The law of additive reaction times in fluid-solid reactions
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I. INTRODUCTION T H E r e a c t i o n b e t w e e n a solid and a fluid in which a solid product or a s h l a y e r is f o r m e d o c c u p i e s a n i m p o r t a n t p o s i t i o n i n m a n y c h e m i c a l and m e t a l l u r g i c a l p r o c e s s e s . B e c a u s e of its i m p o r t a n c e much r e s e a r c h has b e e n devoted to the s u b j e c t . The r e a d e r i s r e f e r r e d to a r e c e n t m o n o g r a p h 1 and r e v i e w a r t i c l e s 2"~ for c o m p r e h e n s i v e r e v i e w s on this topic. The a n a l y s i s of the h e t e r o g e n e o u s r e a c t i o n s y s t e m m u s t s t a r t f r o m the r e c o g n i t i o n that the r e a c t i o n takes p l a c e at an i n t e r f a c e and hence m a s s ~ d heat m u s t be t r a n s p o r t e d to and f r o m this r e a c t i o n i n t e r f a c e . It follows that the s t r u c t u r e , p e r t i n e n t to heat and m a s s t r a n s f e r , of the solid before, d u r i n g , and a f t e r the r e a c t i o n plays a n i m p o r t a n t r o l e on the o v e r a l l r a t e of r e a c tion. T h u s , the p r e v i o u s l y p r o p o s e d m o d e l s d e s c r i b ing this type of f l u i d - s o l i d r e a c t i o n s can be l a r g e l y divided into the following two groups: 1) F o r a n i n i t i ally nonporous solid p r o d u c i n g a p o r o u s p r o d u c e l a y e r : the s h r i n k i n g - c o r e m o d e l and 2) F o r a n i n i t i a l l y p o r ous solid p r o d u c i n g a p o r o u s product l a y e r : the g r a i n model. The scope of this a r t i c l e does not allow d e t a i l e d des c r i p t i o n s of these m o d e l s . The r e a d e r i s r e f e r r e d to a p p r o p r i a t e a r t i c l e s cited i n this p a p e r . V e r y b r i e f l y , the s h r i n k i n g core m o d e l a s s u m e s the r e a c t i o n to take place at a s h a r p i n t e r f a c e between the u n r e a c t e d core and the p o r o u s p r o d u c t l a y e r . As the r e a c t i o n p r o c e e d s , the u n r e a c t e d core d i m i n i s h e s in s i z e while its shape r e m a i n s the s a m e as the o r i g i n a l shape, thus f o r m i n g p a r a l l e l p l a t e s , coaxial c y l i n d e r s , or c o n c e n t r i c s p h e r e s depending the o r i g i n a l shape. The
H. Y. SOHN is Associate Professor, Department of Metallurgy and Metallurgical Engineering,University of Utah, Salt Lake City, UT 84112. Manuscript submitted July 19, 1977. METALLURGICAL TRANSACTIONSB
a n a l y s i s of this s y s t e m has b e e n r e v i e w e d and g e n e r a l ized by Sohn z'4 and Szekely et a l ) The g r a i n m o d e l v i s u a l i z e s the p o r o u s solid to be made up of i n d i v i d u a l p a r t i c l e s ( g r a i n s ) . B e c a u s e of the i n i t i a l p o r o s i t y of the solid, the r e a c t i o n of the solid g r a i n s o c c u r s while the fluid r e a c t a n t diffuses into the p o r e s . T h u s , the r e a c t i o n o c c u r s in g e n e r a l in a diffuse zone r a t h e r than at a s h a r
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