Viscosity Measurement and Modeling of Borate and Borosilicate Melts

Transcription

1 Viscosity Measurement and Modeling of Borate and Borosilicate Melts Zhijing Zhang, Graduate Student Dr. Ramana G. Reddy, ACIPC Professor Department of Metallurgical and Materials Engineering The University of Alabama Tuscaloosa, AL Presented in TMS Annual Meeting on /8-/4, 999

2 utline! Introduction! Experimental studies Viscosity measurements Investigation on rheological behavior Preparation of samples and Experiment description! Results and discussion! Viscosity model for ternary sodium borosilicate system! Summary! Acknowledgements

3 Introduction! Viscosity of molten oxides is one of the most important physical properties.! nly limited viscosity data of complex molten oxides in literature are available. The agreement between different investigations is not satisfactory.! The present studies are to enhance our fundamental understanding on the viscous behavior of borate and borosilicate melts.

4 Experimental studies! Viscosity measurements on the systems: Na -B Na -Si and Na -Si -B! Investigation on rheological behavior of Na -Si -B melts! Preparation of samples and Experiment description 4

5 Experimental setup Thermocouple + - Viscometer Gas utlet Dimension in mm Ar Gas Experimental Setup Spindle Crucible + - Thermocouple Lindberg Furnace Heating Elements Crucible Support d 6 d.7 d 6.7 d 8. Dimensions of graphite crucible and spindle 5

6 Viscosities of Na -B and Na -Si melts Temperature K B mol% Viscosity Pa.s Temperature K Si mol% Viscosity Pa.s solidified solidified solidified 6

7 Viscosities of Alkali Silicate Melts and Alkali Borate Melts lg viscosity, (Poise) Si Si 4 / Na 4 / + + Na Na Na + + Si Si / / o C o C lg viscosity, (Poise) + B / + M M B/ B/ + M 4 / M + [ B ] + Na, 8 o C Na, 9 o C Li, 8 o C Li, 9 o C K, 8 o C K, 9 o C Na Isothremal viscosities of sodium silicate melts M Isothermal viscosities of alkali borate melts 7

8 Viscosities of Na -Si -B melts Present expt. Nakashima et al. Shiraishi et al B, 6Na Si, K 6B, 4Na 5Si, K 4B, 6Na Si, 7 K log η, Pa.s.. Viscosity, Pa.s 8 6 6B, 4Na 5Si, 7 K Temperature, K Fig. : Viscosity as a function of temperature for Na -4B -4Si melt Shear rate, sec - Fig. : Viscosity as a function of shear rate 8

9 Phase diagram of the system Na -B -Si 9

10 Composite plots of the liquidus in the system Na -B -Si and isothermal viscosities Temperature, o C B Na.4B.8 Na.B Na.B.6 9 o C o C o C Na.B X Si.Na B log η, Pa.s Temperature, o C B.8 9 o C o C o C Na.4B Na.B Na.B Na.B Na.Si Si X.Na B Si /Na = log η, Pa.s Si /Na =.5

11 Composite plots of the liquidus in the system Na -B -Si and isothermal viscosities 4. 9 o C.5 Temperature, o C B.8 Na.4B.6 9 o C o C o C Na.B.Si Na.Si Si X.Na B log η, Pa.s Temperature, o C B.8 o C o C Na.4B Quartz Tridymite X 5Si B.Na Si /Na = log η, Pa.s Si /Na =

12 Viscosity Model! The slipping and sliding of layers of liquid against each other provides the macroscopic explanation of viscosity.! According to the hole model, viscous drag arises from the momentum transferred between moving fluid layers when holes jump from one layer to another.! Based on the hole model and molecular-kinetic theory, Bockris and Reddy presented a viscosity expression as equation (): η = N h R h ( π m k T ) exp E RT ()

13 Viscosity model for ternary sodium borosilicate system! ) Constant term (πmkt) / : ( πm k T ) = ( πw / R) W + WB + Where N is mole fraction of bridging oxygen in the melts.! 4) Calculation of : = N! ) Calculation of R h : h B N k T Si 4+ W ( Rh ) N 4 ( R ) B Si h 4 R = N B Si! ) Calculation of N h : N h N = A V N X = B X = B 6. N N + X Si + X Si n + Si 4 n Where is the number of non bridging oxygen bonded to only one boron or silicon atom, which can be calculated by expression: ( exp( G / RT )) (X B + 4( X + B X ( n Si X Si ) + )( n )(X ) B + X Si ) = Where G is the Gibbs energy of the depolymerization reaction. For sodium borosilicate melts, + o o o G = N G B Na B N G + ( ) 4 + Si ( Na Si )

14 Viscosity model for sodium borosilicate system (cont.)! The calculation of E: The energy of ionic unit for viscous flow is a function of composition and temperature. The value of energy is calculated from the present experimental data by non-linear regression. E = η = (X f ( T, X B, X / Si X Na Si + X! Substituting (πmkt) /,R h,n h, and E into equation [], the following expression can be obtained and the viscosity of sodium borosilicate melts can be calculated. (6.4X B ) Si N + 8.9X T ) N B E exp( ) RT ) (.84X Si ( Pa s) +.77X B ) () 4

15 Comparison of calculated results with measured results calculated viscosities, Pa.s X Si /X Na =.5 X Si /X Na =. X Si /X Na =. X Si /X Na = measured viscosities, Pa.s 5

16 Summary! Viscosities of sodium borates and sodium borosilicate melts are measured.! It is found that the viscosities of borate and borosilicate melts increase or decrease according to the changes in rigidity and spatial connectivity of the glass network.! Based on the present experimental results, a structure based viscosity model has been developed. This viscosity model relates viscosity of sodium borosilicate melts to the degree of polymerization. The calculated results by the present model are in excellent agreement with the experimental data. 6

17 Acknowledgements! ACIPC! The University of Alabama Pyrometallurgy Funds 7