iron.

Figure 3 .
Figure 3. Photo of a molten metal sample when the static contact angle was measured on a nongasified coke substrate.a) Fe-1.88%C, b) Fe-3.77%C, c) Fe-5.10%C and d) pig-iron.

Figure 4 .
Figure 4. Falling angle of Fe-C liquid and molten pig iron on coke plotted against C concentration in those metals.

Figure 6 .
Figure 6.Relationship between the estimated contact area fraction and falling angle.

Table 1 .
Static contact angle and falling angle of metal droplets on coke and graphite substitute.

Table 2 .
Estimated contact area fraction of Fe-C melts and molten pig iron on coke.