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Marangoni effect in refractory slag line dissolution
Y. Chen McMaster University 1280 Main Sf. West Hami/ton, ON, L8S 4L7
G. Brooks CS1RO Minerals Box 3} 2 Clay/on South, Vi 3169 Melbourne, Australia
S. Nightingale Materials Engineering University ofWollongong Wollongong, Australia 2522
K. Coley & M. Hamed McMaster University J 280 Main Sf. West Hamilton, ON, L8S 4L7
ABSTRACT
513
The Marangoni effect plays a significant role in slag line corrosion of refractories. Previous experimental studies for various refractory Islag systems and mathematical models are reviewed and show that Marangoni flow is important in stag line corrosion under static conditions. Recent work by the authors is presented which also shows significant slag-line corrosion of MgO refractory in Si02-CaO-FeOx-MgO slag. The rate of attack of the MgO was marginally slower in the case of slags containing alumina. A semi-empirical model developed by Erma ba<;ed on mass transfer control described reasonably well the observed progression of corrosion with time. Further work is proposed to evaluate this modeL
Advances in R~rractoric.'l for the MdallurgicDllndu.~trie,1 IV Fourth Internatiunal Sympusium
43'" Annual Confcrcnce or Meral lurgists of elM Hamolto!1, OrH;lrlO, Cana<la
fOditcd by M. Rig. ud nnd C. Allaire
514 FOURTH INTERN A nONAL SYMPOSIUM
INTRODUCTION
It is well known that refractories are dissolved locally at the slag~gas and sJagmetal interface in glass and steelmaking technologies. The local dissolution of refractories is a serious problem for many industries because it limits the life of the refractories. (11) Severa] researches have proposed that the local dissolution of solid oxide by molten slag is caused by interfacial motion of the molten slag induced by the Marangoni effect in the vicinity of the interface. (1,2,3)
The dissolved anion or cation species from the oxide ceramic wall may dissolve at the liquid phase interface, increasing or decreasing local interfacial tension gradients causing Marangoni flow. The direction of flow depends on whether the interfacial tension is increased or decreased . The dis~olved species, in the melt adjacent to the vertical wall, will change the physical properties of the melt. In particular the local melt density will be changed, thereby leading to buoyancy flows driven by density gradient. If there is no forced convection, e.g., caused by agitation or rotation, the relative strength and interactions between these basic flow types will determine the rate of refractory dissolution and the shape of the corrosion profile. (l,2)
In order to understand, and furthermore, quantify the role of Marangoni flow in ~Iag line corrosion, this paper will examine previous experi.mental studies and mathematical models. Current experimental work performed by the authors will be described and data obtained evaluated using a mathematical model .
REVIEW OF PREVIOUS EXPERIMENTAL STUDIES
Several previous experimcntal (1,3,6) S1udies have been reported in the literature. These studies were mainly based on SiOl a~ the refractory or SiC, which required oxidation to Si02 before dissolving into the slag. The slags used can be classified into two groups: surface tension increasing with dissolved refractory: such as PbO~Si02, PbPhO-Si02, and surface tension decreasing with dissolved refractory: such as FeO-Si02,
NaO-SiOl , and CaO~Si02-Ah03 . It was found that in both systems under static conditions, significant slag line corrosion could be observed.
Mukai (l,3) has made several investigations of the Marangoni effect in refractory slag line corrosion and proposed the mechanisms of slag Jine corrosion in both slag surface tension increasing with dissolved refractory and slag surface tension decreasing with dissolved refractory. The detailed descriptions were given as following: (1, 3)
In the solid silica Si02(s)-(PbO-Si02) slag system, the slag surface tension is increased by dissolved Si02. The flow patterns principally composed of wide zones of rising film and narrow zones of falling film, according to the contour of the specimen, as shown in Figur<:: 1. In the case of a cylindrical specimen, the position of the falling zone moves gradually on the surface of the specimen. However, the prism specimen always
ADVANCES IN REFRACTORlES FOR THE METALLURGICAL INDUSTRIES 515
has one zone of rising film at, and around, each corner of the specimen and one narrow zone of falling film at each plane side of the specimen, as shown in Figure! .(3)
Mukai (3) proposed that since contact time of the upper film with the specimen is longer than that for the lower film, the upper film has a higher Si02 content, due to tbe dissolution of Si02 from the specimen into the film. The differences in SiOl content cause a surface tension gradient in the vertical direction. Since the surface tension of a PbO-Si02 slag increases with increasing Si02 content, the slag film is continuously pulled up by the surface tension gradient. When the weight of the risen slag exceeds the surface tension gradient, the falling film is formed. The degradation rate is controlled by mass transport of the dissolved component Si02 in the slag film under Marangoni flow of the film. So the local degradation proceeds largely as a result of the wall-washing of solid silica with a fresh thin, rising slag film induced by the Marangoni effect. (3)
Sp~cime"
'II' \ f V "I~ ...... j
I I 1 I II
~ \, II ( ('
Bulk slag BuDr slog
Figure 1 - Typical flow pattern of slag film on a cylindrical and prism silica specimen immersed in PbO-Si02 slag (3)
Dissolution of silica
Specimen
Slag
rigurc 2 - Marangoni flow in PeO-Si02 slag film on silica specimen due to concentration gradient of Si02 dissolved from the specimen (3)
In the solid silica Si02(s)-(FeO-Si02) slag system, Si02 reduces the surface tension of the slag. The local degradation zone of this system fonns a steep groove and the vertical width of the local degradation zone is narrower than that of the Si02(s)-(PbOSi02) slag system. In this system, the Si02 content in the upper part of the slag film
516 FOURTH INTERNATIONAL SYMPOSIUM
surface is higher than in the lower part of the surface, SiO, content also decreases with distance from the specimen. Thus, by reducing the Si02 concentration in the slag, the surface tension far away from the specimen is higher than surface tension near the specimen, the slag film pulls away by surface tension gradient from the specimen a<; shown in Figure 2.
Stirring studies were carried by Fagerlund and Sun (6) comparing the refractory corrosion rate caused by Marangoni flow. At the high rotation speed, the necking effect, which caused by Maragoni effect, disappeared. The critical rotation speed was defined as the speed at which, the visible necking effect seemed to disappear. Rotation experiments were also conducted by Mukai. (3) The magnitude of the Marangoni effect was found to be significant under stagnant conditions, but was dominated by bulk flow when the linear velocity of the flowing melt reached values in the range of 0.09-0.16 mfs. (3) Both stirring experiments implied that in highly agitated vessels, the Marangoni effect may not be a predominant cause refractory wear at the slag line. (],6)
Monghan and Nightingale conducted stirring studies of dissolution of MgO refractory in CaO-Si02 slag under forced convection. It showed that the rate of dissolution was controlled by mass transfer at speeds up to about 600 rpm, beyond which chemical reaction rate appeared to become dominant. (10)
This studies show that the Marangoni effect plays an important role in refractory degradation process and the slag line corrosion mechanisms for different refractory/slag systems have been proposed. But there is little quantifiable analysis available on how Marangoni flows affect the refractory degradation.
MATHEMATICAL MODELS
Some mathematical studies have been performed and models developed to quantify the corrosion of refractory due to the Marangoni effect. (7,8) The following discussion will examine existing models.
Hrma Model (7)
Hrma (7) studied the dissolution rate governed by surface free convection caused by a surface tension gradient, as presented schematically in Figure 3. The dissolution occurs at the meniscus of the solid. The formulations are based on following assumptions:
1. The dissolved solid should not be surface active. So that, ncar to the solid surface, the concentration of dissolved solid remains saturated, the interfacial tension gradient is continuously kept at a high level.
ADVANCES 1N REFRACTORffiS FOR THE METALLURGICAL INDUSTRIES 517
2. The density driven free convection is not too intensive compared to the surface tension flows since the dissolution governed by the surface free convection could not be brought about if the density free convection should become predominant.
3. The dissolution of the solid in liquid and the transfer of dissolved materials across the phase boundary are faster than the diffusion transfer from the bOlmdary to the bulk. Thus the dissolution process is diffusion controlled, not reaction controlled; hence, at the boundary, the solution is saturated.
4. The contact angles between solids and their saturated solutions are low. "Inercfore, when the corrosion groove or cavity is fully developed, the solid-liquid and liquid-gas interface in the meniscus are nearly parallel.
5. The liquid in this meniscus thus fonns only a thin layer and the dissolution of the solid in the meniscus area is essentially into a thin liquid layer.
rigure 3 - The cross section of the corrosion cavity and groove for flux-line and upward drilling, I . solid, 2. liquid, 3. gaseous pha~e (7)
A semi-empirical mathematical model was developed based on this material balance. Since the transfer of solute by diffusion along the meniscus may he neglected, the mass balance of solute at steady state can be expressed as follows:
d JY 8c - cv dy ,. D (- -) = 0 Ix 0 x n ~ y~O
{ Il uy (1)
where XI] is the distance measured along the solid-liquid interface, v" is the velocilY component directed along XI} . Do is the diffusion coefficient of the ~;olute in solvent for the concentration at the interface, C is the concentration and y is the distance from
518 FOURTH INTERNATIONAL SYMPOSIUM
interface measured in the direction of the normal, Y is the thickness of the liquid layer in the meniscus.
The relationship between the rate of dissolution Us and the mass flux density at the interface j o .
. _ _ D (ae) -,,, - PI P By y~O' (2)
is given by:
(3)
where PI is the density of dissolving solid.
Eliminating the meniscus thickness Y and reorganizing Equation 1 and 2, the dissolution rate u, was given as: (7)
(4)
Where B is a constant, LIe is the difference between concentration at the solid-liquid interface and concentration of the bulk, Llcr"=LlaI rr (Llo- is the surface tension difference between solid-liquid interface, (J" is the surface tension of bulk), and v is kinematic viscosity.
The parameter B in this equation is a function of the velocity and concentration distributions in the meniscus and also the geometrical shape of both interfaces building up the meniscus. Hrma used two methods to calculate the constant B: a theoretical method and an experimental method. The theoretical method calculates B by using various velocities, concentration distributions and corrosion profiles. B can be calculated between to be O.2~0.4. (7)
Hrma used the following systems to validate the model: sodium nitrite-methanol and a-naphthol-octano!. The rate of dissolution governed by sUlface free convection has been measured in the flux-line at 20°C. The time dependence of the change in diameter at the flux line is shown in Figure 4. The rates of dissolution u., were found from the slopes of the linear parts of the curves. So the material constants and the rates of dissolution were available and the values of B could be calculated from Equation 4. Using this experimental method, Hrma suggested B should in the range O.3~0.4. (7)
ADVANCES TN REFRACTORIES FOR THE METALLURGICAL INDUSTRIES 519
L, em
t, sec Figure 4 - Time dependence of dissolution of (I) a-naphthol-octano! and (2) sodiwn nitrite in methanol; the linear loss was measured at thc flux-line (7)
Thc Hrma model considered the effects of surface tension gradients, contact angle and wetting behavior in slag line corrosion. However, there are some significant weaknesses in this model. First, the model assumed a regular geometry. In experimental conditions, the geometry is not regular. The variation from the regular geometry should be included to develop a more accurate model. Secondly, this model uses a constant B, but an accurate B value is difficult to obtain. Thirdly, it is assumed that surface tension has a linear relationship with concentration, but the relationship between surface tension and concentration is complex and not linear. Accurate surface tension data for slag is difficult to obtain, which will affect the accuracy of the model.
Tlfotridis Model (8)
Tsotridis (8) developed a mathematical model focused on predicting the dissolution of a partially immersed vertical crucible wall into a molten substance. The physical situation is presented in Figure 5. Three convection flows were considered in this paper: convection flow caused by a density gradient arising from a temperature gradient, convection flow caused by density gradient arising from a concentration gradient and convection flow due to a surface tension gradient. The problem was be based on the following assumptions:
1. I-leat lost by conduction through thc walls of the crucible, rc~mlts in a temperature gradient in which the melt adjacent to the crucible wall was cooler, and therefore denser, than in the center. This temperature induced density gradient drives convection currents downwards at vertical crucible walls.
520 JiOURTl T INTERNA TlONAL SYMPOSIUM
2. The crucible material was slightly soluble in the melt. Dissolution of the crucible wall in the melt was a diffusion controlled process. Thus the depth and shape of the corrosion depended on number parameters: (l) diffusion coefficient; (2) the saturation concentration of the dissolved material in the melt; and (3) the flow pattern of the molten material, especially the velocity near the wall.
llQuklle~1
1 2
j
I~---v ----1-1 Figure 5 - Schematic representations of the dimensional slot and of the coordinate system.
The problem was formulated by considering the Navier-Stokes equations coupled with the energy and diffusion equations. The velocity field is determined by the equations of motion and energy, where the concentration distribution is determined by the convective diffusion equation, Marangoni number and surface tension were induced to solve the boundary conditions. A two-dimensional transient flow computer program was developed which simultaneously solves the equations of motion and diffusion.(8)
Tsotridis used a numerical method to solve these equations. The distributions of concentration and flow patterns could he obtained from the compute simulations. The shapes of the corrosion profiles were studied for different cases, and different concentration distributions and flow patterns were achieved. (8)
Although Tsotridis model can give predictions of the solid dissolution process, there are some weaknesses in his model. These weaknt:sses limit the application and accuracy of the modeL First, the wetting behavior between liquid and solid is not considered in this model. For a dissolution process, the wetting behavior between liquid and solid is very important. A "wetting" system will have larger corrosion than the noowetting system and is a crucial aspect in the corrosion process. Second, the model assumes that the geometry changes during the corrosion process couJd not change the flow pattern. But the geometry changes will affect the flow patterns, especially the flow patterns near the wall and surface area. Third, the model a<;sumed a flat free surface. Actually, the free surface is not flat but deformed when Marangoni flow forms .
ADVANCES IN RHRACTORfES FOR THE MET ALUJRGICAL INDUSTR(ES 521
RECENT EXPERIMENTAL WORK
An joint experimental program was established at McMaster University and the University of Wollongong to further explore the role of Marangoni flow in rcfmetory dissolution . Results of preliminary experiments are reported in detail elsewhere (9) . A summary of these results is reported in this paper to provide a greater insight in discussing the work reviewed above.
A high temperature dip technique was used to study the Marangoni phenomenon. (9) Cylindrical MgO samples were used to react with CaO-SiOrAbOrMgO-FeOx slags at 1530°(, The slag compositions used arc listed in Table I.
Table I - Slag compositions (wt%)
CaO Si02 AhO) MgO FeOx Slag A 46 46 :1 5 Slag B 36 36 20 3 5
A total of 8 experiments were carried out. Results of wear measurements are summarized in hgure 6. Clear slag-line corrosion was observed in all samples. It was also found that the depth of corrosion increased with time for both slag compositions . The slag with Al20 3 had a lower corrosion rate than slag without AbO}.
froztn slags were ob~erved on the surfaces of all MgO samples . The MgO
concentrations in the slags measured using SEM-EDS are sununarized in Table II . The
MgO concentration in bulk slags was obtained by chemical analysis and found to increase from the initial concentration, which was 3%. MgO concentration in bulk slags
is also summarized in Table III . Figure 7 and figure 8 show the MgO concentration at
the interface and bulk slags, and their relationship with lime.
Table II - wt%MgO in slag as a function of time
Time (min) 15 30 60 90 Slag A at interface 12.7 15 .0 15.2 12.3 Slag B at interface 10.1 14 .4 16.2 12.7
_ ~1I1~~ag ~ __ 4.0 5.4 6.6 8.4 Bulk slag R 3.4 4.1 6.0 7.4
522
90min
60min
~Omin
ISmin
FOURTH INTERNATIONAL SYMPOSIUM
r-----·27.~----; r----'27.5- - --,
90min
(A) slog without AI203 (8) slog with AI203
(All dimensions ore in mm)
Figure 6- Change in diameter of MgO samples as a function of time
18.00
16.00
'{j 14.00 C .g 12,00 f i: 10.00 B I: 8.00
8 6.00 o ~ 4.00
2,00
0.00
... - t ..
-
o
-
! ± ---
.. .- --- -
20 40 60 BO TIme(mln)
• Slag without AI203 at interface ... Slag without Al203 In bulk
!-- -..
-
100
Figure 7 - wt%MgO alumina free in slag as a function of time.
ADVANCES IN REFRACTORIES FOR THE METALLURGICAL INDUSTRIES 523
18.00
16.00
~ 1400 i:" .~ 12.0C
~ "E 10.00 8 '" 8.00 a
(.J o 6.00 01 :i: 4.()0
2.00
0.00
'! 1-- -.-. - _ .
- -!- -
• .... • ...
- --_.
a 20 40 60 80 100 nme(mlnl
• Slag wilh AI203 at interface • Slag with AI203 in bulk
Figure 8 - wt%MgO in slag in 20% alumina slag as a function oftime.
MATHEMATICAL MODEL EVALUATION
Hnna's(7) mathematical model was used to analyze the experiment data. The time dependence of the change in diameter at flux line is shown in Figure 9. By drawing the
slope of the curve, the dissolution rate Us could be found . Table III summarizes the
material constants and the rates of dissolution. These data were used to calculate the
value of B, which is also listed in Table III, B value is in the range 0.35-0.36, which is in
the range of values suggested by Hrma (7).
16 ,------------------------.
E 14 EO -=- 12 -1-----------.. e 10+- ------
i~~~-o "" - -. ---~-----r------I
o 20 40 60 80 100
I(mln)
-+- slag with 20% AI203
___ slag without AI203
Figure 9 - Time dependence of dissolution of MgO-Slag system<;
524 FOURTH mTERNATIONAL SYMPOSIUM
1 fowc:ver there are some weaknesses in applying this model to these results . First, this model was based on regular geometry. From the experimental observation, it was found that the corrosion geometry was not regular. Secondly, this model was ba.<;ed on direct dissolution. Dissolution of MgO in AhO] containing slag can fonn R spinel phase on the MgO sample surface, (9) so it is an indirect dissolution process.
Table II! ~ The properties ofMgO~SJag system (4)
Dem;ity Viscosity Diffusion (g/cmJ) (fiem.sec) coefficient {em'ls} Concentration gradIent
~ 2.74 2.30 5.47x IO·5 0.10 SlagB 2.82 5.00 5.47x I0·s 0.10
Surface tension Surface tension Dissolution (N/m) 
ADVANCES IN REFRACTORIES FOR THE METALLURGICAL INDUSTRIES 525
driven convective flows can explain this phenomenon. For the AhOy Si02-CaO-FeOxMgO slag system, the formation of spinel in AI20 3 containing slag leads to indirect dissolution, (9) which is not considered in Hrma's model. Indirect dissolution one of the possihle reasons that why the B for this slag system is not in the range suggested by Hrma. Further investigation of the effect of AI20 J will be required to prove above the assumption.
Although significant studies have been performed to investigate slag line corrosion, there are some important aspects still unknown, for example, what is effect of temperature on slag line corrosion and what is the effect of refractory grain size. The authors' further work are currently planning based on high temperature experiments, and development of an improved mathematical model based on these experiments.
CONCLUSION
A review of previous experimental studies shows that the Marangoni effect is the main effect re.sponsible for refractory corrosion in static conditions. Recent work in authors ' laboratory on the corrosion of MgO refractory in Si02-CaO-FeOx-MgO and AbOJ-Si02-CaO-FeOx-MgO slagsis also found consistent with previous studies. The Hrma model, based on the assumption that surface tension driven mass transfer controls the dissolution process, provided a reasonable estimate of the rate ofMgO dissolution for direct dissolution, but could not describe well indirect dissolution.
ACKOWLEDGEMENTS
The authors would like to thank Lee Brunckhurst and Ahmed Mosbah; University of Wollongong, Wollongong, Australia; the Australian Research Council; Blucscope Steel Ltd., Australia; and the McMaster Steel Research Center, Canada.
REFERENCE
t. K. Mukai, E. Ikeda and Z. Yu, First International Conference on Processing Materials for Properties, TMS, Hawaii, 1993, p273-276
2. S. Nightingale and G. A. Brooks, Journal of Australian Ceramic Society, 34[2], 2000, p13-38.
3. K. Mukai, Philosophical Transactions of The Royal Society A, 1998, plOI5-1026.
4. Vereio Deutscher Eisenhuttenlcute , Slag Atlas, 1995, Verlag Stahleiscn Gmbh, 0-Dusseldorf.
526 FOURTH lNTERNA TIONAL SYMPOSIUM
5. F. D. Richardson, Canadian Metallurgical Quarterly. 1982, Vol.21, No.2, plll-1\9.
6. K.O.FagerJund and S.Sun, 6th International Conference on Molten Slags, Fluxes and Salts, Stockholm-Helsinki, 2000.
7. P. I-Irrna, Chemical Engineering Science, 1970, Vol.25, P 1679-1688.
8. G. Tsotridis, Journal of Applied Physics, 81(3),1 Feb., 1997, p1231-1243
9. Y. Chen, G. Brooks and S. Nightingale, Slag Line Corrosion of MgO Refractory. submitted to Canadian Metallurgical Quarterly, May 2004
10. B. J. Monaghan, S. A. Nightingale, L. Chen and G. A. Brooks, 71h International Conference on Molten Slags Fluxes and Salts, The south African Institute of Mining and Metallurgy, Cape TOWIl, South African, 2004, pS85-594
II. K. C. Mills and S. Sridhar, 2000 Belton Symposium Proceedings, ISS, Sydney, Australia, 2000, p211-226
