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1. Z. Asuki, Y. Fukanaka, T. Nagase,and Y. Kondo: Met. Tran&, 1974, vol. 5, p. 381. 2. A. W. D. Hillsand A. Paulin: Trans. Sec. C Inst. Min. andMet., 1971, vol. 80, p. 121. 3. R. H. Spitzer, F. S. Manning, and W. O. Philbrook: Trans. TMS-AIME, 1966, vol. 236, p. 726. 4. N. A. Warner: Proc. Aust. Inst. Min. Met., 1964, vol. 210, p. 31. 5. A. W. D. Hills:Heterogeneous Kinetics at Elevated Temperatures, G. R. Belton and W. L. Worrell,eds., p. 449, Plenum Press, New York, 1970. 6. A. W. D. Hills: Chem. Eng. Sci., 1968, vol. 23, p. 297. 7. T. R. Ingrahamand P. Marier: Can. s Chem. Eng., 1963, vol. 41, p. 170. 8. P. Hyatt, I. B. Curler, and M. E. Wadsworth:J. Amer. Ceram. Sac., 1958, vol. 41, p. 70. 9. F. R. Campbell,A. W. D. Hills,and A. Paulin: Chem. Eng. Sci., 1970, vol. 25, p. 929.
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Authors' Reply
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Fig. 1--The variation with time of the fractional mass of d e composing calcium carbonates spheres plotted as the cube of the fractional reaction front radius (r~ = r i / r o ). The full curves a r e theoretical predictions made assuming the decomposition to be controlled by heat and mass transfer, the individual points are measurements made in independent kinetic experiments.
A N D Y. K O N D O
The a u t h o r s thank D r . H i l l s f o r h i s v a l u a b l e d i s c u s s i o n on o u r l i m e s t o n e p a p e r . 1 He m e n t i o n e d t h a t E q s . [1] t h r o u g h [3] in h i s p a p e r w h i c h w e r e b a s e d on m i x e d c o n t r o l , c h e m i c a l c o n t r o l and m a s s t r a n s f e r p l u s d i f fusion control, respectively, are the alternative interp r e t a t i o n s of t h e e x p e r i m e n t a l r e s u l t and t h a t t h e a p p r o p r i a t e v a l u e s of t h e p a r a m e t e r s , k c , D e and h g , a r e to b e u s e d so t h a t t h e d e n o m i n a t o r s of t h e s e e q u a tions have the same value. It is known t h a t the c o n t r o l l i n g s t e p of t h e o v e r a l l r a t e of a r e a c t i o n c h a n g e s a c c o r d i n g to t h e e x p e r i m e n t a l c o n d i t i o n s , and it i s p r e f e r a b l e to e m p l o y a model which applies under the operating conditions c o v e r i n g a w i d e r a n g e and to e s t a b l i s h the r a t e e q u a t i o n in w h i c h a l l s t e p s of h e a t and m a s s t r a n s f e r and of i n t e r f a c i a l r e a c t i o n a r e i n v o l v e d . It s h o u l d a l s o b e m e n t i o n e d t h a t e a c h of t h e p a r a m e t e r s a p p e a r i n g in this rate equation has the same value as the respect i v e o n e s in t h e r a t e e q u a t i o n s in w h i c h a c e r t a i n r a t e c o n t r o l l i n g s t e p is a s s u m e d . F o r e x a m p l e , t h e f o l l o w i n g r a t e e q u a t i o n is a l w a y s v a l i d f o r t h e m a s s t r
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