Effect of system geometry on the leaching behavior of cobalt metal: Mass transfer controlling case
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L E A C H I N G r e a c t i o n s in m e t a l l u r g i c a l s y s t e m s a r e h e t e r o g e n e o u s in n a t u r e and the o v e r a l l l e a c h i n g p r o c e s s can be b r o k e n down into a n u m b e r of s e q u e n t i a l r e a c t i o n s t e p s . F o r a nonporous solid, one or m o r e r e a c t a n t s diffuse f r o m the bulk s o l u t i o n t h r o u g h the b o u n d a r y l a y e r on the solid and r e a c t with c o n s t i t u e n t s of the solid at the s o l i d / l i q u i d i n t e r f a c e . The s o l u b l e p r o d u c t s so f o r m e d then diffuse back t h r o u g h the bounda r y l a y e r into the bulk of the s o l u t i o n phase. The r a t e of leaching can be e x p r e s s e d a s : dCb - k(C s - Cb). clt
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(The m e a n i n g s of the s y m b o l s a r e given in the n o m e n clature.) The bulk c o n c e n t r a t i o n of the product, Cb, and hence the r a t e of change of c o n c e n t r a t i o n in the bulk solution, dC b dt ' can be m e a s u r e d e x p e r i m e n t a l l y . The a p p a r e n t r a t e constant, k, cannot be r e a d i l y e v a l u a t e d u n l e s s the s u r f a c e c o n c e n t r a t i o n , Cs, is known; or, c o n v e r s e l y , the s u r f a c e c o n c e n t r a t i o n C s cannot be found u n l e s s k is known. The s u r f a c e c o n c e n t r a t i o n of the s o l u b l e p r o d u c t f r o m a r e a c t i o n which is l i m i t e d by the r a t e of m a s s t r a n s f e r is often a s s u m e d to be ~he e q u i l i b r i u m c o n c e n t r a t i o n . However, this a s s u m p t i o n can lead to a n e r r o n e o u s r e s u l t , b e c a u s e the type of r e a c t i o n and the c h e m i s t r y at the s o l i d / l i q u i d i n t e r f a c e a r e c o m p l e x and the q u a n t i t a t i v e a n a l y s i s at the i n t e r f a c e is e x t r e m e l y difficult. T h e r e a r e e x p e r i m e n t a l r e a c t i o n s y s t e m s in which the a p p a r e n t r a t e constant for s u c h diffusion c o n t r o l l e d r e a c t i o n s can be c a l c u l a t e d f r o m e i t h e r b a s i c p r i n c i p l e s or e m p i r i c a l c o r r e l a t i o n s . The m a s s t r a n s f e r coefficient to or f r o m a smooth r o t a t i n g d i s k in l a m i n a r flow for e x a m p l e can be c a l c u l a t e d f r o m b a s i c p r i n c i p l e s . 1 It is for this r e a s o n that the r o t a t i n g d i s k geo m e t r y is often used in s t u d y i n g k i n e t i c s of leaching. 2'3 The a p p a r e n t r a t e c o n s t a n t t o g e t h e r with the e x p e r i m e n t a l r a t e data can then be used in the c a l c u l a t i o n of
the c o n c e n t r a t i o n s of r e a c t a n t s o r p r o d u c t s at the solid/liquid interface. ~ T h e obvious q u e s t i o n i s t h e n w h e t h e r o r not such c o n c e n t r a t i o n s found at the i n t e r f a c e f r o m this r a t h e r s p e c i a l g e o m e t r y can be g e n e r a l i z e d and applied to m o r e p r a c t i c a l e x p e r i m e n t a l
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