Mineral Matter and Ash in Coal - ACS Publications - American

16 Viscosity of Fluxes for the Continuous Casting of Steel W. L . McCauley and D . Apelian

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Materials Engineering, Drexel University, Philadelphia,PA19104

The effects of composition and temperature on the viscosity of oxide melts suitable for use as casting fluxes is discussed. A relation to express the tem perature dependence of viscosity for oxide melts based on the Clausius-Clapeyron Equation is evaluated, v i z . , lnη = C + C /T + C lnT. This relation produces a better description of the temperature dependence of fused oxides than the more familiar Arrhenius equation. 1

2

3

Mold f l u x e s a r e r o u t i n e l y used i n b o t h c o n t i n u o u s c a s t i n g and bottom pouring of s t e e l . These f l u x e s a r e g e n e r a l l y c a l c i u m s i l i c a t e based c o m p o s i t i o n s w i t h a l k a l i o x i d e s [ ( L i , Na, K ) 0 ] and f l u o r i d e s [ C a F , NaF] added as f l u i d i z e r s . The c o m p o s i t i o n s f r e q u e n t l y use f l y a s h as t h e base m a t e r i a l because i t p r o v i d e s a s i g n i f i c a n t c o n c e n t r a t i o n of s i l i c a i n a p r e f u s e d form e a s i l y d i s s o l v e d as t h e powder m e l t s on the l i q u i d s t e e l . A v a r i e t y o f p r o p e r t i e s o f t h e f l u x must be c o n t r o l l e d , i n c l u d i n g f u s i o n c h a r a c t e r i s t i c s ( f u s i o n temperature range and s i n t e r i n g c h a r a c t e r i s t i c s ) , i n s u l a t i o n c h a r a c t e r i s t i c s , flow p r o p e r t i e s of the powder, v i s c o s i t y o f t h e m o l t e n f l u x , and n o n - m e t a l l i c a b s o r p t i o n ability. The v i s c o s i t y i n f l u e n c e s t h e consumption r a t e o f f l u x , heat t r a n s f e r i n t h e mold, and n o n - m e t a l l i c d i s s o l u t i o n r a t e , and has been the s u b j e c t o f p u b l i s h e d and u n p u b l i s h e d work o v e r t h e l a s t t e n y e a r s . In t h i s p a p e r , r e c e n t work on t h e v i s c o s i t y o f mold f l u x compo s i t i o n s i s r e v i e w e d , and a r e l a t i o n t o d e s c r i b e t h e temperature de pendence o f v i s c o s i t y i s d i s c u s s e d . T h i s r e l a t i o n i s based on t h e C l a u s i u s - C l a p e y r o n E q u a t i o n and was o r i g i n a l l y d e v e l o p e d by K i r c h o f f and Rankine t o d e s c r i b e t h e temperature dependence o f v a p o r p r e s s u r e . 2

2

P r e v i o u s Work S e v e r a l r e c e n t p u b l i c a t i o n s have d i s c u s s e d t h e e f f e c t s o f composi t i o n a l v a r i a b l e s on t h e v i s c o s i t y o f o x i d e m e l t s f o r use as mold fluxes. L a n y i (1) measured t h e v i s c o s i t y o f s e v e r a l c o n t i n u o u s c a s t i n g f l u x e s and found t h a t t h e v i s c o s i t y c o r r e l a t e d w e l l w i t h t h e combined s i l i c a and alumina c o n t e n t o f t h e f l u x . The f l u x e s

0097-6156/ 86/ 0301 -0215506.00/ 0 © 1986 American Chemical Society

Vorres; Mineral Matter and Ash in Coal ACS Symposium Series; American Chemical Society: Washington, DC, 1986.

216

MINERAL MATTER AND ASH IN COAL

e v a l u a t e d c o n t a i n e d 30 t o 55% S i 0 + A 1 0 , 20 t o 45% CaO + MgO, 0 t o 8% FeO, 15 t o 35% R 0 + F, and 0 t o 5% B 0 . The v i s c o s i t y a t 1300°C ranged from 0.06 t o 3.2 Pa*s. L a n y i was a l s o a b l e t o c o r r e l a t e t h e a c t i v a t i o n energy f o r v i s c o u s f l o w i n the A r r h e n i u s E q u a t i o n w i t h the f l u x b a s i c i t y r a t i o and v i s c o s i t y . McCauley and A p e l i a n (2) measured the v i s c o s i t y o f m i x t u r e s con t a i n i n g o n l y S i 0 , A 1 0 , CaO, N a 0 , and C a F , i n an attempt t o i s o l a t e the e f f e c t s o f g l a s s network m o d i f i e r s and network b r e a k e r s i n mold f l u x type c o m p o s i t i o n s . V i s c o s i t y a t 1300°C ranged from 0.1 t o 2.8 Pa»s. T h e i r r e s u l t s showed t h a t the f l u x v i s c o s i t y c o u l d be ex p r e s s e d as a q u a d r a t i c f u n c t i o n o f the r a t i o o f network f o r m i n g c a t i o n s ( s i l i c o n and aluminum) t o a n i o n s (oxygen and f l u o r i n e ) . Riboud, e t a l . (3) examined a s l i g h t l y b r o a d e r range o f c o n t r o l l e d c h e m i s t r i e s than McCauley and A p e l i a n as w e l l as s e v e r a l i n d u s t r i a l f l u x e s s i m i l a r t o t h o s e used by L a n y i . Riboud used t h e Frenkel r e l a t i o n 2

2

2


2

3

2

2

3

2

3

2

η = A Τ exp(B/T)

(1)

to d e s c r i b e b o t h the c o m p o s i t i o n a l and temperature e f f e c t s on v i s c o s i t y , η. I n E q u a t i o n 1, the v i s c o s i t y p a r a m e t e r s , A and B, a r e e x p r e s s e d i n terms o f the c o m p o s i t i o n a l v a l u e s . T h i s r e l a t i o n y i e l d s a p r e d i c t e d v i s c o s i t y w i t h i n 20% o f the measured v a l u e s o v e r a wide c o m p o s i t i o n range. N i c h o l s (4) measured the v i s c o s i t y o f s e v e r a l bottom p o u r i n g f l u x compositions. These f l u x e s c o n t a i n e d o n l y 5 t o 20% a l k a l i o x i d e s and f l u o r i d e s and 50 t o 70% S i 0 + A 1 0 . V i s c o s i t y ranged from 5 t o 80 Pa-s a t 1500°C, much h i g h e r than c o n t i n u o u s c a s t i n g fluxes. A l t h o u g h the c o r r e l a t i o n f a i l s f o r the lower v i s c o s i t y f l u x e s , N i c h o l s a l s o showed good c o r r e l a t i o n f o r v i s c o s i t y w i t h the s i l i c a content. The r e s u l t s i n d i c a t e t h a t , f o r mold f l u x o x i d e c o m p o s i t i o n s , the v i s c o s i t y i s dependent on the q u a n t i t y o f network f o r m i n g o x i d e s p r e s e n t , p r i n c i p a l l y s i l i c a and a l u m i n a . T h i s i s demonstrated by the r e s u l t s o f McCauley (2) i n F i g u r e 1. In t h i s c a s e , i t i s the r a t i o of network f o r m i n g i o n s t o t o t a l a n i o n c o n c e n t r a t i o n . However, as shown i n F i g u r e 2, the v i s c o s i t y / r e c i p r o c a l temperature r e l a t i o n s h i p i s not l i n e a r and cannot be a d e q u a t e l y r e p r e s e n t e d by the A r r h e n i u s E q u a t i o n over a wide temperature range. 2

2

3

V i s c o s i t y v s . Temperature V i s c o s i t y can be c o n s i d e r e d as a measure o f the ease o f movement o f molecules i n a l i q u i d undergoing shear. S e v e r a l f a c t o r s may i n f l u ence t h i s ease o f movement i n c l u d i n g m o l e c u l e s i z e and i n t e r m o l e c u l a r a t t r a c t i o n , but a major f a c t o r i s the amount o f space a v a i l a b l e between the m o l e c u l e s , hence, the v a r i e t y o f models i n c o r p o r a t i n g a f r e e volume term. The C l a u s i u s - C l a p e y r o n e q u a t i o n r e l a t e s p r e s s u r e w i t h tempera t u r e , e n t h a l p y , and volume, and has been used t o d e v e l o p semit h e o r e t i c a l e x p r e s s i o n s o f vapor p r e s s u r e 05). Many p r o p e r t i e s , i n c l u d i n g v i s c o s i t y , can be r e l a t e d t o an energy b a r r i e r , f r e e volume and temperature. The attempt h e r e i s t o e x p r e s s v i s c o s i t y i n the form o f the C l a u s i u s - C l a p e y r o n e q u a t i o n .


Viscosity of Casting


MCCAULEY AND APELIAN

0

L_LL_I

I

Q29

0.27

I

I

1

0.31

0.33

1

Fluxes

1

1

1

0.35

1

ί 0 39

0.37

Κι

F i g u r e 1. V i s c o s i t y a t 1500°C as a f u n c t i o n o f network ions f o r the f l u x e s i n Table I .

1500

1400

ι

1

ι

5.5

6.0

TEMPERATURE C C ) 1300 1200

1

MOO

1

6.5

forming

1 — I

7.0

73

RECIPROCAL TEMPERATURE (κ'κΚΓ ) 4

F i g u r e 2. T y p i c a l v i s c o s i t y r e s u l t s v s . r e c i p r o c a l f o r some o f t h e f l u x e s l i s t e d i n T a b l e I .

temperature


218


The dP dT

C l a u s i u s - C l a p e y r o n e q u a t i o n can be w r i t t e n ΔΗ TAV

=

=

AH T(V-V )

(2)

0


where Ρ, T, and ΔΗ have t h e i r u s u a l meaning. F o r t h i s d i s c u s s i o n , Δν i s a measure o f f r e e volume o r t h e d i f f e r e n c e between t h e volume a t temperature and t h e volume a t some s t a n d a r d s t a t e , e.g., a t abso l u t e z e r o o r s o l i d volume a t t h e m e l t i n g p o i n t . E q u a t i o n 2 can be r e w r i t t e n as d(l,nP) d(l/T)

=

AH RAz

m V

;

where Δζ = PV/RT - PV /RT Q

Expanding ΔΗ t o t h e s e r i e s form and i n t e g r a t i n g w i t h r e s p e c t t o 1/T yields £nP = I

[ a - ^ψ- + b£nT + dT + |τ

2

+....

J

(4)

I f t h e h i g h e r o r d e r terms a r e i g n o r e d , t h e e x p r e s s i o n reduces t o

£nP = A - γ + C£nT

(5)

Such a d e r i v a t i o n was o r i g i n a l l y developed and used by K i r c h o f f [1858] and Rankine [1849] (5) t o e x p r e s s t h e temperature dependence of v a p o r p r e s s u r e . I t was a l s o s u c c e s s f u l l y used by Brostow (6) t o e x p r e s s the temperature dependence o f t h e i s o t h e r m a l c o m p r e s s i b i l i t y o f a wide v a r i e t y o f o r g a n i c l i q u i d s , some m e t a l l i c l i q u i d s and water. By a s i m i l a r a n a l o g y , we have used i t t o e x p r e s s t h e v i s c o s i t y o f l i q u i d mold f l u x e s . Regression A n a l y s i s The v i s c o s i t y o f twenty f l u x c o m p o s i t i o n s determined e a r l i e r (2) were used t o e v a l u a t e t h e K i r c h o f f - R a n k i n e E q u a t i o n . The composi t i o n s o f t h e s e f l u x e s a r e g i v e n i n T a b l e I w i t h a summary o f t h e v i s c o s i t i e s g i v e n i n T a b l e I I . The f l u x v i s c o s i t y d a t a was f i t t e d to t h e K i r c h o f f - R a n k i n e e q u a t i o n as

and

Q η = e x p ( C ! + -y

+ C £nT)

to the Arrhenius

Equation

(6)

3

η = A exp(E/RT) u s i n g t h e Marquardt method o f n o n - l i n e a r l e a s t squares the S t a t i s t i c a l A n a l y s i s Systems [SAS] program package r e s u l t s o f the r e g r e s s i o n are given i n Table I I I , with d e v i a t i o n and an average d i f f e r e n c e between c a l c u l a t e d values.

(7) regression i n (7_) . The the standard and measured



34.8 34.4 34.5 34.6 34.6 34.7 26.7 30.7 31.2 35.2 33.5 38.8 41.9 48.0 46.8 30.6 30.0 39.6 32.4 39.1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2

Si0

Flux

10.2 9.8 10.0 10.1 10.3 10.1 9.8 8.9 10.4 10.3 10.4 10.4 10.6 10.6 10.4 10.0 10.2 10.4 10.4 10.4

2

A1 0 3

CaO 7.6 8.4 7.6 7.8 8.0 7.2 11.7 2.3 7.6 3.3 11.5 3.5 7.8 3.3 5.5 7.0 8.2 4.7 11.7 1.7

2

10.7 10.9 11.0 10.8 10.9 10.8 14.4 12.9 5.7 5.7 15.1 15.1 6.8 6.5 10.7 10.3 18.6 4.0 10.8 11.3

2

CaF 0.9 0.7 0.7 0.6 0.7 0.6 0.6 0.7 0.8 0.9 0.5 0.7 0.7 0.8 0.6 1.0 0.8 1.0 0.7 0.9

MgO

Fluxes - F r i t

Na 0

Experimental

32.7 32.1 32.7 32.5 32.3 33.0 31.8 32.6 40.3 40.8 24.9 26.2 29.5 28.6 22.2 36.2 27.8 35.7 30.4 32.6

Table I.

0.6 0.6 0.7 0.6 0.5 0.6 1.9 8.8 0.7 0.8 0.4 0.9 0.9 1.4 2.7 2.1 1.6 1.3 1.1 1.2

Zr0 2

Composition,

97.5 96.9 97.2 97.0 97.3 97.0 96.9 96.9 96.7 97.0 96.3 95.6 98.2 99.2 98.9 97.2 97.2 96.7 97.5 97.2

Total

wt%


0.94 0.93 0.95 0.94 0.93 0.95 1.19 1.06 1.29 1.16 0.77 0.67 0.77 0.60 0.47 1.18 0.93 0.90 0.94 0.83

V-ratio


220


Table I I .

Flux

V i s c o s i t y at 1300°C, Ns π Γ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.395 0.310 0.340 0.485 0.290 0.510 0.110 NA* 0.280 6.00 0.270 0.930 1.15 2.80 2.40 7.00 0.160 1.40 0.250 1.40

*Not

2

Summary o f F l u x V i s c o s i t i e s Viscosity at 1400°C, Ns π Γ

2

Viscosity at 1500°C, Ns n f

2

0.135 0.112 0.128 0.125 0.088 0.122 0.035 NA* 0.080 0.180 0.114 0.270 0.280 0.710 0.725 0.090 0.059 0.380 0.094 0.410

0.230 0.175 0.205 0.235 0.190 0.230 0.065 NA* 0.160 0.360 0.150 0.460 0.530 1.30 1.30 0.170 0.115 0.670 0.130 0.720

available

In some c a s e s , v i z . , F l u x e s 5, 6 and 13 i n T a b l e I I I , t h e s i g n s o f t h e c o e f f i c i e n t s a r e r e v e r s e d , and a concave downward c u r v e i s generated. T h i s i s most l i k e l y caused by t h e r e g r e s s i o n b e i n g t r a p p e d a t a l o c a l minimum i n t h e d a t a and assuming convergence a t that p o i n t . I t i s r e q u i r e d f o r these cases t h a t the s i z e o f the r e g r e s s i o n s t e p s h o u l d be i n c r e a s e d t o a v o i d t h e l o c a l minima, which SAS does n o t a l l o w . A l s o , t h e r e may n o t be enough d a t a p o i n t s t o expand t h e r e g r e s s i o n s t e p as i s p r o b a b l y t r u e f o r F l u x e s 6 and 13. For t h e m a j o r i t y o f f l u x e s e v a l u a t e d , t h e s t a n d a r d d e v i a t i o n , s, and t h e average p e r c e n t v a r i a t i o n , Δ%, i s lower f o r t h e K i r c h o f f Rankine f i t t e d e q u a t i o n v s . t h e A r r h e n i u s E q u a t i o n , i n d i c a t i n g a b e t t e r f i t of the experimental data. The d i f f e r e n c e i s most p r o nounced f o r t h o s e f l u x e s where t h e n o n l i n e a r i t y o f t h e e x p e r i m e n t a l &ηη v s . 1/T d a t a i s g r e a t e s t . Discussion When t h e n o n l i n e a r i t y o f t h e l o g v i s c o s i t y v s . r e c i p r o c a l tempera t u r e d a t a was f i r s t o b s e r v e d , t e s t s were made t o i n s u r e t h a t t h e c u r v a t u r e was r e a l and n o t an a r t i f a c t o f t h e e x p e r i m e n t a l a p p a r a t u s . H y s t e r e s i s c u r v e s and c o n s t a n t temperature f o r extended time t e s t s showed t h a t t h e n o n l i n e a r i t y was n o t caused f ;ovolatilization a l k a l i o r f l u o r i d e c o n s t i t u e n t s o r from t h e r m a l d e v i a t i o n s i n t h e furnace setup. I t was found t h a t t h e o b s e r v e d c u r v a t u r e o f t h e d a t a was n o t an a r t i f a c t and r e p r e s e n t e d t h e t r u e p h y s i c a l b e h a v i o r o f the m a t e r i a l s . The a p p l i c a t i o n o f t h e K i r c h o f f - R a n k i n e e q u a t i o n 0



Δ%

n

tt

ttt

1

8.65E-3 2.66E-2 1.48E-2 1.62E-1

1.43E-2 6.00E-2 5.19E-2 2.26E-1 1.32E-1 _

nexp

ncalc

η exp

χ

1

0

Q

= number o f o b s e r v a t i o n s

=

t

7.03E-3 1.99E-2 8.92E-3 1.82E-2 2.15E-2 2.33E-2 1.31E-2 1.22E-2 _

s

Equation

e(î?exp - n c a l c ) / ( n - l )

2

33783 36304 30095 41748 29493 41814 41439 30736 36000* 32510 45110 40700 48579 40568 30000* 32981 39880 32313 50240

8.831E-6 2.704E-6 2.332E-6 8.016E-7 2.528E-5 8.079E-7 1.963E-7 1.496E-5 7.5E-3 7.820E-6 4.828E-7 2.661E-6 5.488E-8 5.761E-6 2.0E-2 5.469E-6 4.126E-6 7.393E-6 1.493E-7

1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20

=

(cal/mole)

(Pa s)

Flux

t

Ε

Andrade-Arrhenius

A

Table

5.05 3.01 7.39 16.46

-

2

51341 68183 47516 71633 -10764 -5309 297516 321853 1735752 63473 62253 -13879 212141 60668 8456727 105664 56382 85334 116706

C 3

20.502 32.337 20.792 31.502 -17.290 -16.447 179.394 192.942 1019.0 31.935 27.155 -21.843 116.012 26.660 5071.8 56.221 22.457 43.656 60.246

c

Kirchoff-Rankine

Analysis Results

-184.35 -282.59 -184.30 -278.11 132.94 123.80 -1511.91 -1626.10 -8603.16 -276.14 -239.51 169.80 -987.72 -233.90 -42701.6 -483.18 -200.79 -377.12 -517.30

Ci

Regression

3.15 2.95 4.69 13.00 5.57

-

2.40 7.98 2.08 2.73 4.14 5.41 7.01 3.15

III.

6.36E-3 1.27E-2 5.68E-3 1.67E-2 2.10E-2 2.29E-2 5.72E-3 1.11E-2 2.83E-2 5.81E-3 3.35E-2 5.00E-2 9.85E-2 6.26E-2 8.69E-2 1.60E-3 1.66E-2 8.69E-3 5.32E-2

s

Equation


*

n 12 6 6 6 14 7 5 6 18 7 12 8 11 10 17 5 6 7 8

ttt

estimated

1.94 3.47 1.42 3.20 3.91 5.68 3.91 3.62 3.97 1.52 1.10 3.89 5.30 3.07 15.8 0.84 1.84 4.89 4.46

Δ%

222


produced a more accurate description of the temperature dependence of viscosity. Additional work on liquid metals, simple chloride salts and some small molecule organic liquids (8) indicates that the advantage of the Kirchoff-Rankine equation over the Andrade-Arrhenius equation improves as the size of the melt species increases. The improvement in the description of viscosity vs. temperature for metals and simple salts (e.g., NaCl and BiCl ) is not great, but for materials with larger melt species (e.g., silicate melts and organic liquids), there is a distinct improvement. 2


Summary The evaluation of the viscosity of mold fluxes has shown that the viscosity is primarily controlled by the concentration of network forming oxides, particularly the s i l i c a content. It has also been demonstrated that the temperature dependence of viscosity can be expressed by the relation, £ηη = C + C /T + C £nT, derived from the Clausius-Clapeyron Equation. This relation produces a better de scription of viscosity vs. temperature than the more familiar Arrhenius Equation. x

2

3

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8.

Lanyi, M. D. M.S. Thesis, University of Cincinnati, 1980. McCauley, W. L.; Apelian, D. Canadian Metallurgical Quarterly, 1984, 20, 247-262. Riboud, P. V.; Roux, Y . ; Lucas, L. D.; Gaye, H. Fach. Huttenpraxis Metalveiterverarbeitung 1981, 19, 1-8. Nichols, M. W.; Lingras, A. P.; Apelian, D. 2nd Int. Sym. on Metallurgical Slags and Fluxes, Fine, Η. Α.; Gaskell, D. R.; Eds.; TMS-AIME, 1984, pp. 235-251. G. W. Thomson, Chemical Review, 1946, 38, 1-39. W. Brostow and P. Maynadier, High Temperature Science, 1979, 11, 7-21. SAS User's Guide, SAS Institute, Inc., Cary, North Carolina, 1979. McCauley, W. L.; Apelian, D. 2nd Int. Sym. on Metallurgical Slags and Fluxes, Fine, Η. Α.; Gaskell, D. R.; Eds.; TMS-AIME, 1984, pp. 925-947.

RECEIVED August 5, 1985


Mineral Matter and Ash in Coal - ACS Publications - American

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