Slag entrainment in continuous casting and effect of interfacial tension

Abstract

In the first part of the present study, the relation between the dimension free critical capillary number Ca* and the material number Λ are introduced as a stability criteria for slag entrainment at the steel/slag interface. With the knowledge of thermophysical properties of the immiscible liquids in contact, critical values of Ca* for slag entrainment as a function of Λ could be estimated. The interfacial tension was investigated at 1823 K for carbon and Cr–Ni steels in contact with ternary slags containing CaO, SiO₂, Al₂O₃, MgO and TiO₂ using the drop weight method. The apparent interfacial tension of CaO–SiO₂–TiO₂ slag systems in contact with Cr–Ni steel decreases with increasing TiO₂ content and was found to be influenced by interfacial area change during droplet formation at the capillary exit, slag composition and reactions at the steel/slag interface. Minimum values of interfacial tension, observed during measurements, increase the possibility for slag entrainment in the continuous casting mould.

Introduction

The entrainment of liquid mould slag in the liquid melt pool, caused by an instability of the steel/slag interface, is a source for non-metallic inclusions and reducing product quality.1, 2 The stability of a liquid/liquid interface is related to thermophysical properties like density (density of the continuous phase ρ _c and density of the dispersed phase ρ _d respectively), viscosity (viscosity of the continuous phase η _c and viscosity of the dispersed phase η _d respectively) and interfacial tension σ, of the phases in contact.3 The capillary number Ca as a function of η _d /η _c is a well studied stability criteria for the break-up of a droplet surrounded by a second fluid (ratio ρ _c /ρ _d = 1).4, 5 Increasing the Ca up to its critical value Ca* results in droplet break-up producing two or more smaller droplets. The Ca number is inversely proportional to the interfacial tension and, hence, directly affected by this property.

Various high temperature methods are available to measure interfacial tension between steel and slag.6 Depending on the method used, the values obtained have to be discussed either as equilibrium or non-equilibrium values. In industrial processes, mainly non-equilibrium conditions exist.

In the present work, dimensionless relations are used to describe the stability of a liquid/liquid interface.7 The interfacial tension as a key parameter for the stability of a fluid interface was investigated at 1823 K for low alloyed carbon and Cr–Ni steels in contact with ternary slag systems containing CaO, SiO₂, Al₂O₃, MgO and TiO₂ using the drop weight method.

Experimental

Experimental procedure

The entrainment of droplets of upper liquid in the lower one was investigated in room temperature experiments using water, and different silicon oils, to simulate a liquid/liquid interface. The experiments were performed in a Plexiglas container, and the relative velocity near the interface was generated with a rotating roller 10 mm below the interface. The development of the interface shape and the production of droplets were recorded using a high speed camera and particle image velocimetry.8

To measure σ between liquid steel and liquid slag, the drop weight method was used.9 The apparatus (see Fig. 1) used in the present study consists of a furnace, an alumina crucible with a capillary tube for molten steel (14 g) and a graphite crucible for liquid slag (35 g), a high precision balance and control unit. The measurements were conducted under argon atmosphere (argon ⩾99·999 vol.-%).

Figure 1.

Left: Schematic of apparatus used for interfacial tension measurements: (1) alumina crucible, (2) graphite crucible, (3) liquid metal, (4) alumina cylinder, (5) capillary tube ZrO₂, (6) liquid slag, (7) copper sealing, Right: weight change versus time during formation and detachment of droplet (I) and (II) droplet growth (III) weight change due to droplet detachment (IV) formation of next droplet (▵m used for calculation of interfacial tension)

Using a ceramic device (4), a droplet of liquid metal (3) is formed at the end of a capillary tube (5), which is dipped into liquid slag (6). If equilibrium between the gravitational force F _g, the interfacial tension force F _ift and the buoyancy force F _b is exceeded, the droplet drops. The weight m of the drop detached from the capillary correlates with σ between the two liquids. Figure 1b shows a typical weight change during formation and detachment of the metal droplet in liquid slag. The weight change after droplet detachment is related to interfacial tension σ by equation (1)10, 11 (1) where g is the gravitational acceleration, r is the inner radius of the capillary tube and φ is a correction factor. The correction factor is a function of drop volume V and r of the capillary tube and is introduced to compensate for failure, in which a small amount of molten metal gets stuck to the capillary tube.12, 13 The value of φ is in the region of 0·6 up to 1·2 and is described by equations (2) and (3)13 (2) where (3) During the experiment, m was recorded as a function of time t by a high sensitive balance (Mettler-Toledo PR1203) with an accuracy of 0·001 g and a linearity of ±0·002 g. Linear fits before and after droplet detachment (see Fig. 1b ) were used to determine the mass m of the droplet.

In the literature,12, 14 droplet frequencies smaller than one per minute have been used for estimation of surface tension σ. In order to ensure the droplet formation in equilibrium in these experiments, σ was measured as a function of volumetric metal flow V. A high precision step motor was used to change V between 25 and 75 μm³ min⁻¹ resulting in time differences between detachments of two droplets of 200–70 s. In the range of V = 25–75 μm³ min⁻¹, σ is independent of V. In the present work, this range was used to realise droplet formation with respect to capillary corrosion.

After the capillary is immersed in the slag, corrosion processes start, so by ensuring a steady metal flow in the capillary, the effect of corrosion on droplet formation can be diminished. Corrosion leads to an increase of r depending on slag composition and contact time t. The contact time was therefore limited to several minutes.

Experimental materials

In room temperature experiments, pure water and silicon oils with viscosities between 0·0006 and 0·4850 kg m⁻¹ s⁻¹ were used as reported previously.8 The interfacial tension between these oils and water varied in a very small range.

Two types of steel were used for the measurements, a low alloyed carbon steel ST1 and Cr–Ni steel, ST2 (see Table 1). The slag samples were prepared by melting powder mixtures consisting of measured quantities of its components in a graphite crucible. The compositions of the slags used are listed in Table 2 (see Chapter 3).

Table 1.

Composition of investigated steels

Steel composition
	C	Si	Mn	Cr	Ni	Ti	Al	O	S
	Mass-%							ppm
ST1	0·07	0·14	0·4	0·13	0·16	0·001	0·002	125	510
ST2	0·02	0·43	1·4	17·8	9·07	0·001	0·01	54	105

Table 2.

Composition of investigated slags and measured interfacial tension (average values of six droplets for each experiment) between steel and slag at 1823 K

Steel	Slag							Steel–slag
Steel	Slag	SiO₂/wt-%	CaO/wt-%	Al₂O₃/wt-%	MgO/wt-%	TiO₂/wt-%	Basicity (CaO/SiO₂)	Interfacial tension/mN m⁻¹
ST1	B1	50·3	31·0	19·0	0	0·1	0·5	996
	B2	45·7	36·0	19·0	0	0·1	0·5	996
	B3	40·5	38·0	21·4	0·2	0	0·7	993
	B4	37·2	44·0	18·9	0	0·0	0·8	1042
ST2	G	59·2	40·5	0·3	0·01	0·1	0·9	1064
	A1	54·8	39·4	5·8	0·02	0·03	0·7	884
	A2	51·4	37·1	11·4	0·04	0·03	0·7	817
	M1	56·5	38·2	0·5	4·8	0·1	0·7	829
	M2	53·7	36·7	0·3	10·3	0·0	0·7	853
	T1	49·1	45·1	0·1	0·03	0·03	0·7	856
	T2	45·5	41·7	0·03	0·02	5·7	0·9	836

Results and discussion

Stability criterion for slag entrainment

Two stratified immiscible liquids of different densities ρ _d (density of upper liquid) and ρ _c (density of lower liquid) with ρ _d <ρ _c, form a liquid–liquid interface. In static equilibrium, the state of the stress at the interface can be described by the Young–Laplace equation (4)15 (4) where Δp is the difference in the pressures in the fluids across the interface, R ₁ and R ₂ are the radii of curvature and σ is the interfacial tension. The interfacial tension of two immiscible fluids (e.g. between liquid steel and liquid slag) is a state property resulting from anisotropic interaction of the oxide melt (slag) and the metallic melt (steel) in the interfacial area A between both melts. A flow velocity u near the interface, initiated by the bulk phase flow of the lower liquid, exposes a shear force in the vicinity of the liquid/liquid interface. The flow acts tangentially on the interface leading to interfacial waves, deformation of meniscus and formation of finger-like protrusions (see Figure 1a–c). If a critical flow velocity u _crit. is reached, droplet break-up from the upper liquid occurs (see Figure 1d). The tendency for droplet break-up is restored by increasing σ. In order to describe the conditions for break-up of droplets from the upper liquid, dimensionless relationships are used.

The capillary number is defined as Ca ^* = u _crit. η_cσ ⁻¹ when material properties are given, and the material number is defined as the ratio of kinematic viscosities Λ = ν _d/ν _c of the two liquid phases. These dimension free numbers represent a stability criterion for a liquid/liquid interface exposed to a shear stress.

The break-up of droplets of one fluid surrounded by another with a density ratio ρ _c/ρ _d equal to 1·0 is a function of Ca and viscosity ratio η _d /η _c describing a stability criterion for stable and unstable droplets.16 For steel–slag systems, the density ratio ρ _c/ρ _d is 2·5, and this value should be taken into consideration. Model investigations with varying properties of immiscible fluids were conducted in order to describe the relation between Ca ^* and the Λ for liquid–liquid systems of varying properties without mass transfer.17, 18 Using the Froude–Weber similarity criterion,19 the measured critical velocities u _crit. were related to the conditions near the steel/slag interface in the industrial continuous casting mould. Equation (5) presents the developed relation between Ca* and Λ for entrainment of the upper phase from a liquid/liquid interface.8 (5)

Slag/metal interfacial tension

In the present study, the interfacial tension σ at 1823 K between low alloyed carbon and stainless Cr–Ni steel and liquid slags was investigated with respect to the effect of slag composition and, therefore, the impact on the stability of the steel/slag interface due to slag entrainment.

The average value of the interfacial tension according to the first six droplets was evaluated as apparent interfacial tension. The values of interfacial tension between low alloyed steel ST1 and ternary slags for different slag basicities (CaO/SiO₂) are shown in Table 2. It is seen that the value of σ increases with increasing slag basicity (B1–B4). This tendency is similar to values published for liquid Fe–C in contact with CaO–SiO₂–Al₂O₃ slags.20

With increasing slag basicity, the sulphur adsorption at the steel/slag interface decreases, leading to higher values of σ. The interfacial tensions for the investigated slags (CaO/SiO₂ = 0·7) in contact with ST2 are between ∼800 and 880 mN m⁻¹ at different TiO₂ contents and for ST1 steel between 993 and 1064 mN m⁻¹ depending on slag basicity. Both steel–slag systems have to be evaluated separately because of the different contents of sulphur and alloying elements in steels and different compositions of slags. A decreasing effect of chromium and nickel on σ for Fe melts in contact with CaO–SiO₂–Al₂O₃ was reported by Sun et al. 21 X-ray sessile drop measurements22 of σ between steel (22Cr–5Ni) and a commercial mould flux 35SiO₂–31CaO–2·3MgO–6Al₂O₃–11Na₂O–4F was estimated to be 870 mN m⁻¹. These values are similar to ST2 in contact with ternary slags (CaO/SiO₂ = 0·7) in the present study (compare Table 2).

Compared to the basic mixture G, the addition of Al₂O₃ (A1 and A2) decreases σ between Cr–Ni steel and ternary slag (compare Table 2). This follows the trend for alumina additions to slags in the system CaO–SiO₂–Al₂O₃, which causes a slight decrease in slag surface tension.23 The droplet formation for ST2 in contact with slag A1 was observed to be very unstable, resulting in a high standard deviation of the measured σ values.

Increasing the MgO content of a CaO–SiO₂ slag up to 10% results in a slight decrease in σ. A sharp decrease in interfacial tension between molten iron and CaO–SiO₂–MgO–Al₂O₃ was reported by Park et al. 24 for more than 20%MgO addition. The decrease was related to solid MgO particles accumulated around the interface. In this case, there are two liquid phases separated by a solid phase. However, in the present study, the compositions studied are far away from MgO saturation, and consequently, the formation of solid particles can be excluded.

Sharan and Cramb25 measured σ for a Fe–20 wt-%Ni alloy in contact with a CaO–SiO₂–TiO₂ slag with increasing TiO₂ content at 1823 K. An addition of 10%TiO₂ resulted in a decrease of σ to 1089 mN m⁻¹. The average σ values of the interfacial tension in the present study for ST2 in contact with T1 and T2 are 836 and 803 mN m⁻¹; however, the minimum σ values are much smaller (compare Fig. 3 and Table 3).

Figure 3.

Comparison of interfacial tension as function of time for droplet generation of ST2 in contact with CaO–SiO₂ slag and increasing TiO₂ content; t = 0 is equal to first detached droplet

Table 3.

Calculated values of density,28 viscosity29 and lowest measured interfacial tension values of investigated steel–slag systems at T = 1823 K; values of Λ are calculated using published relation30 at 1823 K for steel density and viscosity (0·005 Pa s);31 Ca values calculated from measured material properties with u = 0·3 m s⁻¹ and critical Ca* values calculated using equation (5)

Steel	Slag	Viscosity η/Pa s	Density ρ/kg m⁻³	Minimum σ values/mN m⁻¹	Λ	Ca experimental/×10⁻³	Ca* critical/×10⁻³
ST1	B1	1·00	2,510	977	509	2·01	4·33
	B2	0·70	2,540	963	352	2·01	3·86
	B3	0·60	2,570	1020	298	1·92	3·69
	B4	0·30	2,650	1088	145	1·88	3·23
ST2	G	0·50	2,540	866	252	2·26	3·55
	A1	0·70	2,560	807	349	2·45	3·85
	A2	0·80	2,530	689	404	2·41	4·01
	M1	0·23	2,550	808	115	2·34	3·15
	M2	0·15	2,880	793	67	2·34	3·00
	T1	0·45	2,680	686	215	2·39	3·44
	T2	0·35	2,770	624	162	2·49	3·28

In Fig. 3, the interfacial tension σ is plotted as a function of time for the generation of one droplet within the first six for CrNi steel ST2. The interfacial tension remains constant up to 420 s droplet generation time in contact with SiO₂–CaO slag and decreases with high TiO₂ slag content. The drop by ∼200 mN m⁻¹ occurs after 200 s. At droplet generation time higher than 300 s, the deviation in the measured values increases strongly. This change of the interfacial tension with TiO₂ content and with contact time indicates the running reactions between both phases. Gradients of element concentration on both sides of a steel/slag interface are reported by different authors, which indicate the exchange reactions.²⁶ 26,27

Mass transfer at steel/slag interface

Gaye et al. 32 listed a number of reactions among liquid, metal and slag causing a drastic decrease in σ. They observed a progressive lowering of interfacial tension when metal and slag were brought into contact, followed by recovery of high σ. In most cases, the reactions corresponded to reduction of the slag with strong deoxidisers dissolved in the metal phase. Oxygen from SiO₂ oxidises Cr, Mn from liquid Cr–Ni steel.33 For the steel–slag system ST2-G, droplet formation is not influenced by the reactions mentioned above, explaining the stable behaviour of σ as a function of time (see Fig. 3). For V<75 μm³ min⁻¹, the reactions at the interface may occur, but the equilibrium during growth of the interfacial area is not disturbed. However, an increasing TiO₂ content in the slag leads to a destabilisation of droplet formation. For the Cr–Ni steel in contact with CaO–SiO₂–TiO₂ slags containing more than 3%TiO₂, the reactions taking place at the interface and the resulting concentration gradients lead to non-equilibrium conditions during the growth of the droplet. X-ray sessile drop measurements of liquid Fe immersed in a CaO–Al₂O₃–SiO₂ slag indicated that after 60 min. the equilibrium σ values were reached.25 In the present study, the droplet formation time was in the range of 70–200 s, and hence, the measured interfacial tensions are considered as non-equilibrium values.

Looking to the stability criteria for droplet separation, the values of the capillary and material number were calculated using measured and estimated properties. Assuming a metal flow velocity of u = 0·3 m s⁻¹ in the vicinity of the steel/slag interface in the industrial casting mould,34 the estimated Ca values are in the range of 1·8–2·4×10⁻³. These values are lower compared to the critical values of Ca* calculated applying equation (5). Under these conditions, the steel/slag interface should be stable, and slag entrainment should not occur.

However, reactions at the steel/slag interface would cause a local decrease of interfacial tension.35, 36 A decrease in σ below 0·4 N m⁻¹ would raise the corresponding Ca number to the critical value, and the interface becomes unstable, leading to slag entrainment.

Error of estimation

Before the experiment, the capillary radius r was measured. Experimental uncertainty analysis was conducted using u(m) = 0·005 g, u(r) = 0·005 mm and u(V) = 5 mm³. For m = 0·4 g, r = 0·615 mm and V = 77 mm³, the systematic error u(σ) was calculated to be ±15 mN m⁻¹. Considering the systematic and random values, the error is assumed to be 5% (±50–80 mN m⁻¹) of the absolute value. For the investigated slag systems (CaO/SiO₂ = 0·7–1·1), it is possible to assume a linear increase in r with 0·05 mm for the first 600 s starting with the first contact with liquid slag.

Conclusions

The Ca number as a function of Λ was introduced as a stability criterion for droplet break-up at a liquid/liquid interface. Decreasing interfacial tension increases the value of the Ca number and decreases the stability of the interface. Therefore, this controlling parameter was experimentally estimated for different slag and steel compositions. The drop weight method was used to measure the interfacial tension. The interfacial tension of carbon steel increases with increasing slag basicity from 996 to 1064 mN m⁻¹. The interfacial tension of Cr–Ni steel in contact with CaO–SiO₂ slags with CaO/SiO₂ = 0·7 was found to be 884 mN m⁻¹. MgO and Al₂O₃ additions up to 10% cause a slight decrease in σ. The values of σ for Cr–Ni steel in contact with a CaO–SiO₂–TiO₂ slag decreases with increasing TiO₂ content, and droplet formation becomes unstable. The error of the estimation was calculated to be ∼5% of the absolute value.

The Ca numbers of the investigated steel–slag systems were estimated to be in the range of 1·8–2·4×10⁻³, and therefore, slag entrainment should not appear under these conditions.

Figure 2.

Drolet separation from upper liquid by increasing Ca number via increasing velocity near interface, a throught c deformation of interface due to increasing rotation rate of the roller, d droplet detachment at critical rotation rate

Footnotes

Acknowledgements

Parts of this research were supported by the DFG (German Research Foundation) research funding organisation under project no. 051201019. This is gratefully acknowledged. The author also wishes to thank Mr D. Dorogokuplia for performing the measurements.

This article is part of a special issue on: Sustainable high temperature metallurgical processes and engineering materials recycling techniques

References

Zhang

Thomas

: ‘State of the art in evaluation and control of steel cleanliness’, ISIJ Int., 2003, 43, 271–291.

Park

: ‘Thermodynamic investigation on the formation of inclusions containing MgAl₂O₄ spinel during 16Cr–Ni austenitic stainless steel manufacturing process’, Mater. Sci. Eng. A, 2008, 472, 43–51.

Savolainen

Fabritius

Mattila

: ‘Effect of fluid physical properties on the emulsification’, ISIJ Int., 2009, 49, 26–36.

Janssen

Boon

Agterof

: ‘Influence of dynamic interfacial properties on droplet breakup in simple shear flow’, AIChE J., 1994, 40, 1929–1939.

Rallison

: ‘The deformation of small viscous drops and bubbles in shear flows’, Annu. Rev. Fluid Mech., 1984, 16, 45–66.

Korenko

Simko

: ‘Measurement of interfacial tension in liquid–liquid high-temperature systems’, J. Chem. Eng. Data, 2010, 55, 4561–4573.

Grassmann

: ‘Physikalische grundlagen der verfahrenstechnik’, 3rd edn; 1983, Aarau, Verlag Sauerländer AG.

Hagemann

Scheller

: ‘Slag entrainment in continuous casting process’, Proc. Euromat Conf. on ‘Sustainable high temperature metallurgical processes and engineering materials recycling techniques’, SF2M Société Francaise de Métallurgie et de Matériaux Montpellier, France, September 2011. Paper 2576.

Campbell

: ‘Surface tension measurement by the drop weight technique’, J. Phys. D: Appl. Phys., 1970, 10D, 1499–1504.

10.

Kingery

: ‘Property measurements at high temperatures’; 1959, New York, John Wiley and Sons.

11.

Adamson

: ‘Physical chemistry of surfaces’, 3rd edn; 1976, New York, John Wiley and Sons.

12.

Harkins

Brown

: ‘Determination of surface tension and the weight of falling drops: the surface tension of water and benzene by the capillary height method’, J. Am. Chem. Soc., 1919, 41, 499–523.

13.

Wilkinson

: ‘Extended use of, and comments on, the drop-weight (drop-volume) technique for the determination of surface and interfacial tensions’, J. Colloid Interface Sci., 1972, 40, 14–26.

14.

El-Gammal

Hinds

Schoneberg

: ‘Influence of alloying elements and metalloids on the emulsion and separation behaviour of steel and slag’. Steel Res. Int., 1991, 62, 152–156.

15.

Cajori

: ‘Sir Isaac Newton’s mathematical principles’; 1946, Berkeley, University of California Press.

16.

Gelfand

: ‘Droplet breakup phenomena in flows with velocity lag’, Prog. Energy Combust. Sci., 1996, 22, 202–263.

17.

Scheller

: ‘The interfacial convection and its effect on mass transport and slag emulsification’, Proc. Roderick Guthrie Honorary Symp. on ‘Process metallurgy’, Montreal, Que., Canada, June 2011, McGill Metals Processing Centre, 160–166.

18.

Scheller

Hagemann

: ‘Emulsification of slag in liquid steel caused by the interfacial convection’, Proc. 1st Int. Conf. on ‘High manganese steels’, Research Institute of Iron and Steel Technology, Yonsei University, Seoul, Korea, May 2011. 1–10.

19.

Zhang

Yang

Cai

Wan

Thomas

: ‘Investigation of fluid flow and steel cleanliness in the continuous casting strand’, Metall. Mater. Trans. B: Process Metall. Mater. Process. Sci., 2007, 38B, 63–83.

20.

Sun

Nakashima

Mori

: ‘Influence of slag composition on slag–iron interfacial tension’, ISIJ Int., 2006, 46, 407–412.

21.

Sun

Yoneda

Nakashima

Mori

: Proc. 5th Int. Conf. on ‘Molten slags, fluxes and salts’, Sydney, NSW, Australia, January 1997, ISS, 149–156.

22.

Elfsberg

Matsushita

: ‘Measurements and calculations of interfacial tension between commercial steels and mould flux slags’, Steel Res. Int., 2011, 82, 404–414.

23.

B. J. Keen : ‘Slag atlas’, 2nd edn, 430; 1995, Düsseldorf, Verlag Stahleisen GmbH.

24.

Park

Gaye

Lee

: ‘Interfacial tension between molten iron and CaO–SiO₂–MgO–Al₂O₃–FeO slag system’, Ironmaking Steelmaking, 2009, 36, 3–11.

25.

Sharan

Cramb

: ‘Interfacial tensions of liquid Fe–Ni alloys and stainless steels in contact with CaO–SiO₂–Al₂O₃-based slags at 1550C’, Metall. Mater. Trans. B: Process Metall. Mater. Process. Sci., 1995, 26B, 87–94.

26.

Ribout

Lucas

: ‘Influence of mass transfer upon surface phenomena in iron and steelmaking’, Can. Metall. Q., 1981, 20, 199–208.

27.

Scheller

: ‘Interfacial phenomena between fluxes for continuous casting and liquid stainless steel’, Ironmaking Steelmaking, 2002, 29, 154–160.

28.

B. J. Keen and K. C. Milles : ‘Slag atlas’, 2nd edn, 345; 1995, Düsseldorf, Verlag Stahleisen GmbH.

29.

K. C. Milles : ‘Slag atlas’, 2nd edn, 364, 372, 374; 1995, Düsseldorf, Verlag Stahleisen GmbH.

30.

Miettinen

: ‘Calculation of solidification-related thermophysical properties for steels’, Metall. Mater. Trans. B: Process Metall. Mater. Process. Sci., 1997, 28B, 281–297.

31.

Iida

Guthrie

RIL

: ‘The physical properties of liquid metals’, 168; 1993, Oxford, Clarendon Press.

32.

Gaye

Lucas

Olette

Riboud

: ‘Metal–slag interfacial properties: Equilibrium values and dynamic phenomena’, Can. Metall. Q., 1984, 23, 179–191.

33.

Scheller

: ‘Oxidation and reduction processes in slags during continuous casting of stainless steel’, High Temp. Mater. Processes, 2003, 22, 387–393.

34.

Dauby

: ‘Real flows in continuous casting molds’, Proc. Roderick Guthrie Honorary Symp. on ‘Process metallurgy’, Montreal, Que., Canada, June 2011, McGill Metals Processing Centre. 387–396.

35.

Scheller

: ‘Mass exchange at the metal–slag interface in the continuous casting process’, Proc. Int. Conf. on ‘Molten slags, fluxes and salts VII’, Cape Town, South Africa, January 2004, South Africa Institute of Mining & Metallurgy. 411–416.

36.

Scheller

: ‘Mass exchange at the metal–mould flux interface’, Steel Res. Int., 2010, 81, 886–890.