Interdendritic fluid flow in a lead-tin alloy
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O N E of the m a j o r f a c t o r s c o n t r i b u t i n g to m a c r o s e g r e gation in c a s t i n g s is fluid flow t h r o u g h d e n d r i t i c a r r a y s d u r i n g s o l i d i f i c a t i o n . The d r i v i n g f o r c e for this flow is due to t e m p e r a t u r e and c o m p o s i t i o n g r a d i e n t s i n the c a s t i n g d u r i n g s o l i d i f i c a t i o n , a s well as v o l u m e s h r i n k a g e and gas evolution. The extent of flow is c l o s e l y r e l a t e d to the s i z e , g e o m e t r y and s t a b i l i t y of the highly i r r e g u l a r liquid c h a n n e l s t h r e a d i n g the d e n dritic array. To e x a m i n e fluid flow as it r e l a t e s to m a c r o s e g r e gation r e q u i r e s a c o n s i d e r a t i o n of both the d r i v i n g f o r c e l e a d i n g to flow and the extent of fluid d r a g within the i n t e r d e n d r i t i c c h a n n e l s . The p r e s e n t i n v e s t i g a t i o n c o n s i d e r s fluid drag; s p e c i f i c a l l y , the m e a s u r e m e n t of i n t e r d e n d r i t i c flow in a m e t a l l i c s y s t e m u n d e r a known d r i v i n g force, and the r e l a t i o n s h i p b e t w e e n the r e s i s t a n c e to flow and the d e n d r i t i c s t r u c t u r e of the c a s t i n g . M e a s u r e m e n t s of i n t e r d e n d r i t i c fluid flow r a t e s in A1-4.5 pct Cu a l l o y s have b e e n r e p o r t e d by P i w o n k a and F l e m i n g s 1 In t h e i r e x p e r i m e n t s they m e a s u r e d the d i s p l a c e m e n t of liquid f r o m the p a r t i a l l y s o l i d alloy, r e s u l t i n g f r o m p r e s s u r e e x e r t e d on one side of the s a m p l e by n i t r o g e n or liquid lead. The r e s i s t a n c e to flow t h r o u g h the d e n d r i t i c a r r a y was then c a l c u l a t e d f r o m the flow v e l o c i t y of the d i s p l a c e d liquid and the applied p r e s s u r e . T h e i r fluid flow r e s u l t s w e r e r e l a t e d to a s i m p l e m o d e l of flow t h r o u g h a p o r o u s m e d i u m , b a s e d on the H a g e n - P o i s e u i l l e equation. C o n s i d e r i n g the s o l i d liquid zone as a bundle of s t r a i g h t p a r a l l e l c a p i l l a r y t u b e s , they plotted the l o g a r i t h m of the p e r m e a b i l i t y (the r e c i p r o c a l of the r e s i s t a n c e to flow) a g a i n s t the l o g a r i t h m of the liquid f r a c t i o n . A s s u m i n g the n u m b e r of flow c h a n n e l s r e m a i n s c o n s t a n t i . e . c o n s t a n t d e n d r i t e spacing, a s t r a i g h t line of slope = 2 should be o b t a i n e d if the m o d e l is a p p l i c a b l e . T h i s was found to be the c a s e for liquid f r a c t i o n s l e s s than 0.3. More r e c e n t l y , the p e r m e a b i l i t i e s of p a r t i a l l y s o l i d i f i e d d e n d r i t i c n e t w o r k s in A1-Si a l l o y s w e r e N. STREAT is Research Engineer, British Columbia Hydro and Power Authority, Vancouver, B.C.F. WEINBERGis Professor, Department of M
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