MODELLING OF SURFACE PROPERTIES OF OXIDE MELTS WITH VARIABLE BASICITY

Transcription

1 , rno, Czech Republc, EU MODELLING OF URFACE PROPERTIE OF OXIDE MELT WITH VARIALE AICITY lve VITÁKOVÁ a, Rostslav DUDEK a, Jana DOROVKÁ a a Faculty of Metallurgy and Materals Engneerng, V Techncal Unversty of Ostrava, 7.lstopadu 5, 708, Czech Republc slve.vtaskova@vsb.cz, rostslav.dudek@vsb.cz, jana.dobrovska@vsb.cz Abstract The subject of ths work s the comparson of numercally obtaned values of surface tenson usng dfferent types of models and epermentally measured data of surface tenson of ode systems. The ternary system of CaO-Al O -O, whch presents smplfed base of the castng powders used n technologcal process, was submtted to the eperment. For mathematc calculaton of surface tenson the sem emprcal models resultng from utler s equaton and Chou model were evaluated as sutable. Further the functonalty of emprc model based on theory of regular onc soluton was tested. Due to hgh rate of unversalty the model utlzng the utler s equaton can be etended n the poly-component systems. Chou model represents model that enables the calculaton of wde spectrum of the ternary systems physcalchemcal propertes. The results of smulaton were compared wth epermentally obtaned values of surface tenson. Wth regard to relatvely hgher temperatures of measurement and character of ternary system a sessle drop method was chosen as optmal method for obtanng epermental data. The changes of temperature dependences of surface tenson of concentraton lne wth growng content of the component O were studed by usng ths method. Keywords: surface tenson, molten slag, mathematcal modellng. INTRODUCTION urface tenson of molten slag systems s mportant physcal-chemcal property, whch s drectly related to technologcal processes n steelmakng [,, ]. It s not always possble to fnd the relevant data on surface tenson of molten slag systems, snce these are poly-component odc-fluorde systems and epermental research s hghly demandng and lmted n great etent by the necessty to work under hgh temperatures. That s why modellng studes play n ths area such an mportant role. In spte of the fact that lately numerous models dealng wth numerc calculatons of surface tenson have been developed, they steel struggle wth the problem of dsagreement of epermentally obtaned data wth calculated values due to complety of processes runnng between slag and metal, and also due to character of slag systems. The submtted work deals wth verfcaton of functonalty of three mathematcal models for calculaton of surface tenson n the system CaO-Al O -O wth varous degrees of bascty.. EXPERIMENT Ternary system CaO-Al O -O, whch represents a smplfed bass of castng powders used n technologcal practce, was chosen for presentaton of results. A concentraton lne wth ncrements of wt. % of O was created for ths system. Its chemcal composton s gven n table. Verfcaton of functonalty of mathematcal models an epermental measurement of surface tenson by sessle drop technque was realsed [].

2 , rno, Czech Republc, EU Tab. : Chemcal composton of concentraton lne O (wt%) CaO (wt%) Al O (wt%) wt% O wt% O wt% O wt% O wt% O MATHEMATICAL MODELLING. Modfed utler s equaton usng onc dstances of components Tanaka et al. [5], developed a model for determnaton of surface tenson of molten odc systems, based on the utler s equaton and on the procedure proposed by peser et al. [6]. They epressed the modfed utler s equaton by on dstances of pure odes partcpatng n the system n the followng manner: O O O RT D σ = σo + ln () A D RT D CaO σ = σcao + ln () ACaO D CaO AlO Al O Al O RT D σ = σalo + ln () A D where N d N d O O D = O O D = O N O d N d () N = CaO d D CaO CaO N d NCaO dcao D CaO = (5) N d D Al O N = Al O d N d Al O D Al O N d Al O Al O = N d (6) σ s calculated the surface tenson [mn/m], σ s the surface tenson of the pure molten component [mn/m], R s the gas constant [J.K -.mol - ], d T s onc dstance of the component n the surface phase and n the bulk phase [m], s the absolute temperature [K], N, s the mole fracton of the component n phase P, A s the molar surface area n monolayer of pure molten component [m.mol - ]. Indvdual nput data were taken from the works [5] and [7].

3 , rno, Czech Republc, EU. Chou model Ths geometrc model [8, 9] enables calculaton of surface tenson of lqud phase of ternary system wth lmted area of solublty, wth use of equlateral trangle. It s based on the followng basc relaton: σ = W σ + W σ + W σ (7) where A A C C W A O C = (8) A C W OC A = (9) A C W C OA = (0) A C A A A A C = () C C C O O O O C = () C C C O O O C C C OC A = () A A A O O O A A A OA = () where σ s the surface tenson of the ternary system solved n the pont O [mnm - ], σ s the surface tenson of the pont [mnm - ], W s the probablty weght of the ponts A,, C, j s mass fracton of the component. asc procedure of soluton of equatons (7) to () was descrbed n detal n the prevous work [0]:. Model of regular soluton Author Kozheurov has ntroduced the theory of regular on solutons. He deduced wth use of methods of statstc thermodynamcs a model of regular on soluton frst for the systems wth a sngle common on [], and later also for the systems wth general number of ons [] wth applcaton for metallurgcal slags. Ths emprc model s based on the followng equaton: σ (5) = X cσc + X Aσ A + Xσ + X cσ AQc A + X cσqc + X AσQ A where σ s surface tenson of pure odes [mnm - ] [5], X s molar fracton, Q -j s surface nteracton parameter [mnm - ], Values of surface nteractons parameters were taken from the lterature [].

4 , rno, Czech Republc, EU. REULT. Modfed utler s equaton usng onc dstances of components In the frst phase of modellng a calculaton of surface tenson for the ternary system CaO Al O O was made wth use of the modfed utler s equaton () - (6). Temperature dependences of surface tenson of the gven addton of wth O ncrements of wt.% and wth the mamum addton of 5wt.% were nvestgated see Fg.. The system of equatons of ths mathematcal model was solved n mathematcal program MATHCAD. Calculaton tself was made by modfed Newton s method. urface tenson [mn/m] T T + wt%o T + 6wt%O T + 9wt%O T + wt%o T + 5wt%O T[ C] Fg. : The temperature dependence of surface tenson of concentraton lne wth addton of O calculated usng a modfed utler s model wth onc dstances of components.. Chou model Fgure presents temperature dependences of surface tenson obtaned by Chou model. Calculaton of surface tenson was made accordng to the relatons (7) (). urface tenson[mn/m] T T + hm%o T + 6hm%O T + 9hm%O T[ C] Fg. : The temperature dependence of surface tenson of concentraton lne wth addton of O calculated usng Chou model.. Model of regular soluton In the last phase of modellng a calculaton of surface tenson of the concentraton lne of the ternary system CaO Al O O was made wth use of emprc model of regular soluton. Fgure shows the obtaned temperature dependences.

5 , rno, Czech Republc, EU surface tenson [mn/m] T T+wt%O T+6wt%O T+9wt%O T+wt%O T+5wt%O T [ C] Fg. : The temperature dependence of surface tenson of concentraton lne wth addton of O calculated usng a model of regular soluton. 5. DICUION AND CONCLUION urface tenson of the concentraton lne of O prepared n laboratory was calculated wth use of three selected mathematcal models. These values were afterwards compared wth the surface tenson data epermentally measured by sessle drop technque. Ths works presents utler s modfed equaton wth use of on dstances of ndvdual components, Chou model and model of regular soluton. Fgure shows evdent decreasng tendency of surface tenson wth an ncreasng content of slcon dode n the utler s modfed equaton. The same tendency of concentraton dependence of surface tenson was repeated also n the Chou model (Fg. ), as well as n emprc model of regular soluton (Fg. ). What concerns behavour of surface tenson wth temperature, the stuaton s qute opposte. Whle n the utler s equaton the surface tenson ncreases wth temperature, n the Chou model and n the model of regular soluton the tendency of temperature dependence s decreasng. Fgure presents comparson of the values of surface tenson calculated numercally by mathematcal models wth the results obtaned from eperments. The best concordance rate was found n the Chou model. Ths model provdes very good results wth a mean devaton from the measured values of %. In case of the utler s modfed equaton the mean devaton was 5%. Model of regular soluton had the bggest mean devaton from the epermental values,.e. appro. 0%. urface tenson [mn/m] T ep. T utler model T Chou model T Model R T [ C] Fg. : Comparson of epermentally obtaned surface tenson values wth calculated data usng the above models.

6 , rno, Czech Republc, EU It s therefore possble to summarse the obtaned results n the followng manner: utler s modfed equaton wth use of on dstances and model of regular soluton can be used, due to comparatvely bg devatons from the measured values, only for an estmaton of ndcatve, values of surface tenson of the order of magntude. The Chou model was found to be sutable for calculaton of surface tenson of the ternary system CaO-Al O -O. A mean devaton of % was determned at comparson of calculated and epermentally obtaned values. ACKNOWLEDGEMENT The work was carred out n the scope of the project of the Czech cence Foundaton (06/09/070) and of the student s project enttled elected studes of heterogeneous systems, and t was fnanced from the specfc research resources of the Faculty of Metallurgy and Materals Engneerng, V-Techncal Unversty of Ostrava, Czech Republc. LITERATURE [] METANA,., et al. Applcaton of Hgh Temperature DTA Technque to Fe ased ystems. From Conference Proceedngs METAL 00: Proceedngs of 9th Internatonal Metallurgcal and Materals Conference. Ostrava: TANGER, 00, p [] ZLÁ,., et al. Dfferental Thermal Analyss and Phase Analyss of Nckel ased uper-alloy IN 78LC. From Conference Proceedngs METAL 00: Proceedngs of 9th Internatonal Metallurgcal and Materals Conference. Ostrava: TANGER, 00, p [] ŽALUDOVÁ, M., et al. tudy of Temperatures of Phase Transformatons of Fe-ased Metallc ystems n the Temperature Range elow 000 C. From Conference Proceedngs METAL 00: Proceedngs of 9th Internatonal Metallurgcal and Materals Conference. Ostrava: TANGER, 00, p [] DUDEK, R.,et al., Modfcaton of the method of a lyng drop appled on norganc melts. Proceesngs of 7th Internatonal Metallurgcal and Materals Conference, METAL 008 [CD-ROM]. Hradec nad Moravcí: Tanger spol s.r.o., 008, p. 6. [5] TANAKA T., HARA,.: Applcaton of thermodynamc databases to evaluaton of nterfacal tenson between lqud steels and molten slags. Zetschrft für Metallkunde, 999, vol. 90, no. 5, p [6] PEIER, R., POIRIER, D.R., K. Yeum, cr. Metall., (987), 687. [7] CHOI, J.-Y., LEE, H.-G. Thermodynamc Evaluaton of the urface Tenson of Molten CaO-O -Al O Ternary lag. IIJ Internatonal. 00, vol., no., p. -8, IN [8] WANG, L.-J., CHOU, K.-CH., CHEN,., CHANG, Y., A.: Estmatng ternary surface penson for systems wth lmted solublty. Zetschrft für Metallkunde, 005, vol. 96, no.8, p [9] CHOU, K.-CH., ZHONG, X., XU, K.: Calculaton of physcochemcal propertes n ternary system wth mscblty gap. Metallurgcal and materals transactons, 00, vol. 5, p [0] VITÁKOVÁ,., DUDEK, R., DOROVKÁ, J., tudy and smulaton of ode melts surface propertes. From Conference Proceedngs METAL 00: Proceedngs of 9th Internatonal Metallurgcal and Materals Conference. Ostrava: TANGER, 00, p [] KOŽEUROV, V.A., Termodnamka metallurgčeskch šlakov, Metallurgzdat, 955. [] KOŽEUROV, V.A., Termodnamka a strojenje rastvorov, IAN R, Moskva 959. [] OCHŇÁK R., DOROVKÝ L., Povrchová adsorpce O v tavennách soustavy CaO Al O O. Kovové materály, ratslava 989, vol. 7, no. 6, p