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UBC Theses and Dissertations

The passage of fibres through slots in pulp screening Gooding, Robert William 1986

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THE PASSAGE OF FIBRES THROUGH SLOTS IN PULP SCREENING by ROBERT WILLIAM GOODING B. Eng., M c G i l l U n i v e r s i t y , 1977 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of Chemical Engineering We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA September 1986 © Robert W i l l i a m Gooding, 1986 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of CJ^r^-(CaJ^ <£*^C^&ZJT^IC^ The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date »V acX^>6^C i i ABSTRACT The s c r e e n i n g of wood p u l p f i b r e s i n aqueous s u s p e n s i o n i s an i m p o r t a n t i n d u s t r i a l p r o c e s s w h i c h i n v o l v e s t h e p a s s a g e o f " a c c e p t " p u l p f i b r e s t h r o u g h a p e r f o r a t e d o r s l o t t e d p l a t e , and t h e r e t e n t i o n of l a r g e r , c o a r s e r f i b r e s on t h e p l a t e . The i n f l u e n c e o f f i b r e , f l o w , and s l o t v a r i a b l e s on f i b r e p a s s a g e was measured i n t h i s t h e s i s . T h e s e f i n d i n g s were r e l a t e d t o t h e o p e r a t i o n o f a c o m m e r c i a l - s c a l e p r e s s u r e s c r e e n . A l s o a mechanism o f s c r e e n i n g was p r o p o s e d b a s e d on f i b r e t r a j e c t o r i e s t h a t were o b s e r v e d u s i n g h i g h s p e e d c i n e -p h o t o g r a p h y . T h i s mechanism has two components: 1) a " w a l l e f f e c t " w h i c h c a u s e s t h e l a y e r of f l o w t h a t p a s s e s t h r o u g h t h e s l o t t o be d e p l e t e of l a r g e f i b r e s , and 2) an " e n t r y e f f e c t " , w h i c h f a v o u r s t h e p a s s a g e of f i b r e s t h a t a r e s h o r t e n o u g h and f l e x i b l e e n o u g h t o f o l l o w t h e s t r e a m l i n e s t h a t t u r n and p a s s t h r o u g h t h e s c r e e n p l a t e s l o t . i i i D E D I C A T I O N T o my f a t h e r , E d w a r d G o o d i n g i v T A B L E OF C O N T E N T S P a g e A B S T R A C T i i L I S T O F T A B L E S v i L I S T OF F I G U R E S v i i A C K N O W L E D G E M E N T S i x 1 . I N T R O D U C T I O N 1 2 . L I T E R A T U R E R E V I E W 4 2 . 1 T h e P h y s i c a l P r o p e r t i e s o f P u l p F i b r e s a n d S h i v e s 5 2 . 2 P u l p S c r e e n D e s i g n 7 2 . 3 P u l p S c r e e n P e r f o r m a n c e 1 0 2 . 4 T h e F l o w N e a r a S c r e e n A p e r t u r e 15 2 . 5 T h e M o t i o n o f F i b r e s i n S c r e e n i n g S i t u a t i o n s 1 5 3 . A N A L Y S I S 18 3 . 1 S h i v e S t i f f n e s s 18 3 . 2 T h e F l o w F i e l d a t a S c r e e n P l a t e A p e r t u r e . . 22 3 . 3 T h e E f f i c i e n c y - R e j e c t R a t e R e l a t i o n s h i p . . 25 4 . E X P E R I M E N T A L WORK 3 5 4 . 1 F i b r e S u s p e n s i o n s 35 4 . 2 F l o w L o o p 38 4 . 3 C i n e - P h o t o g r a p h y 44 5 . R E S U L T S AND D I S C U S S I O N 4 9 5 . 1 P e r m e a b i l i t y M e a s u r e m e n t s 49 5 . 2 F i b r e T r a j e c t o r i e s N e a r a S l o t t e d P l a t e . . . . 5 3 5 . 3 A M o d e l f o r F i b r e P a s s a g e 69 V Page 6. SUMMARY AND CONCLUSIONS 73 7. RECOMMENDATIONS FOR FUTURE WORK 77 NOMENCLATURE 79 BIBLIOGRAPHY 82 APPENDIX I : E x p e r i m e n t a l D a t a 85 APPENDIX I I : Computer Programmes 96 APPENDIX I I I : E x p e r i m e n t a l A p p a r a t u s D e t a i l s 112 APPENDIX IV: F i b r e L e n g t h D i s t r i b u t i o n s 116 v i L IST OF TABLES Page I P h y s i c a l P r o p e r t i e s o f P u l p F i b r e s and S h i v e s .. 6 I I P h y s i c a l P r o p e r t i e s o f E x p e r i m e n t a l F i b r e s .... 36 I I I F i b r e M o t i o n Types 62 IV C h a n n e l L a y e r D e f i n i t i o n s 63 V F i l m D a t a Summary 64 VI F i b r e V e l o c i t y and O r i e n t a t i o n 69 VI I H i g h Speed C i n e - F i l m s 86 V I I I P e r m e a b i l i t y Measurements 87 IX T e s t s 65-68 F i b r e L e n g t h / P e r m e a b i l i t y Measurements 90 X T e s t s 69-71 F i b r e L e n g t h / P e r m e a b i l i t y Measurements 92 XI T e s t s 72-74 F i b r e L e n g t h / P e r m e a b i l i t y Measurements 94 X I I L e n g t h D i s t r i b u t i o n o f l x . 0 4 3 mm N y l o n F i b r e s 117 X I I I L e n g t h D i s t r i b u t i o n o f 1.5x.043 mm N y l o n F i b r e s 118 XIV L e n g t h D i s t r i b u t i o n o f 3x.043 mm N y l o n F i b r e s 120 XV L e n g t h D i s t r i b u t i o n o f l x . 0 1 2 mm Rayon F i b r e s 121 XVI L e n g t h D i s t r i b u t i o n o f l x . 0 2 0 mm Rayon F i b r e s 122 XVII L e n g t h D i s t r i b u t i o n o f p l 0 . r l 4 K r a f t F i b r e s 123 X V I I I L e n g t h D i s t r i b u t i o n o f p l 4 . r 2 8 K r a f t F i b r e s 124 XIX L e n g t h D i s t r i b u t i o n o f K r a f t P u l p F i b r e s 125 XX L e n g t h D i s t r i b u t i o n o f CTMP P u l p F i b r e s 126 v i i L IST OF FIGURES Page 1. C e n t r i s o r t e r - t y p e P r e s s u r e S c r e e n 9 2. S c r e e n P e r f o r m a n c e C u r v e s 12 3. S t r e a m l i n e s a t a Flow B i f u r c a t i o n i n a S l o t t e d P l a t e 15 4. I d e a l i z e d F i b r e and S h i v e C r o s s - S e c t i o n s 19 5. R e l a t i o n s h i p Between S h i v e S t i f f n e s s and S i z e .. 21 6. F l o w A d j a c e n t t o a S c r e e n P l a t e i n a P r e s s u r e S c r e e n 25 7. Flow Loop S c h e m a t i c 39 8. F l o w Loop and P l e x i g l a s C h a n n e l 40 9. P l e x i g l a s C h a n n e l and H i g h Speed C i n e - C a m e r a ... 41 10. F i l m A n a l y z i n g Equipment 46 11. E f f e c t s of F i b r e L e n g t h and F i b r e Type on P e r m e a b i l i t y 50 12. E f f e c t o f F i b r e S t i f f n e s s on P e r m e a b i l i t y 51 13. E f f e c t s o f S l o t V e l o c i t y and F i b r e Type on P e r m e a b i l i t y 54 14. E f f e c t s o f S l o t V e l o c i t y and U p s t r e a m V e l o c i t y on P e r m e a b i l i t y 55 15. E f f e c t s o f S l o t V e l o c i t y and S l o t W i d t h on P e r m e a b i l i t y 56 16. E f f e c t o f E n t r y L e n g t h on P e r m e a b i l i t y 57 17. M o t i o n o f F i b r e s Near a S l o t ( C i n e - F i l m ) 60 18. M o t i o n o f F i b r e s Near a S l o t ( C o m p u t e r i z e d Image) 61 19. C o r r e l a t i o n o f F i b r e M o t i o n , F i b r e P o s i t i o n and F i b r e O r i e n t a t i o n f o r F i l m 1 65 v i i i 20. C o r r e l a t i o n o f F i b r e M o t i o n , F i b r e P o s i t i o n a n d F i b r e O r i e n t a t i o n f o r F i l m 2 66 21. C o r r e l a t i o n o f F i b r e M o t i o n , F i b r e P o s i t i o n and F i b r e O r i e n t a t i o n f o r F i l m 3 67 i x ACKNOWLEDGEMENTS I w i s h t o t h a n k S o n y a f o r h e r s u p p o r t , p a t i e n c e a n d t o l e r a n c e d u r i n g t h e p a s t few y e a r s . Many o t h e r i n d i v i d u a l s and o r g a n i z a t i o n s h a v e a l s o made i m p o r t a n t t e c h n i c a l a n d f i n a n c i a l c o n t r i b u t i o n s t o t h i s work: * My t h e s i s s u p e r v i s o r , P r o f . R i c h a r d K e r e k e s * The members of my t h e s i s a d v i s o r y c o m m i t t e e , Mr. W i l l i a m Holmes, P r o f . John G r a c e and P r o f . R i c h a r d B r a n i o n * My c o l l e a g u e s , R o b e r t S o s z y n s k i and P e t e r Tam Doo * The f a c u l t y and s t a f f o f t h e Department o f C h e m i c a l E n g i n e e r i n g , U n i v e r s i t y o f B r i t i s h C o l u m b i a * The P u l p and Paper R e s e a r c h I n s t i t u t e o f Canada and i t s s t a f f , e s p e c i a l l y M i s s G e o r g i n a W h i t e * Mr. Mark F r i t h , and M a c M i l l a n B l o e d e l L t d . * N a t i o n a l S c i e n c e and E n g i n e e r i n g R e s e a r c h C o u n c i l o f Canada * Mr. Sven Smeds, K a j a a n i A u t o m a t i o n L t d . * Mr. Ted Hooper, S.W. Hooper and Co. L t d . * M e s s r s . Doug Young and Bob P e d e r s o n , C a n a d i a n I n g e r s o l l -Rand L t d . * M e s s r s . P e t e r F l y n n and Bob N i c h o l s , B i r d M a c h i n e Co. I n c . 1 1. INTRODUCTION Wood c o n s i s t s mainly of t u b u l a r f i b r e s a l i g n e d p a r a l l e l to one another and bonded together with l i g n i n . Chemical or mechanical means can be used t o d i v i d e wood i n t o f i b r e s . These f i b r e s a re c o l l e c t i v e l y c a l l e d pulp, and the process t h a t p r o d u c e s them i s c a l l e d p u l p i n g . C h e m i c a l p u l p i n g i n v o l v e s d i s s o l v i n g l i g n i n t o l i b e r a t e t h e f i b r e s . In mechanical p u l p i n g , f o r c e s are a p p l i e d to the wood to d i v i d e i t i n t o f i b r e - s i z e p i e c e s , though not n e c e s s a r i l y a l o n g n a t u r a l f i b r e boundaries. Both chemical and mechanical p u l p i n g processes produce s m a l l q u a n t i t i e s o f " s h i v e s " , w h i c h a r e b u n d l e s o f u n s e p a r a t e d f i b r e s . Shives lower the s t r e n g t h and o p t i c a l q u a l i t y of paper and must be removed i n o r d e r t o p r o d u c e h i g h - q u a l i t y paper. Screening pulp while i t i s i n aqueous suspension i s a means of removing s h i v e s . P r e s s u r i z e d pulp s c r e e n s , a l s o c a l l e d "pressure screens", are commonly used f o r t h i s purpose, and they are the sub j e c t of t h i s t h e s i s . T h e r e i s g r e a t i n c e n t i v e to i n c r e a s e the c a p a c i t y of pr e s s u r e s c r e e n s , to reduce t h e i r power c o n s u m p t i o n , and e s p e c i a l l y to i n c r e a s e t h e i r e f f i c i e n c y . A pressure screen may r e j e c t 10% of the pulp fed to i t i n order to reduce the s h i v e c o n c e n t r a t i o n from 1.0% to 0.5%. To r e c l a i m some of the f i b r e that i s i n a d v e r t e n t l y r e j e c t e d , the " r e j e c t s " are 2 p a s s e d t o s e c o n d a r y and t e r t i a r y s c r e e n i n g s y s t e m s . D e s p i t e t h e w i d e s p r e a d use o f p r e s s u r e s c r e e n s f o r s h i v e r e m o v a l , l i t t l e h a s b e e n p u b l i s h e d t h a t p r o v i d e s a f u n d a m e n t a l u n d e r s t a n d i n g o f how s h i v e s a r e s e g r e g a t e d f r o m p u l p . A l s o , no e x p l a n a t i o n i s a p p a r e n t f r o m an i n s p e c t i o n o f t h e s c r e e n i n g e q u i p m e n t . T h e r e i s a s c r e e n p l a t e i n a p r e s s u r e s c r e e n t h r o u g h w h i c h t h e a c c e p t p u l p m u s t p a s s . However, t h e a p e r t u r e s i n a t y p i c a l s c r e e n p l a t e a r e l a r g e r t h a n t h e minimum d i a m e t e r o f many s h i v e s . Thus t h e s c r e e n p l a t e i s n o t a p h y s i c a l b a r r i e r t o a l l s h i v e s . The l a c k of u n d e r s t a n d i n g o f why s h i v e s do not g e n e r a l l y p a s s t h r o u g h t h e a p e r t u r e s h a s c a u s e d p r e s s u r e s c r e e n d e s i g n t o r e l y on i n t u i t i o n , and t r i a l and e r r o r . The g e n e r a l o b j e c t i v e of t h i s t h e s i s was t o u n d e r s t a n d what c o n t r o l s t h e p a s s a g e o f f i b r e s * t h o u g h a s l o t ; t h a t i s , t o know how p u l p f i b r e s a r e s e g r e g a t e d f r o m s h i v e s a t an a p e r t u r e i n a p r e s s u r e s c r e e n . T h e s p e c i f i c o b j e c t i v e s were f i r s t , t o d e t e r m i n e how v a r i o u s f i b r e , f l o w , and s c r e e n p l a t e v a r i a b l e s i n f l u e n c e t h e l i k e l i h o o d t h a t f i b r e s w i l l p a s s t h r o u g h a s c r e e n p l a t e a p e r t u r e ; and n e x t , t o p r e d i c t p r e s s u r e s c r e e n p e r f o r m a n c e f r o m t h i s i n f o r m a t i o n . The s p e c i f i c t a s k s u n d e r t a k e n were t o : 1. D e f i n e t h e m e c h a n i c a l p r o p e r t i e s o f wood p u l p f i b r e s and s h i v e s . 3 2. E s t i m a t e t h e f l o w c o n d i t i o n s a t a s l o t t e d a p e r t u r e i n a p r e s s u r e s c r e e n . 3. C o n s t r u c t a f l o w l o o p and c h a n n e l s i m u l a t i n g t h e f l o w c o n d i t i o n s a t a s l o t i n a p r e s s u r e s c r e e n . 4 . M e a s u r e t h e c o n c e n t r a t i o n o f f i b r e s i n t h e f l o w p a s s i n g t h r o u g h t h e s l o t , r e l a t i v e t o t h a t i n t h e f e e d f l o w f o r v a r i o u s f i b r e t y p e s and f l o w r a t e s . 5. O b s e r v e t h e m o t i o n o f f i b r e s a t a s l o t e n t r y u s i n g c i n e - p h o t o g r a p h y , a n d c o m p a r e t h e t r a j e c t o r i e s o f f i b r e s t h a t go t h r o u g h t h e s l o t t o t h o s e t h a t do n o t . * N o t e : I n e m b r a c i n g s h i v e s and t h i s t h e s i s , " f i b r e " i s a l l r o d - l i k e p a r t i c l e s , s y n t h e t i c f i b r e s . u s e d as a i n c l u d i n g g e n e r a l t e r m , p u l p f i b r e s , 4 2. LITERATURE REVIEW S c r e e n i n g i s an a n c i e n t a n d w i d e s p r e a d m e t h o d f o r s e p a r a t i n g l a r g e and s m a l l p a r t i c l e s , and g e n e r a l s c r e e n i n g p r i n c i p l e s have been d e s c r i b e d i n s e v e r a l r e v i e w s (B1,M1,M2, P1,R1). In t h e s i m p l e s t f o r m o f s c r e e n i n g , t e r m e d " p o s i t i v e s c r e e n i n g " , a mesh or p e r f o r a t e d p l a t e p r e s e n t s a g e o m e t r i c a l b a r r i e r t o a l l l a r g e p a r t i c l e s , b ut p e r m i t s s m a l l p a r t i c l e s t o p a s s t h r o u g h . An a l t e r n a t e and p e r h a p s more w i d e s p r e a d f o r m o f s c r e e n i n g i s " p r o b a b i l i t y s c r e e n i n g " . Here t h e " s i z e o f s e p a r a t i o n " ( i . e . t h e s i z e o f a p a r t i c l e w i t h a 50% c h a n c e o f p a s s i n g t h r o u g h an a p e r t u r e ) i s somewhat l e s s t h a n t h e a p e r t u r e s i z e . P a r t i c l e s a r e p r e s e n t e d t o a p e r t u r e s a l i m i t e d number of t i m e s , and p a s s a g e may depend n o t o n l y on s i z e , b u t on p a r t i c l e o r i e n t a t i o n , v e l o c i t y , o r o n i n t e r a c t i o n w i t h o t h e r p a r t i c l e s ( B 2 ) . P u l p s c r e e n i n g i s a somewhat u n i q u e p r o c e s s s i n c e , 1) t h e v a l u e o f t h e c l e a n e d p u l p i s low, and any t r e a t m e n t must o f e c o n o m i c n e c e s s i t y be s i m p l e a n d h a v e a h i g h t h r o u g h p u t ; 2) s e p a r a t i o n must o c c u r w h i l e t h e p u l p i s i n aqueous s u s p e n s i o n , and 3) p u l p f i b r e s a n d s h i v e s must be s e p a r a t e d a c c o r d i n g t o d i f f e r e n c e s i n w i d t h or s t i f f n e s s , b e c a u s e t h e y do not d i f f e r much i n l e n g t h . P r e s s u r i z e d p u l p s c r e e n i n g i s a f o r m o f p r o b a b i l i t y s c r e e n i n g t h a t i s q u i t e d i f f e r e n t f r o m s c r e e n i n g p r o c e s s e s i n t h e t e x t i l e , m i n e r a l or 5 a g r i c u l t u r a l i n d u s t r i e s . Indeed i t i s u n l i k e other methods of s c r e e n i n g f i b r e i n the pulp and paper i n d u s t r y . The f i r s t commercial i n s t a l l a t i o n of a pressure screen occurred a f t e r 1960, and there have been no p u b l i s h e d s c i e n t i f i c s t u d i e s of i t s o p e r a t i n g p r i n c i p l e s b e f o r e or s i n c e . The r e m a i n i n g s e c t i o n s of t h i s chapter d e s c r i b e how a p r e s s u r e s c r e e n works and how s c r e e n p e r f o r m a n c e i s a s s e s s e d . Some r e l a t e d t o p i c s w i l l a l s o be reviewed: the p h y s i c a l p r o p e r t i e s of pulp f i b r e s and s h i v e s , the motion of f i b r e s i n d i l u t e suspensions, and the flow p a t t e r n at a s l o t i n a channel. 2.1 The P h y s i c a l P r o p e r t i e s of Pulp F i b r e s and Shives The p r o p e r t i e s of wood f i b r e s are d e s c r i b e d i n numerous p u b l i c a t i o n s , such as Macdonald (M3), Panshin et a l . (P2), and Sjostrom ( S I ) . The p r o p e r t i e s which bear most d i r e c t l y on pulp s c r e e n i n g are summarized in Table I. The range of v a l u e s g i v e n f o r f i b r e p r o p e r t i e s r e f l e c t t h e s u b s t a n t i a l n a t u r a l v a r i a t i o n t h a t e x i s t s w i t h i n a t r e e , from t r e e to t r e e , and from s p e c i e s to s p e c i e s . S h i v e s do not have a p r e c i s e , w i d e l y a c c e p t e d , geometric d e f i n i t i o n . A working d e f i n i t i o n can be based on t h e l a b o r a t o r y d e v i c e s used to measure the amount of s h i v e s i n a pulp sample, such as the S o m e r v i l l e s c r e e n (Tl) and the STFI Shives Analyzer (Hi) . Other d e f i n i t i o n s of shives are drawn from 6 T a b l e I : P h y s i c a l P r o p e r t i e s o f P u l p F i b r e s and S h i v e s length(mm) width(mm) w a l l t h i c k n e s s ( m m ) s t i f f n e s s ( x l O - 1 2 Nm2) m e c h a n i c a l p u l p c h e m i c a l p u l p p u l p f i b r e s 2-4 .02-.04 .002-.008 81 2 s h i v e s 3-6 .10-.60 n o t a p p l i c a b l e 1 0 4 - 1 0 7 n o t e s t i m a t e d N o t e : The d a t a g i v e n above r e l a t e t o b l a c k s p r u c e f i b r e s and s h i v e s . 7 publications that relate various problems caused by shives to t h e i r size (B3,CI,H2,LI,M4). The shive dimensions given i n Table I are based on a l l of these sources. In t h i s study, both f i b r e s and shives are considered to be neutrally buoyant. The walls of pulp f i b r e s have a basic d e n s i t y of 1.5 g/cm3 (Kl), but water w i l l swell the f i b r e walls and f i l l the f i b r e lumens. The apparent d e n s i t y of pulp f i b r e s and shives i n aqueous suspension i s therefore only s l i g h t l y greater than that of water. Pulp f i b r e s t i f f n e s s has been measured i n recent work by Tam Doo and Kerekes (T2), and data from t h e i r work are i n c l u d e d i n Table I . I t i s evident that mechanical pulp f i b r e s are s t i f f e r than chemical pulp f i b r e s , which i s a consequence of the higher l i g n i n content of the mechanical p u l p . There are no p u b l i s h e d measurements of s h i v e s t i f f n e s s . However, the s t i f f n e s s of shives may be estimated by assuming shives to be simple, beam-like f i b r e composites, as d i s c u s s e d i n Chapter 3. Such shive s t i f f n e s s estimates are shown in Table I. 2.2 Pulp Screen Design There have been three generations of pulp screen design: 1) f l a t screens, 2) atmospheric screens, and 3) pressure screens. Each of these screens i s intended mainly for shive removal, and each has a screen plate which the accept pulp 8 must pass through. However, the dynamics of the screens and t h e i r o p e r a t i n g p r i n c i p l e s d i f f e r c o n s i d e r a b l y (C2,L2,S2). F l a t s c r e e n s , the f i r s t type of screen to be used f o r wood pulp, segregate shives from pulp by p o s i t i v e s c r e e n i n g ; that i s , the screen p l a t e aperture i s s m a l l e r than the s m a l l e s t s h i v e diameter. The accept pulp i s p e r f e c t l y c l e a n ; however t h e s e s c r e e n s have low c a p a c i t i e s and h i g h m a i n t e n a n c e r e q u i r e m e n t s . F l a t s c r e e n s now f i n d o n l y l i m i t e d use i n modern pulp m i l l s . The a t m o s p h e r i c ( c e n t r i f u g a l and r o t a r y type) screen succeeded the f l a t s c reen. I t p r o v i d e s good s c r e e n i n g with a higher throughput. The screen p l a t e apertures i n t h i s type of s creen are s e v e r a l times l a r g e r than t h e a v e r a g e s h i v e diameter, but the s h i v e s do not g e n e r a l l y pass through. I t i s b e l i e v e d that a mat of f i b r e s forms on the feed s i d e of t h e s c r e e n p l a t e w h i c h impedes the p a s s a g e of s h i v e s . Atmospheric screens are s t i l l i n widespread use, but they are s t e a d i l y b e i n g r e p l a c e d by p r e s s u r e s c r e e n s . P r e s s u r e screens compensate f o r t h e i r lower e f f i c i e n c y (H3) and higher energy demand by having a higher c a p a c i t y . The e s s e n t i a l f e a t u r e s of a t y p i c a l p r essure screen are shown i n F i g u r e 1. P u l p e n t e r s t h e f e e d chamber tangen-t i a l l y , then passes down the annular gap between the r o t o r and ( s t a t i o n a r y ) c y l i n d r i c a l s c r e e n p l a t e . A c c e p t p u l p passes r a d i a l l y through the screen p l a t e , whereas the r e j e c t Figure 1 Centrisorter-type Pressure Screen 10 pulp continues down the gap to the r e j e c t o u t l e t . Rotor designs vary among screen manufacturers, but t h e i r purpose i s the same: to induce pressure pulses which unplug s c r e e n p l a t e a p e r t u r e s , and to a c c e l e r a t e the pulp s l u r r y p a r a l l e l to the screen p l a t e . The drum-type r o t o r shown i n F i g u r e 1 i s studded with lugs on i t s p e r i p h e r y . T h i s s t y l e of r o t o r i s i n widespread use, as are r o t o r s t h a t i n v o l v e v e r t i c a l f o i l s or paddles. S c r e e n p l a t e c o n f i g u r a t i o n i s c r i t i c a l t o s c r e e n performance, and pulp screens are designed to permit screen p l a t e s t o be r e a d i l y changed. S i n c e t h e a p e r t u r e s i z e a p p r o p r i a t e f o r a g i v e n a p p l i c a t i o n cannot be p r e d i c t e d r e l i a b l y , t he c h o i c e i s made by t r i a l and e r r o r . Other s e l e c t i o n s i n v o l v e the shape of the s c r e e n p l a t e a p e r t u r e ( e i t h e r hole or s l o t ) , and the p r o f i l e of the i n s i d e s u r f a c e of the screen p l a t e ( e i t h e r smooth or contoured). Some t y p i c a l screen dimensions and throughputs are given i n Chapter 3. In that chapter, estimates are a l s o made of the flow v e l o c i t i e s i n s i d e a pressure s c r e e n . 2.3 Pulp Screen Performance The two most common parameters of screen performance are " e f f i c i e n c y " , E, and " r e j e c t r a t e " , R. E f f i c i e n c y i s d e f i n e d as t h e p o r t i o n of s h i v e s i n the f e e d t h a t p a s s e s to the r e j e c t stream. S i m i l a r l y , r e j e c t r a t e i s the o v e r a l l p o r t i o n 11 o f t h e f e e d p u l p t h a t p a s s e s t o t h e r e j e c t s t r e a m ( T 3 ) . R e j e c t r a t e s may be c a l c u l a t e d on a v o l u m e t r i c b a s i s , b u t i n t h i s t h e s i s r e j e c t r a t e i s b a s e d on t h e p u l p mass f r a c t i o n s . T h e r e l a t i o n s h i p between e f f i c i e n c y and r e j e c t r a t e i s us e d t o a s s e s s s c r e e n p e r f o r m a n c e , and a t y p i c a l E-R c u r v e i s shown i n F i g u r e 2. Good s c r e e n p e r f o r m a n c e i s one h a v i n g a h i g h e f f i c i e n c y a t a low r e j e c t r a t e ; t h a t i s , t h e maximum r e m o v a l o f s h i v e s w i t h t h e minimum l o s s of good p u l p . I n i n d u s t r y , an E-R c u r v e i s d e t e r m i n e d e x p e r i m e n t a l l y , by m e a s u r i n g e f f i c i e n c y a t v a r i o u s r e j e c t f l o w s e t t i n g s ( i . e . f o r v a r i o u s r e j e c t r a t e s ) . Two t h e o r e t i c a l e q u a t i o n s a l s o e x i s t w h i c h r e l a t e e f f i c i e n c y and r e j e c t r a t e : E = 1 - (A QR ( 2 - 1 } E = R c (2.2) In E q u a t i o n s 2.1 and 2.2 'Q' and ' C a r e s c r e e n i n g i n d i c e s t h a t a r e c o n s t a n t f o r a g i v e n p u l p f u r n i s h and s c r e e n p l a t e . E q u a t i o n 2.1 i s t h e one i n more w i d e s p r e a d u s e , a n d i t c o n f o r m s w e l l t o i n d u s t r i a l s c r e e n i n g d a t a , as shown i n F i g u r e 2. A p u b l i c a t i o n b y N e l s o n ( N l ) d e s c r i b e s t h e u s e f u l n e s s of t h i s e q u a t i o n and how Q can be d e t e r m i n e d f r o m s c r e e n p e r f o r m a n c e m e a s u r e m e n t s a t a s i n g l e f l o w s e t t i n g . N e l s o n a t t r i b u t e d E q u a t i o n 2.1 t o a c o l l e a g u e named B o l t o n , 12 F i g u r e 2 Screen Performance Curves 13 but Nelson gave no d e r i v a t i o n of the equation or d e s c r i p t i o n of i t s u n d e r l y i n g assumptions. F o l l o w i n g Nelson's p u b l i c a t i o n , Wahren (Wl) attempted to d e r i v e E q u a t i o n 2.1 by assuming t h a t each a p e r t u r e i n a screen p l a t e a c t s i n p a r a l l e l , and t h a t what i s r e j e c t e d by a s i n g l e a p e r t u r e i s r e c i r c u l a t e d back to t h a t a p e r t u r e . A s i m i l a r , but simpler d e r i v a t i o n i s o f f e r e d i n the f o l l o w i n g chapter of t h i s t h e s i s . In t h i s model, mixing i n the annular s c r e e n i n g zone i s c o n s i d e r e d t o be i n s t a n t a n e o u s and complete. Hence Equation 2.1 w i l l subsequently be r e f e r r e d to as the "mixed flow" s c r e e n i n g e q u a t i o n . Equation 2.2 i s based on Kubat and Steenberg's a n a l y s i s of a f l a t s creen (K2). They assumed that apertures i n the screen act i n s e r i e s , and that t h e r e i s no "back m i x i n g " . Thus the c o n c e n t r a t i o n of s h i v e s i n the pulp suspension increases as the suspension moves from the " f e e d " to the " r e j e c t " end of the s c r e e n i n g zone. In the f o l l o w i n g chapter, t h i s model i s adapted to a pressure screen and E q u a t i o n 2.2 i s d e r i v e d . This w i l l be c a l l e d the "plug flow" s c r e e n i n g equation. T h i s t h e s i s i s , i n l a r g e p a r t , based on the p l u g f l o w m o d e l , a n d 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 were c h o s e n a c c o r d i n g l y . The p l u g flow model was chosen f o r t h i s study i n s t e a d of the mixed flow model because the a s s o c i a t e d flow f i e l d i s e a s i e r t o d e f i n e , and t h u s e a s i e r t o model e x p e r i m e n t a l l y . The amount of mixing i n the annular screening 14 z o n e m a y w e l l b e s i g n i f i c a n t , a n d a t s o m e f u t u r e d a t e t h e p l u g f l o w m o d e l m a y b e a d a p t e d t o a c c o u n t f o r m i x i n g . 2 . 4 T h e F l o w N e a r a S c r e e n A p e r t u r e T h o m a s a n d C o r n e l i u s ( T 4 ) i n v e s t i g a t e d a f l o w t h a t i s d i r e c t l y r e l e v a n t t o p r e s s u r i z e d p u l p s c r e e n i n g : t h e f l o w a t a b i f u r c a t i o n a b o v e a s l o t t e d p l a t e . T h e y o b s e r v e d t h e f l o w p a t t e r n s h o w n i n F i g u r e 3 . I n p a r t i c u l a r , t h e y f o u n d a r e c i r c u l a t i n g z o n e a d j a c e n t t o t h e u p s t r e a m s i d e o f t h e s l o t t h a t c h a n g e s i n s i z e a c c o r d i n g t o t h e f l o w c o n d i t i o n s . T h o m a s a n d C o r n e l i u s a l s o n o t e d t h a t f l o w p a s s i n g t h r o u g h t h e s l o t c a m e f r o m a n " e x i t l a y e r " i n t h e m a i n f l o w , a d j a c e n t t o t h e p l a t e . B e c a u s e o f t h e v e l o c i t y p r o f i l e p r e s e n t n e x t t o t h e p l a t e , t h e f l o w r a t e i n t h e e x i t l a y e r w a s l e s s t h a n t h a t i n t h e m a i n f l o w . 2.5 T h e M o t i o n o f F i b r e s i n S c r e e n i n g S i t u a t i o n s I n i n d u s t r y , p u l p i s s c r e e n e d a t c o n s i s t e n c i e s o f 1 - 4 % , w h e r e t h e r e i s s u b s t a n t i a l i n t e r a c t i o n b e t w e e n f i b r e s . K e r e k e s e t a l . ( K 3 ) e s t i m a t e d t h a t a t s u c h c o n s i s t e n c i e s t h e r e m a y b e h u n d r e d s o f f i b r e s w i t h i n t h e v o l u m e " s w e p t " b y a s i n g l e f i b r e , i . e . w i t h i n a s p h e r i c a l v o l u m e t h a t h a s a d i a m e t e r e q u a l t o a f i b r e l e n g t h . T h i s t h e s i s , h o w e v e r , c o n s i d e r s t h e s i m p l e r p r o b l e m o f s c r e e n i n g s u s p e n s i o n s w h i c h a r e s u f f i c i e n t l y d i l u t e t h a t 15 F i g u r e 3 S t r e a m l i n e s a t a F low i n a S l o t t e d P l a t e B i f u r c a t i o n 16 f i b r e i n t e r a c t i o n i s i n s i g n i f i c a n t . T h i s i s a f i r s t s tep to u n d e r s t a n d i n g i n d u s t r i a l pulp s c r e e n i n g . Mason's " c r i t i c a l c o n c e n t r a t i o n " (M5) was u s e d t o s u g g e s t t h e maximum c o n c e n t r a t i o n at which f i b r e i n t e r a c t i o n c o u l d be n e g l e c t e d . The " c r i t i c a l c o n c e n t r a t i o n " i s c a l c u l a t e d by assuming t h a t there i s only one f i b r e w i t h i n each volume swept by a f i b r e . Pulp s c r e e n i n g i s u l t i m a t e l y concerned with the motion of f i b r e s near a screen p l a t e a p e r t u r e . Ries'e et a l . (R2) con s i d e r e d a d i l u t e suspension of r i g i d f i b r e s approaching a p e r f o r a t e d p l a t e at normal i n c i d e n c e . They found that f l u i d f o r c e s a l i g n a f i b r e p e r p e n d i c u l a r to the p l a t e . Increased flow through the p l a t e i n c r e a s e s the alignment e f f e c t , along w i t h the p r o b a b i l i t y of f i b r e p a s s a g e t h r o u g h a p l a t e a p e r t u r e . A c c o r d i n g l y , a f i b r e approaching an aperture from a flow p a r a l l e l to the s c r e e n p l a t e c o u l d be e x p e c t e d to r o t a t e to some degree as i t passes over the a p e r t u r e . Mason c o n s i d e r e d the o r i e n t a t i o n of r i g i d f i b r e s i n s i m p l e shear f l o w , and p r e d i c t e d that f i b r e s w i l l tend to a l i g n i n the d i r e c t i o n of the f l o w ( M 5 ) . The v e l o c i t y g r a d i e n t a d j a c e n t t o a s c r e e n p l a t e s u r f a c e might have a s i m i l a r e f f e c t on the flow p a r a l l e l to a screen p l a t e i n a p r e s s u r e s c r e e n : t h u s f i b r e s would t e n d t o be a l i g n e d p a r a l l e l to a s c r e e n p l a t e and be r e q u i r e d t o r o t a t e s u b s t a n t i a l l y to pass through a screen p l a t e a p e r t u r e . Anderson and Bartok i n v e s t i g a t e d the passage of f i b r e s 17 t h r o u g h a m e s h ( A l ) . T h e i r w o r k i s o f p a r t i c u l a r i n t e r e s t b e c a u s e l i k e T h o m a s a n d C o r n e l i u s , t h e y c o n s i d e r e d a f l o w w h i c h h a s a s u b s t a n t i a l c o m p o n e n t p a r a l l e l t o t h e s c r e e n i n g s u r f a c e . A l s o , l i k e R i e s e , A n d e r s o n a n d B a r t o k u s e d a d i l u t e f i b r e s u s p e n s i o n t o r e m o v e t h e i n f l u e n c e o f f i b r e i n t e r a c t i o n o n s c r e e n i n g . T h e y d e f i n e d " p e r m e a b i l i t y " a s t h e r e l a t i v e c o n c e n t r a t i o n o f f i b r e s o n t h e a c c e p t a n d f e e d s i d e s o f a s c r e e n p l a t e ( o r m e s h ) . A p e r m e a b i l i t y o f o n e r e p r e s e n t s t h e c a s e o f f i b r e s f l o w i n g f r e e l y t h r o u g h a s c r e e n p l a t e , w h i l e a p e r m e a b i l i t y o f z e r o r e p r e s e n t s t h e s i t u a t i o n w h e r e n o f i b r e c a n p a s s t h r o u g h t h e s c r e e n p l a t e . A n d e r s o n a n d B a r t o k o b s e r v e d t h a t p e r m e a b i l i t y i n c r e a s e d w i t h d e c r e a s e d f i b r e l e n g t h a n d i n c r e a s e d f i b r e s t i f f n e s s . 18 3 . A N A L Y S I S S h i v e s t i f f n e s s a n d t h e f l o w c o n d i t i o n s n e a r a s c r e e n p l a t e a p e r t u r e a r e b e l i e v e d t o b e k e y v a r i a b l e s i n p r e s s u r i z e d p u l p s c r e e n i n g . I n t h i s c h a p t e r , r e p r e s e n t a t i v e v a l u e s o f t h e s e v a r i a b l e s a r e e s t i m a t e d i n o r d e r t o e s t a b l i s h 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 r e q u i r e d t o s i m u l a t e i n d u s t r i a l p r e s s u r e s c r e e n i n g . A l s o , a n e f f i c i e n c y - r e j e c t r a t e c u r v e i s d e r i v e d t o r e l a t e i n d u s t r i a l s c r e e n p e r f o r m a n c e t o f i b r e a n d s h i v e p e r m e a b i l i t i e s a t a s i n g l e a p e r t u r e . 3 . 1 S h i v e S t i f f n e s s T h e s t i f f n e s s o f a n a t u r a l l y - o c c u r r i n g s h i v e d e p e n d s o n i t s c r o s s - s e c t i o n a l d i m e n s i o n s , t h e w o o d s p e c i e s , t h e s i z e o f t h e c o n s t i t u e n t f i b r e s , t h e d e g r e e o f d e l i g n i f i c a t i o n ( i . e . t h e e x t e n t o f t h e p u l p i n g p r o c e s s ) a n d t h e p r e s e n c e o f d e f e c t s i n t h e s h i v e . T h e a n a l y s i s b e l o w a s s u m e s t h a t s h i v e s a n d w o o d f i b r e s a r e f r e e o f d e f e c t s a n d s q u a r e i n c r o s s -s e c t i o n . A s c h e m a t i c i l l u s t r a t i o n o f w o o d f i b r e a n d s h i v e c r o s s - s e c t i o n s i s g i v e n i n F i g u r e 4. A l s o , t o s i m p l i f y t h e a n a l y s i s , a l l w o o d f i b r e s i n a b u n d l e a r e a s s u m e d t o b e i d e n t i c a l a n d i n t i m a t e l y b o n d e d t o e a c h o t h e r . I n g e n e r a l , t h e s t i f f n e s s o f a b e a m i s e q u a l t o t h e p r o d u c t o f t h e m o d u l u s o f e l a s t i c i t y ( E ) , w h i c h i s a m a t e r i a l p r o p e r t y , a n d t h e m o m e n t o f i n e r t i a ( I ) , w h i c h i s a g e o m e t r i c 19 W O O D F I B R E C R O S S - S E C T I O N N I N E W O O D F I B R E B U N D L E C R O S S - S E C T I O N F i g u r e 4 I d e a l i z e d F i b r e and Shive C r o s s - S e c t i o n s 20 p r o p e r t y . The moment of i n e r t i a of a sh i v e c r o s s - s e c t i o n i s assessed about i t s n e u t r a l a x i s and through i t s c e n t r o i d . I t can be c a l c u l a t e d using standard e n g i n e e r i n g formulae (P3). For a s i n g l e f i b r e . z l = ^ll + ( b ~ 2 t ) t 3 + ( b - 2 t ) ( b - t ) 2 t (3.1) where t = f i b r e w a l l t h i c k n e s s , and b = o v e r a l l f i b r e width. For a n i n e - f i b r e bundle, I 9 = 9 I 1 + 24b*t(b-t) (3.2) And f o r a bundle of "n" wood f i b r e s , n + 2 n 0 , 5 ( 4 t ) ( b - t ) b 2 [ r f t 3 b + ( b - 2 t ) t 3 + ( b - 2 t ) ( b - t ) 2 t ] 2 2 + 2 + 3 + . . . + 0.5 . _ (n- ^ - V (3.3) The s t i f f n e s s of a s i n g l e u n d e l i g n i f i e d f i b r e i s g i v e n i n Table I as EI = 81 x 1 0 ~ 1 2 Nm2 . Equation 3.3 may be a p p l i e d to t h i s value to estimate the s t i f f n e s s of s h i v e s , as shown i n F i g u r e 5. For t h i s purpose, f i b r e diameter i s assumed to 21 4x4 • i i i 1 1 1 ' — 10° 10* I0 4 I0 6 Number of fibre cross-sections F i g u r e 5 R e l a t i o n s h i p Between Shive S t i f f n e s s and S i z e Shive s t i f f n e s s may be p r e d i c t e d from the s t i f f n e s s of a s i n g l e f i b r e u s i n g e n g i n e e r i n g formulae. The v a l i d i t y of t h i s technique i s s u p p o r t e d by the agreement between t h e estimated s t i f f n e s s of a 4x4 inch wood beam ( c i r c l e ) and the measured "textbook" value (square). 22 be 30 microns and f i b r e w a l l t h i c k n e s s to be 4 microns. As a ch e c k , the s t i f f n e s s of a 4 inch - by - 4 inch wood beam (black spruce) may be estimated by t h i s method and compared to p u b l i s h e d s t i f f n e s s measurements (M6). This comparison i s shown i n F i g u r e 5, and the c l o s e agreement supports the use of Equation 3.3 i n e s t i m a t i n g s h i v e s t i f f n e s s . 3.2 The Flow F i e l d at a Screen P l a t e Aperture In t h i s s e c t i o n , the flows w i t h i n a t y p i c a l p r e s s u r e screen (see F i g u r e 1) are an a l y z e d , and estimates are made of the flow v e l o c i t i e s : 1) i n the annular zone between the r o t o r and s c r e e n p l a t e , and 2) w i t h i n a scre e n p l a t e a p e r t u r e . The bulk v e l o c i t y of the flow through an ap e r t u r e , V s, i s estimated by assuming that each hole (or s l o t ) passes an equal share of the accept flow, Q a. Thus, V = Q a (3.4) s ~~A s where A s i s t h e t o t a l open area of the screen p l a t e . The a p e r t u r e v e l o c i t y i s equal to 1.0 m/s f o r t y p i c a l screening c o n d i t i o n s , i . e . f o r Qa=0.107 m/s, and A s=0.103 m2. Passage of the r o t o r lugs past an ape r t u r e causes flow pulses to be s u p e r i m p o s e d on the f l o w through the a p e r t u r e . Given the l a r g e c i r c u m f e r e n t i a l d i s t a n c e between l u g s , the time between 23 p u l s e s m a y b e a s s u m e d t o b e m u c h g r e a t e r t h a n t h e p u l s e d u r a t i o n . T h u s , a s a f i r s t a p p r o x i m a t i o n , t h e p u l s e s c a n b e n e g l e c t e d . T h e b u l k v e l o c i t y o f t h e f l o w i n t h e a n n u l a r g a p i s t h e r e s u l t a n t o f t w o v e l o c i t y c o m p o n e n t s : t h e a x i a l b u l k f l o w d o w n t h e g a p a n d t h e c i r c u m f e r e n t i a l f l o w i n d u c e d b y t h e r o t o r . T h e a x i a l v e l o c i t y c o m p o n e n t , V z , d e c r e a s e s l i n e a r l y a l o n g t h e s c r e e n a x i s a s p a r t o f t h e f l o w i s d r a w n o f f t h r o u g h t h e s c r e e n p l a t e . T h u s , = 1 ( Q . - Z Q ) ( 3 . 5 ) z w h e r e A z i s t h e c r o s s - s e c t i o n a l a r e a o f t h e a n n u l u s , Q f i s t h e f e e d f l o w r a t e , H i s t h e h e i g h t o f t h e a n n u l a r s c r e e n i n g z o n e , a n d Z i s t h e a x i a l d i s t a n c e f r o m t h e e n t r y o f t h e a n n u l a r s c r e e n i n g z o n e t o t h e p o i n t o f i n t e r e s t . F o r a t y p i -c a l p r e s s u r e s c r e e n , V z d e c r e a s e s f r o m 1 . 8 t o 0 . 3 m / s , g i v e n t h a t Q f = 0 . 1 2 6 m 3 / s , A z = 0 . 0 6 8 m 2 , H = 0 . 5 1 6 m a n d Q a = 0 . 1 2 6 m 3 / s . T h e c i r c u m f e r e n t i a l v e l o c i t y c o m p o n e n t , V t , w i l l v a r y w i t h l o c a t i o n i n t h e w a k e o f t h e l u g . A s a f i r s t a p p r o x i -m a t i o n V^- m a y b e t a k e n a s c o n s t a n t a n d e s t i m a t e d f r o m t h e f l o w i n t h e w a k e o f a c y l i n d e r a t a d i s t a n c e e q u a l t o h a l f t h e c i r c u m f e r e n t i a l d i s t a n c e b e t w e e n l u g s ( S 3 ) . S p e c i f i c a l l y , V t m a y b e e x p r e s s e d i n t e r m s o f t h e t i p s p e e d o f t h e r o t o r , 24 V r , a n d a s l i p f a c t o r , S : V f c = ( 1 - S ) V r ( 3 . 6 ) T h e c i r c u m f e r e n t i a l v e l o c i t y c o m p o n e n t h a s a v a l u e o f 4 . 8 m / s g i v e n t h a t V r = 3 2 m / s a n d S = 0 . 8 5 . T h e r e s u l t a n t v e l o c i t y , V u , i s t h e v e c t o r s u m o f t h e a x i a l a n d t a n g e n t i a l v e l o c i t y c o m p o n e n t s : V = ( V 2 + V 2 ) 0 - 5 ( 3 . 7 ) u z t A r e j e c t p a r t i c l e t h u s t r a c e s a h e l i c a l p a t h d o w n t h e a n n u l a r s c r e e n i n g z o n e , a n d i t s v e l o c i t y v a r i e s f r o m 5 . 1 t o 4 . 8 m / s . A s a f i r s t a p p r o x i m a t i o n , V u may b e a s s u m e d t o h a v e a v a l u e o f 5 m / s e v e r y w h e r e i n t h e a n n u l a r s c r e e n i n g z o n e . T h e e s t i m a t e s o f V u a n d t h e s l o t v e l o c i t y , V s , a n d t h e d i r e c t i o n o f t h e s e f l o w s a r e s h o w i n F i g u r e 6 . 3 . 3 T h e E f f i c i e n c y - R e j e c t R a t e R e l a t i o n s h i p T w o e q u a t i o n s w e r e g i v e n i n S e c t i o n 2 . 3 t o d e s c r i b e p u l p s c r e e n p e r f o r m a n c e : t h e " m i x e d f l o w " e q u a t i o n , a n d t h e " p l u g f l o w " e q u a t i o n . I n t h i s s e c t i o n b o t h e q u a t i o n s a r e d e r i v e d . I f o n e a s s u m e s t h a t m i x i n g i n t h e a n n u l a r s c r e e n i n g z o n e i s i n s t a n t a n e o u s a n d c o m p l e t e , t h e p u l p i n t h e r e j e c t s t r e a m p = vs, c s ,n, c u F i g u r e 6 F l o w A d j a c e n t t o a S c r e e n P l a t e i n a P r e s s u r e S c r e e n 26 w i l l be the same as the pulp in the screening zone. A l l apertures w i l l act in p a r a l l e l , and what happens at any a p e r t u r e w i l l be r e p r e s e n t a t i v e of o v e r a l l s c r e e n p e r f o r m a n c e . As d i s c u s s e d i n the p r e v i o u s c h a p t e r , p e r m e a b i l i t y , Pp, i s the r e l a t i v e c o n c e n t r a t i o n of pulp fi b r e s on the two sides of a screen p l a t e . Thus for the mixed flow model of screening, PD = ° a-P (3.8) p C r.p where C a #p is the concentration of pulp in the accept stream and C r >p is the concentration of pulp in the reject stream, which is taken as equal to the pulp concentration in the annular screening zone. Given Equation 3.8, a material balance of the flows into and out of a pressure screen w i l l lead d i r e c t l y to the mixed flow screening equation. Q,C, Q C + Q C (3.9) f f.p a a.p v r r.p where Qf, Q a and Qr are the feed, accept and reject flows; and Cf^p, C a >p and C r >p are pulp concentrations in the feed, accept and reject streams. Equations analogous to 3.8 and 3.9 2 7 c a n a l s o b e g i v e n f o r s h i v e c o n c e n t r a t i o n : P , = C a . s h ( 3 . 1 0 ) s h — r . s h Q f C f . s h = Q a C a . s h + Q r C r . s h ( 3 ' 1 1 } D e f i n i t i o n s o f e f f i c i e n c y a n d r e j e c t r a t e c a n b e e x p r e s s e d a l g e b r a i c a l l y : Q r C r . s h ( 3 . 1 2 ) Q f C f . s h Q r C r . p ( 3 . 1 3 ) Q f C f n t f . p D i v i d i n g E q u a t i o n 3 . 1 1 b y E q u a t i o n 3 . 9 c u Q^C. , - Q C , a . s h f f . s h r r . s h C Q.C. - Q C a . p f f . p r r . p S u b s t i t u t i n g i n E q u a t i o n 3 . 8 a n d 3 . 1 0 : P C s h r . s h P C p r . p Q F C F - Q C f f . s h r r . s h Q f C . - Q C f f . p r r . p 28 S u b s t i t u t i n g i n E q u a t i o n s 3.12 a n d 3.13 0 C _ _ r r . s h - Q C , P , C , r r . s h s h r . s h E P C Q C n „ p r . p ^ r r . p - Q C — r r . p C a n c e l l i n g o u t l i k e t e r m s : p s h 4- - 1 P ~~D 1 R e a r r a n g i n g : E P R P s h ( 1 _ 1 } + X P s h ( 1 _ D + ! P v R P P R + s h - s h R P P P P (3.14) 2 9 B y c o m p a r i n g t h e a b o v e e q u a t i o n t o E q u a t i o n 2 . 1 o n e r e c o g n i z e s t h a t , P s h = 1 - - p ^ - ( 3 . 1 5 ) P w h e r e Q i s N e l s o n ' s s c r e e n i n g c o n s t a n t . S u b s t i t u t i n g E q u a t i o n 3 . 1 5 i n t o E q u a t i o n 3 . 1 4 : E = R R + ( 1 - Q ) - ( 1 - Q ) R E " 1 - Q + QR ( 2 ' 1 ) T h i s a n a l y s i s s h o w s t h a t f o r E q u a t i o n 2 . 1 t o h o l d , 1 ) T h e r e m u s t b e p e r f e c t m i x i n g i n t h e s c r e e n i n g z o n e ; a n d 2 ) T h e r a t i o o f s h i v e a n d p u l p p e r m e a b i l i t i e s m u s t b e c o n s t a n t , i . e . t h e p e r m e a b i l i t y r a t i o i s u n a f f e c t e d b y c h a n g e s i n r e j e c t r a t e . T h e o t h e r m o d e l o f p r e s s u r e s c r e e n i n g , t h e p l u g f l o w m o d e l , i s b a s e d o n t h e a s s u m p t i o n t h a t t h e f l o w d o w n t h e a n n u l a r s c r e e n i n g z o n e i s o r d e r e d , i . e . m i x i n g o c c u r s o n l y t o t h e e x t e n t t h a t r a d i a l h o m o g e n e i t y i s e n s u r e d . T h i s i s r e a s o n a b l e s i n c e f o r a p u l p s c r e e n s u c h a s t h a t s h o w n i n F i g u r e 1 , t h e r a d i a l " t h i c k n e s s " o f t h e s c r e e n i n g z o n e i s 30 small compared with the height and circumference of the zone. The a n a l y s i s using t h i s model proceeds by c o n s i d e r i n g an annular element e x t e n d i n g r a d i a l l y from the r o t o r t o the screen p l a t e . The element i s l o c a t e d at an a x i a l d i s t a n c e Z from the e n t r y t o t h e a n n u l a r s c r e e n i n g zone and has an elemental t h i c k n e s s "dZ". B a l a n c i n g the flows i n t o and out of t h i s element g i v e s , dQ = - TT D V dZ z a where Q z i s the a x i a l flow, V a i s the average r a d i a l v e l o c i t y at the screen p l a t e s u r f a c e , and D i s the outer diameter of the annular zone. C o n s i d e r i n g the flow of pulp f i b r e s i n t o and out of the annular element: where C z # p i s the average c o n c e n t r a t i o n of pulp at a d i s t a n c e "Z" from the entry to the annular s c r e e n i n g zone, and Pp i s pulp p e r m e a b i l i t y , as d e f i n e d i n Equation 3.8. S i m p l i f y i n g Equation 3.17: Q C z z.p = (Q+dQ ) (C +dC ) - TT DV P C dZ (3.17) z z z.p z.p a p z . p dC • V1* (3.18) z.p C z.p 3 1 A s s u m i n g t h a t P p i s i n d e p e n d e n t o f Z , o n e m a y i n t e g r a t e t h e a b o v e e q u a t i o n t o o b t a i n : r . p "f . p d C z . p z . p Q, N o t e : W h e n Z = 0 , Q z = Q f ; w h e n Z = H , Q z = Q r i d e n t i t i e s h o l d f o r t h e c o n c e n t r a t i o n v a r i a b l e s . S i m i l a r I n r . p " f . p J ( P - l ) I n l_ « f f . p n ( V 1 } ( 3 . 1 9 ) A n a n a l o g o u s e q u a t i o n c a n b e d e r i v e d f o r t h e r e l a t i v e c o n c e n t r a t i o n o f s h i v e s : r . s h  : f . s h ^ s h " 1 * ( 3 . 2 0 ) 32 C o m b i n i n g E q u a t i o n 3.19 w i t h t h e d e f i n i t i o n o f r e j e c t r a t e ( E q u a t i o n 3 . 1 3 ) g i v e s : L- Q f - J ( 3 . 2 1 ) L i k e w i s e E q u a t i o n 3 . 2 0 c a n b e c o m b i n e d w i t h t h e d e f i n i t i o n o f e f f i c i e n c y ( E q u a t i o n 3 . 1 2 ) t o g i v e : ( 3 . 2 2 ) C o m b i n i n g E q u a t i o n s 3.21 a n d 3.22 g i v e s : s h E = ( 3 . 2 3 ) A l t h o u g h P p a n d P s j j h a v e b e e n a s s u m e d t o b e i n d e p e n d e n t o f Z , o n e w o u l d e x p e c t P p a n d P s ^ t o b e a f f e c t e d b y c h a n g e s i n V s . T h e s l o t v e l o c i t y i s i n t u r n , i s d i r e c t l y r e l a t e d t o R . T o s i m p l i f y E q u a t i o n 3 . 2 3 , s o m e a s s u m p t i o n s m u s t b e m a d e c o n c e r n i n g t h e r e l a t i o n s h i p s b e t w e e n P p a n d R , a n d P s n a n d R . A s a f i r s t a p p r o x i m a t i o n , o n e m a y a s s u m e t h a t P p a n d P s n b o t h i n c r e a s e l i n e a r l y w i t h V s o v e r t h e r a n g e o f i n t e r e s t . T h i s 3 3 a s s u m p t i o n i s s u p p o r t e d b y t h e e x p e r i m e n t a l f i n d i n g s o f t h i s t h e s i s , d e s c r i b e d i n C h a p t e r 5 . T h u s , ( 3 . 1 9 ) ( 3 . 2 0 ) w h e r e k^ a n d k 2 a r e c o n s t a n t s o f p r o p o r t i o n a l i t y . C o m b i n i n g E q u a t i o n s 3 . 1 8 - 3 . 2 0 : E = R C ( 2 . 2 ) w h e r e C i s a c o n s t a n t , a s d e f i n e d b e l o w , P C = s h P P T h e p h y s i c a l s i g n i f i c a n c e o f C c a n b e a p p r e c i a t e d b y c o n s i d e r i n g t h r e e e x t r e m e s c r e e n i n g s i t u a t i o n s : 1 ) S h i v e p e r m e a b i l i t y i s e q u a l t o f i b r e p e r m e a b i l i t y ( i . e . C = l ) . I n t h i s s i t u a t i o n t h e r e i s n o s c r e e n i n g e f f e c t a n d e f f i c i e n c y i s e q u a l t o t h e r e j e c t r a t e . T h e s c r e e n m a y b e c o n s i d e r e d t o b e a c t i n g l i k e a t e e i n a p i p e n e t w o r k . 2 ) S h i v e p e r m e a b i l i t y i s m u c h l e s s t h a n f i b r e p e r m e a b i l i t y ( i . e . C a p p r o a c h i n g 0 ) . T h i s c o r r e s p o n d s t o n e a r - i d e a l 34 s c r e e n i n g , s i n c e e f f i c i e n c y w i l l a p p r o a c h o n e ( i . e . 1 0 0 % ) e v e n f o r a v e r y s m a l l r e j e c t r a t e . 3 ) S h i v e p e r m e a b i l i t y i s m u c h g r e a t e r t h a n f i b r e p e r m e a b i l i t y ( i . e . C > 1 ) . T h i s i s a n u n u s u a l s i t u a t i o n s i n c e e f f i c i e n c y w o u l d b e l e s s t h a n t h e r e j e c t r a t e a n d t h e a c c e p t p u l p w o u l d c o n t a i n m o r e s h i v e s t h a n t h e f e e d p u l p . O n e m i g h t c a l l t h i s " r e v e r s e s c r e e n i n g " . T h e d e r i v a t i o n s p r e s e n t e d a b o v e f o r t h e m i x e d f l o w s c r e e n i n g e q u a t i o n a n d t h e p l u g f l o w s c r e e n i n g e q u a t i o n a r e s i m p l e a n d s t r a i g h t f o r w a r d . T h e a s s u m p t i o n s u n d e r l y i n g t h e t w o m o d e l s a r e c l e a r l y s t a t e d . M o s t i m p o r t a n t l y , t h e s e e q u a t i o n s p r o v i d e a m e a n s o f r e l a t i n g p e r m e a b i l i t y m e a s u r e m e n t s m a d e a t a s i n g l e a p e r t u r e i n a l a b o r a t o r y , t o i n d u s t r i a l s c r e e n p e r f o r m a n c e . 35 4 . E X P E R I M E N T A L WORK T h e p r e c e d i n g a n a l y s i s r e l a t e s f i b r e p e r m e a b i l i t y a t a s i n g l e s l o t t o o v e r a l l p u l p s c r e e n p e r f o r m a n c e . T h e e x p e r i m e n t a l p a r t o f t h i s w o r k e x a m i n e s t h e m o t i o n o f f i b r e s i n a d i l u t e s u s p e n s i o n n e a r t h e e n t r y o f a s i n g l e s l o t . T h e o b j e c t i v e s o f t h e e x p e r i m e n t a l w o r k w e r e t o d e t e r m i n e : 1 . T h e i n f l u e n c e o f f i b r e , f l o w a n d s l o t v a r i a b l e s o n p e r m e a b i l i t y . 2 . How f i b r e s m o v e a t a c h a n n e l - s l o t f l o w b i f u r c a t i o n . A f l o w l o o p w i t h a p l e x i g l a s c h a n n e l w a s c o n s t r u c t e d t o s i m u l a t e t h e f l o w p a s t a s c r e e n p l a t e s l o t i n a p r e s s u r e s c r e e n . P e r m e a b i l i t y w a s m e a s u r e d b y s a m p l i n g t h e ( a c c e p t ) f l o w t h r o u g h t h e s l o t a n d t h e ( r e j e c t ) f l o w d o w n s t r e a m o f t h e s l o t . F i b r e t r a j e c t o r i e s i n t h e p l e x i g l a s c h a n n e l w e r e o b s e r v e d u s i n g h i g h s p e e d c i n e - f i l m s . A d e s c r i p t i o n o f t h e a p p a r a t u s , e x p e r i m e n t a l p r o c e d u r e s a n d a n a l y t i c p r o c e d u r e s i s g i v e n b e l o w . 4 . 1 F i b r e S u s p e n s i o n E i g h t t y p e s o f f i b r e s w e r e u s e d i n t h i s s t u d y , a n d t h e i r p r o p e r t i e s a r e l i s t e d i n T a b l e I I . D e t a i l e d l e n g t h d i s t r i b u t i o n s o f t h e i n d i v i d u a l f i b r e t y p e s a r e g i v e n i n A p p e n d i x I V . 3 6 T a b l e I I : P h y s i c a l P r o p e r t i e s o f E x p e r i m e n t a l F i b r e s m a t e r i a l a v e r a g e n o m i n a l e s t i m a t e d l e n g t h d i a m e t e r s t i f f n e s s (mm) (mm) ( x l O - 1 2 N m 2 ) n y l o n 1 . 0 . 0 4 3 3 5 0 n y l o n 1 . 5 . 0 4 3 3 5 0 n y l o n 3 . 1 . 0 4 3 3 5 0 n y l o n 3 . 1 . 2 3 0 2 9 0 0 0 0 r a y o n 1 . 0 . 0 1 2 0 . 5 r a y o n 1 . 2 . 0 2 0 4 7 p l 0 . r l 4 3 . 3 . 0 3 0 4 k r a f t p u l p 8 p l 4 . r 2 8 2 . 6 . 0 3 0 4 k r a f t p u l p 9 w h o l e 2 . 6 . 0 3 0 4 k r a f t p u l p 1 0 w h o l e 1 . 8 . 0 3 0 1 0 0 C T M P p u l p 3 7 I n p r e p a r i n g t h e f i b r e s u s p e n s i o n , c a r e w a s t a k e n t o e n s u r e t h a t t h e f i b r e s w e r e d i s c r e t e , d i m e n s i o n a l l y s t a b l e , u n d a m a g e d , a n d p r e s e n t a t t h e a p p r o p r i a t e c o n c e n t r a t i o n . B e c a u s e w o o d f i b r e s a r e p r o n e t o e n t a n g l e m e n t , t h e y w e r e d i s p e r s e d i n a d i s i n t e g r a t o r b e f o r e u s e . S y n t h e t i c f i b r e s w e r e f o u n d b o n d e d t o g e t h e r , b u t n o t i n s i g n i f i c a n t c o n c e n -t r a t i o n s . A l l f i b r e s w e r e s t o r e d i n w a t e r t o e n s u r e t h a t n o c h a n g e i n p h y s i c a l p r o p e r t i e s o c c u r r e d a t t h e s t a r t o f a t r i a l b e c a u s e o f w a t e r a b s o r p t i o n . F i b r e s w e r e i n s p e c t e d b e f o r e a n d a f t e r a t r i a l t o v e r i f y t h a t t h e y w e r e u n d a m a g e d . T o m i n i m i z e t h e r i s k o f f i b r e d a m a g e , t r i a l d u r a t i o n w a s s h o r t ( l e s s t h a n f i f t e e n m i n u t e s ) a n d f i b r e s w e r e u s e d f o r n o m o r e t h a n t h r e e t r i a l s . T w o t e c h n i q u e s w e r e u s e d t o m e a s u r e f i b r e c o n c e n t r a t i o n i n t h i s s t u d y . I n a d i r e c t m e t h o d , f i b r e s w e r e f i l t e r e d f r o m a 5 0 0 m l s a m p l e a n d c o u n t e d u s i n g a 1 2 . 5 p o w e r s t e r e o m i c r o s c o p e . T h i s m e t h o d i s u s e f u l w h e n a l l o f t h e f i b r e s i n t h e s u s p e n s i o n a r e a l i k e ( e g . f o r p r e c i s e l y - c u t s y n t h e t i c f i b r e s ) . T h e r a n g e o f c o n c e n t r a t i o n o v e r w h i c h t h i s m e t h o d c a n b e u s e d e f f e c t i v e l y w a s f o u n d t o b e 5 0 0 t o 2 0 0 0 f i b r e s p e r l i t r e . L o w e r c o n c e n t r a t i o n s g a v e h i g h 1 y - v a r i a b 1 e m e a s u r e m e n t s , w h i l e h i g h e r c o n c e n t r a t i o n s m a d e c o u n t i n g d i f f i c u l t . T h e s e c o n d m e t h o d o f d e t e r m i n i n g f i b r e c o n c e n t r a t i o n i n v o l v e d a K a j a a n i F S - 1 0 0 F i b r e L e n g t h A n a l y z e r ( P 4 ) . T h i s 3 8 i n s t r u m e n t c o u n t s f i b r e s a s w e l l a s m e a s u r i n g t h e i r l e n g t h s . O n e m a y t h u s u s e f i b r e s o f v a r i o u s l e n g t h s i n a t e s t , a n d s i m u l t a n e o u s l y m e a s u r e c h a n g e s i n f i b r e c o n c e n t r a t i o n f o r a r a n g e o f f i b r e l e n g t h s . T h e F S - 1 0 0 o p e r a t e s b y d r a w i n g a 4 0 t o 8 0 m l s a m p l e t h r o u g h a c a p i l l a r y t u b e a n d p a s t a r o w o f p h o t o d i o d e s . T h e s i g n a l f r o m t h e p h o t o d i o d e s i s t h e n i n t e r p r e t e d t o p r o v i d e a m e a s u r e o f t h e n u m b e r o f f i b r e s a n d t h e f i b r e l e n g t h d i s t r i b u t i o n . A d i s a d v a n t a g e o f t h e F S - 1 0 0 i n t h i s a p p l i c a t i o n i s t h a t i t r e q u i r e s a c o n c e n t r a t i o n o f a b o u t 5 0 0 0 0 f i b r e s p e r l i t r e . A s d i s c u s s e d i n C h a p t e r 5 , s u c h a h i g h c o n c e n t r a t i o n m a y c a u s e f i b r e s t o a c c u m u l a t e a t t h e s l o t e n t r y a t a r a t e t h a t a f f e c t s p e r m e a b i l i t y m e a s u r e m e n t s . I n f u t u r e w o r k , i t m a y b e p r e f e r a b l e t o o p e r a t e t h e f l o w l o o p w i t h a f i b r e c o n c e n t r a t i o n o f 1 0 0 0 f i b r e s p e r l i t r e , a n d t h e n c o n c e n t r a t e t h e s a m p l e s f o r a n a l y s i s w i t h t h e K a j a a n i F S - 1 0 0 . 4 . 2 F l o w L o o p T h e p r i n c i p a l c o m p o n e n t s o f t h e f l o w l o o p u s e d i n t h i s s t u d y a r e s h o w n i n F i g u r e s 7 , 8 a n d 9 . E a c h c o m p o n e n t s h o w n i n F i g u r e 7 a n d i t s f u n c t i o n a r e d e s c r i b e d b e l o w . A . R e s e r v o i r . T h e r e s e r v o i r s e r v e d t w o f u n c t i o n s : I t w a s w h e r e f i b r e c o n c e n t r a t i o n a n d w a t e r t e m p e r a t u r e w a s a d j u s t e d p r i o r t o t h e s t a r t o f a t r i a l . A n d d u r i n g a t r i a l , t h e r e s e r v o i r w a s t h e p u m p ' s s u p p l y t a n k . W a t e r t e m p e r a t u r e 39 R e s e r v o i r P u m p R e t u r n L i n e F e e d L i n e P l e x i g l a s T e s t S e c t i o n F . A c c e p t L i n e G . A c c e p t S a m p l i n g R e c e p t a c l e H . R e j e c t I . R e j e c t S a m p l i n g L i n e J . R e j e c t S a m p l i n g R e c e p t a c l e F i g u r e 7 F l o w L o o p S c h e m a t i c 4 0 F i g u r e 8 F l o w L o o p a n d P l e x i g l a s C h a n n e l 4 1 F i g u r e 9 P l e x i g l a s C h a n n e l a n d H i g h S p e e d C i n e - C a m e r a 4 2 i n the r e s e r v o i r was set to 2 0 degrees Centigrade, i . e . room temperature. The op e r a t i n g water volume i n the r e s e r v o i r was only 8 0 l i t r e s , i n order to minimize the number of f i b r e s r e q u i r e d to conduct an experiment. B.C.D. Pump and F e e d P i p i n g . An ope n - i mpe 11 e r c e n t r i f u g a l pump (B) was used to pump the suspension through a pipe (D) to the p l e x i g l a s t e s t channel ( E ) . The bypass l i n e (C) was shut o f f ex c e p t when a very low flow to the channel was r e q u i r e d . A l l pipes i n the loop were 1.5 i n c h PVC. E. P l e x i g l a s Test S e c t i o n . The p l e x i g l a s t e s t s e c t i o n i s the key element i n the flow l o o p and i t i s shown i n F i g u r e 9. I t contains a s t r a i g h t 3 0 cm long square channel with a height (19 mm) that i s roughly e q u a l t o the r a d i a l d i s t a n c e between the r o t o r drum and s c r e e n p l a t e i n an i n d u s t r i a l screen. The bottom w a l l of the channel c o n t a i n s a s i n g l e s l o t , p e r p e n d i c u l a r to the channel a x i s . T h i s s l o t s i m u l a t e s an a p e r t u r e i n a p r e s s u r e s c r e e n . D i f f e r e n t , i n t e r c h a n g e a b l e t e s t s e c t i o n s were used i n t h i s study that had s l o t widths of 0 . 2 5 mm, 0 . 5 mm and 1 mm. (Note: t h e s e are the nominal widths at the s l o t e n t r y . The width of the s l o t on the discharge s i d e was s l i g h t l y g r e a t e r , as i s normal with commercial screen p l a t e s ) . Turbulence was generated by an abrupt c o n t r a c t i o n at the c h a n n e l e n t r y . The l e v e l of turbule n c e at the s l o t was v a r i e d by using channels that had 4 3 t h e s l o t a t d i f f e r e n t d i s t a n c e s f r o m t h e c h a n n e l e n t r y . M o s t t r i a l s w e r e r u n w i t h t h e s l o t l o c a t e d 8 e q u i v a l e n t d i a m e t e r s f r o m t h e c h a n n e l e n t r y . O n e t r i a l w a s r u n w i t h a n e n t r y l e n g t h o f 2 e q u i v a l e n t d i a m e t e r s , a n d a n o t h e r w i t h 1 4 e q u i v a l e n t d i a m e t e r s . A n e s t i m a t e o f t h e t u r b u l e n c e i n t e n s i t y a t t h e s l o t c a n ' b e m a d e f r o m m e a s u r e m e n t s i n t h e l i t e r a t u r e . L i s s e n b u r g e t a l . f o u n d t h a t t h e r a t i o o f t h e t u r b u l e n c e v e l o c i t y c o m p o n e n t t o t h e l o c a l m e a n v e l o c i t y i n a p i p e t e n d i a m e t e r s b e y o n d a c o n s t r i c t i o n i s a b o u t 0 . 0 9 a t t h e c e n t r e o f t h e p i p e a n d 0 . 3 5 " v e r y c l o s e t o t h e w a l l " ( L 3 ) . F . D i s c h a r g e P i p i n g ( A c c e p t F l o w ) . T h e f l o w t h r o u g h t h e s l o t i n t h e p l e x i g l a s c h a n n e l p a s s e s i n t o a s m a l l c h a m b e r a n d t h e n f l o w s t o t h e r e s e r v o i r t h r o u g h f l e x i b l e t u b i n g ( L i n e F ) . T h e t u b i n g o u t l e t may b e m o v e d e a s i l y f r o m t h e r e s e r v o i r t o S a m p l i n g R e c e p t a c l e K f o r f l o w r a t e a n d f i b r e c o n c e n t r a t i o n m e a s u r e m e n t s . T a p e r e d p l a s t i c i n s e r t s , i n s t a l l e d i n t h e t u b i n g o u t l e t , r e s t r i c t t h e l i n e a n d c o n t r o l t h e f l o w r a t e w i t h o u t i m p e d i n g t h e f l o w o f f i b r e s . T h e v e l o c i t y i n a 0 . 5 mm w i d e s l o t m a y b e v a r i e d f r o m 0 t o 9 m / s . A s d e s c r i b e d p r e v i o u s l y , t h e s l o t v e l o c i t y i n a c o m m e r c i a l s c r e e n i s e s t i m a t e d t o b e 1 m / s . S q u e e z i n g t h e t u b i n g c a u s e s b a c k -f l u s h i n g t h r o u g h t h e s l o t . B e f o r e a t r i a l , b a c k f l u s h i n g w a s u s e d t o p u r g e a i r f r o m t h e t e s t s e c t i o n , o r t o c l e a r t h e s l o t o f a n y f i b r e a c c u m u l a t i o n . 44 H . D i s c h a r g e P i p i n g ( R e j e c t F l o w ) : M o s t o f t h e f l o w f r o m t h e p l e x i g l a s t e s t s e c t i o n r e t u r n s t o t h e r e s e r v o i r v i a L i n e H . A d i a p h r a g m v a l v e i n t h i s l i n e p e r m i t s t h e f e e d v e l o c i t y i n t h e p l e x i g l a s c h a n n e l t o b e v a r i e d f r o m 0 t o 8 m / s . T h i s r a n g e i n c l u d e s t h e a v e r a g e v e l o c i t y p a r a l l e l t o a s c r e e n p l a t e i n a n i n d u s t r i a l s c r e e n ; e s t i m a t e d i n S e c t i o n 3 . 2 t o b e 5 m / s . T h e t h r e e - w a y v a l v e i n L i n e F i s n o r m a l l y s e t t o d i r e c t t h e f l o w a n d b a c k t o R e s e r v o i r A . T h i s f l o w c r e a t e s e n o u g h t u r b u l e n c e i n t h e r e s e r v o i r t o m a i n t a i n a u n i f o r m f i b r e s u s p e n s i o n . T o s a m p l e t h e r e j e c t f l o w , t h e t h r e e - w a y v a l v e i s t u r n e d t o r e d i r e c t t h e f l o w a l o n g L i n e I a n d i n t o S a m p l i n g R e c e p t a c l e J f o r a c a r e f u l l y m e a s u r e d l e n g t h o f t i m e . T h e s a m p l e i s t h e n w e i g h e d ( t o d e t e r m i n e t h e f l o w r a t e ) a n d s u b s a m p l e s a r e t a k e n f o r f i b r e c o n c e n t r a t i o n m e a s u r e m e n t . A d d i t i o n a l t e c h n i c a l d e t a i l s o f t h e f l o w l o o p a r e g i v e n i n A p p e n d i x I I I . 4 . 3 C i n e - P h o t o g r a p h y H i g h s p e e d c i n e - f i l m s w e r e t a k e n o f f i b r e m o t i o n n e a r t h e s l o t e n t r y i n t h e p l e x i g l a s t e s t s e c t i o n . U s i n g b a c k -l i g h t i n g a n d 3 mm b l a c k n y l o n f i b r e s , c l e a r s i l h o u e t t e i m a g e s w e r e o b t a i n e d . T h e f i e l d o f f o c u s w a s l i m i t e d ( a p p r o x i -m a t e l y ) t o t h e c e n t r a l h a l f o f t h e c h a n n e l . T h u s f i b r e s n e a r e i t h e r s i d e w a l l w e r e n o t i n f o c u s , a n d c o u l d b e i d e n t i f i e d 4 5 a n d d i s r e g a r d e d . T o e s t a b l i s h t h e f i e l d o f f o c u s , t h e p i p e i m m e d i a t e l y d o w n s t r e a m o f t h e c h a n n e l w a s r e m o v e d a n d a t h i n w i r e w a s i n s e r t e d a n d m o v e d b a c k a n d f o r t h . A f r a m i n g r a t e o f a p p r o x i m a t e l y 3 0 0 0 p i c t u r e s p e r s e c o n d w a s u s e d f o r t h e t h r e e f i l m s d i s c u s s e d i n t h e n e x t c h a p t e r . N o t e : T h e 1 0 0 f o o t f i l m s u s e d i n t h i s s t u d y c o n t a i n j u s t o v e r 4 0 0 0 f r a m e s e a c h . T h e f i b r e c o n c e n t r a t i o n s u s e d f o r t h e s e f i l m s w e r e a b o u t 2 0 0 0 f i b r e s p e r l i t r e ; a b o v e t h i s c o n c e n t r a t i o n f i b r e s o v e r l a p a n d t r a c k i n g i n d i v i d u a l f i b r e s b e c o m e s d i f f i c u l t . F u r t h e r t e c h n i c a l d e t a i l s o f t h e f i l m i n g a n d l i g h t i n g e q u i p m e n t a r e g i v e n i n A p p e n d i x I I I . T h e p o s i t i o n a n d o r i e n t a t i o n o f e a c h f i b r e i n e a c h f i l m f r a m e w a s r e c o r d e d b y m a n u a l l y d i g i t i z i n g t h e f i b r e i m a g e s . T h e f i l m w a s p r o j e c t e d t o r e f l e c t f r o m a m i r r o r o n t o a h o r i z o n t a l d i g i t i z i n g p a d . T h e o p e r a t o r e n t e r e d t h e l o c a t i o n o f e a c h f i b r e e n d - p o i n t a n d m i d - p o i n t w i t h a c u r s o r , t h e n a d v a n c e d t h e f i l m o n e f r a m e a n d r e p e a t e d t h e p r o c e s s . T h e m i r r o r a n d d i g i t i z i n g p a d a r e s h o w n i n F i g u r e 1 0 , a l o n g w i t h t h e c o m p u t e r u s e d f o r d a t a s t o r a g e . C o m p u t e r p r o g r a m m e s w e r e w r i t t e n t o m e e t t h e v a r i o u s n e e d s o f t h e d i g i t i z i n g p r o c e d u r e : s t o r a g e o f f i b r e p o s i t i o n s a n d a s s o c i a t e d f r a m e n u m b e r s o n c o m p u t e r d i s k e t t e s ; c o r r e c t i o n o f f i b r e p o s i t i o n s t o a c c o u n t f o r r e l a t i v e m o t i o n b e t w e e n t h e c a m e r a a n d c h a n n e l d u e t o c a m e r a v i b r a t i o n ; 46 F i g u r e 1 0 F i l m A n a l y z i n g E q u i p m e n t 4 7 i n s t a n t d i s p l a y o f f i b r e i m a g e s o n t h e c o m p u t e r m o n i t o r ; c o l l e c t i o n o f i s o l a t e d f i b r e i m a g e s t o f o r m f i b r e t r a j e c -t o r i e s ; a n d t h e p r i n t i n g o f a l i s t o f a l l ' f i b r e e n d - p o i n t c o o r d i n a t e s , f i b r e a n g l e s , l i n e a r a n d r o t a t i o n a l v e l o c i t i e s , t r a j e c t o r y i n d i c e s a n d f i l m f r a m e i n d i c e s . T h e s e c o m p u t e r p r o g r a m m e s a r e l i s t e d i n A p p e n d i x I I a l o n g w i t h p r o g r a m m e s f o r t h e r e t r i e v a l a n d a n a l y s i s o f d i g i t i z e d f i b r e t r a j e c -t o r i e s . F i b r e l o c a t i o n w a s d e f i n e d a s t h e m i d - p o i n t o f t h e l i n e s e g m e n t c o n n e c t i n g t h e e n d p o i n t s o f t h e f i b r e . T h e d i s t a n c e f r o m t h e f i b r e t o t h e s c r e e n p l a t e w a s a s s e s s e d a t a p l a n e 1 . 7 5 mm u p s t r e a m o f t h e u p s t r e a m e d g e o f t h e s l o t . T h i s d i s t a n c e c o r r e s p o n d s t o h a l f t h e d i s t a n c e b e t w e e n s l o t s i n a t y p i c a l i n d u s t r i a l s c r e e n . L o c a l f i b r e c o n c e n t r a t i o n s c a n n o t b e a s s e s s e d s i m p l y b y c o u n t i n g t h e n u m b e r o f f i b r e s t h a t a p p e a r i n a n y p a r t i c u l a r z o n e b e c a u s e t h e a v e r a g e v e l o c i t y t h r o u g h t h e z o n e w i l l v a r y a c c o r d i n g t o t h e w a l l p r o x i m i t y , a s d i s c u s s e d i n C h a p t e r 2 . T h e p r o c e d u r e f o l l o w e d h e r e w a s t o c o n s i d e r i s o l a t e d f i l m f r a m e s a n d a s s e s s t h e r e l a t i v e c o n c e n t r a t i o n i n e a c h z o n e o f t h e s e " s n a p s h o t s " o f t h e f l o w . M e a s u r e m e n t s f r o m t h e f i l m f r a m e s w e r e a c c u m u l a t e d t o g i v e a n a s s e s s m e n t o f t h e f i b r e c o n c e n t r a t i o n r e l a t i v e t o t h a t i n t h e c e n t r e o f t h e c h a n n e l . F i b r e t r a j e c t o r i e s w e r e c l a s s i f i e d m a n u a l l y i n t o s i x c a t e g o r i e s , a s d i s c u s s e d i n C h a p t e r 5 . F i b r e v e l o c i t y a n d 4 8 r o t a t i o n r a t e w e r e o b t a i n e d b y m u l t i p l y i n g t h e c h a n g e i n f i b r e p o s i t i o n ( o r f i b r e a n g l e ) b e t w e e n i m a g e s o n e i t h e r s i d e o f t h e a f o r e m e n t i o n e d p l a n e o f i n t e r e s t b y t h e f i l m f r a m i n g r a t e . F r a m i n g r a t e s a n d a d e s c r i p t i o n o f h o w t h e y a r e d e t e r m i n e d a r e g i v e n i n A p p e n d i x I I I . 4 9 5 . R E S U L T S AND D I S C U S S I O N T h e i n f l u e n c e o f f i b r e , f l o w a n d s l o t v a r i a b l e s o n p e r m e a b i l i t y , a n d t h e m o t i o n o f f i b r e s n e a r a s l o t a r e e x a m i n e d i n t h i s c h a p t e r . F i n a l l y , a m o d e l i s p r o p o s e d t o d e s c r i b e w h a t f a c t o r s l i m i t t h e p a s s a g e o f f i b r e s t h r o u g h a s c r e e n s l o t . 5 . 1 P e r m e a b i l i t y M e a s u r e m e n t s T h e e f f e c t s o f f i b r e l e n g t h a n d f l e x i b i l i t y o n p e r m e a b i l i t y a r e s h o w n i n F i g u r e 1 1 . F o r a l l t h r e e f i b r e t y p e s c o n s i d e r e d i n t h i s s t u d y ( k r a f t , C T M P , a n d n y l o n ) , p e r m e a b i l i t y d e c r e a s e s s h a r p l y w i t h i n c r e a s e d f i b r e l e n g t h . T h e a s s o c i a t e d i n f l u e n c e o f f i b r e f l e x i b i l i t y ( i . e . f i b r e t y p e ) i s a l s o d e p e n d e n t o n f i b r e l e n g t h . F l e x i b i l i t y h a s l i t t l e e f f e c t o n p e r m e a b i l i t y f o r s h o r t f i b r e s ( l e s s t h a n 1 mm l o n g ) , b u t i t s i n f l u e n c e i n c r e a s e s w i t h i n c r e a s e d f i b r e l e n g t h . T h e p e r m e a b i l i t y o f 3 mm l o n g k r a f t p u l p f i b r e s i s a b o u t f i v e t i m e s t h a t o f t h e s t i f f e r n y l o n f i b r e s . T h e s e r e l a t i o n s h i p s b e t w e e n f i b r e l e n g t h , f i b r e f l e x i b i l i t y a n d p e r m e a b i l i t y a r e a l s o s h o w n i n F i g u r e 1 2 . T h e s e f i n d i n g s a r e c o n s i s t e n t w i t h i n d u s t r i a l p u l p s c r e e n i n g d a t a o b t a i n e d b y F r i t h a n d F i s h e r ( F l ) . T h e i r d a t a s h o w t h a t t h e l i k e l i h o o d o f s h i v e s p a s s i n g t h r o u g h t h e s c r e e n a p e r t u r e s d e c r e a s e s w i t h i n c r e a s e d s h i v e l e n g t h a n d w i d t h . Fibre length (mm) F i g u r e 11 E f f e c t s o f F i b r e L e n g t h a n d F i b r e T y p e o n P e r m e a b i l i t y 1.0 O I mm rayon • I mm nylon • 3 mm kraft pulp • 3 mm nylon Fibre stiffness (l\Lm2) F i g u r e 12 E f f e c t o f F i b r e S t i f f n e s s o n P e r m e a b i l i t y 5 2 T h e r e i s s o m e d i s c r e p a n c y b e t w e e n p e r m e a b i l i t y m e a s u r e m e n t s b a s e d o n m a n u a l c o u n t s , a n d m e a s u r e m e n t s m a d e w i t h t h e K a j a a n i F S - 1 0 0 F i b r e L e n g t h A n a l y z e r , a s s h o w n i n F i g u r e 1 1 . F o r k r a f t p u l p f i b r e s , t h e m a n u a l c o u n t s g a v e h i g h e r p e r m e a b i l i t y v a l u e s ; b u t f o r n y l o n f i b r e s t h e r e w a s n o s i g n i f i c a n t d i f f e r e n c e . T h i s e f f e c t i s l i k e l y d u e t o t h e h i g h e r f i b r e c o n c e n t r a t i o n s u s e d i n t e s t s i n v o l v i n g t h e K a j a a n i F S - 1 0 0 , a n d t h e t e n d e n c y f o r f l e x i b l e f i b r e s t o " s t a p l e " a t t h e s l o t e n t r y . T h e p h e n o m e n o n o f f i b r e s t a p l i n g i s c o n s i d e r e d l a t e r i n t h i s c h a p t e r . I n m o s t t e s t s , t h e a m o u n t o f f i b r e s s t a p l e d a t t h e s l o t e n t r y w o u l d n o t b e s u f f i c i e n t t o a f f e c t t e s t r e s u l t s . H i g h e r f i b r e c o n c e n t r a t i o n s a n d t h e u s e o f f l e x i b l e f i b r e s h o w e v e r , w e r e o b s e r v e d t o c a u s e i n c r e a s e d s t a p l i n g . I n t e s t s i n v o l v i n g t h e K a j a a n i F S - 1 0 0 a n d f l e x i b l e k r a f t p u l p f i b r e s , t h e a c c u m u l a t i o n o f s t a p l e d f i b r e s may h a v e i m p e d e d t h e p a s s a g e o f f i b r e s t h r o u g h t h e s l o t a n d c a u s e d a d r o p i n p e r m e a b i l i t y . S i n c e t h i s t h e s i s i s m a i n l y c o n c e r n e d w i t h t h e p a s s a g e o f f i b r e s t h r o u g h u n o b s t r u c t e d s l o t s , k r a f t f i b r e p e r m e a b i l i t y d a t a u s e d s u b s e q u e n t l y i n t h i s t h e s i s w i l l b e b a s e d o n m a n u a l c o u n t s . T h e d a t a p r e s e n t e d i n F i g u r e s 1 1 a n d 1 2 s u p p o r t t h e c l a i m t h a t w h a t h a p p e n s i n t h e s l o t o f t h e e x p e r i m e n t a l t e s t s e c t i o n u s e d i n t h i s s t u d y c o r r e s p o n d s i n a g e n e r a l w a y , t o w h a t h a p p e n s a t a n a p e r t u r e i n a n i n d u s t r i a l p r e s s u r e s c r e e n . 5 3 T h e r e i s a f o r t y - t w o f o l d d i f f e r e n c e i n p e r m e a b i l i t y b e t w e e n ( 2 . 6 mm l o n g ) k r a f t p u l p f i b r e s a n d (3 mm l o n g ) s h i v e - l i k e n y l o n f i b r e s . T h i s r a t i o g i v e s a v a l u e o f C = 0 . 0 2 i n E q u a t i o n 2 . 2 . T h e r e s u l t i n g e f f i c i e n c y - r e j e c t r a t e c u r v e i s t y p i c a l o f c u r v e s f o u n d i n i n d u s t r y , a n d o u r a t t e m p t t o s i m u l a t e i n d u s t r i a l p u l p s c r e e n i n g m a y b e c o n s i d e r e d s u c c e s s f u l . A s e c o n d a n d i m p o r t a n t c o n c l u s i o n i s t h a t , s i n c e t h e s e r e s u l t s w e r e o b t a i n e d u s i n g v e r y d i l u t e f i b r e s u s p e n s i o n s , s i g n i f i c a n t f i b r e i n t e r a c t i o n i s n o t a p r e r e q u i s i t e f o r p u l p s c r e e n i n g . I n c r e a s e d s l o t v e l o c i t y a n d d e c r e a s e d u p s t r e a m v e l o c i t y b o t h c a u s e d i n c r e a s e d p e r m e a b i l i t y , a s s h o w n i n F i g u r e s 1 3 a n d 1 4 . T h e r a n g e o f s l o t v e l o c i t i e s s t u d i e d w a s e x t e n d e d f a r b e y o n d t h e e s t i m a t e d 1 m / s s l o t v e l o c i t y o f a n i n d u s t r i a l p r e s s u r e s c r e e n i n o r d e r t o e x a g g e r a t e a n d c l a r i f y t h e e f f e c t o f i n c r e a s e d s l o t v e l o c i t y . W i d e r s l o t s a r e a s s o c i a t e d w i t h i n c r e a s e d f i b r e p e r m e a -b i l i t i e s f o r b o t h 1 mm a n d 3 mm n y l o n f i b r e s , a s s h o w n i n F i g u r e 1 5 . C h a n g e s i n c h a n n e l e n t r y l e n g t h t o t h e s l o t d o n o t , h o w e v e r , a f f e c t f i b r e p e r m e a b i l i t y m u c h , a s s h o w n i n F i g u r e 1 6 . 5 . 2 F i b r e T r a j e c t o r i e s N e a r a S l o t t e d P l a t e C o n s i d e r a b l e i n s i g h t i n t o p u l p s c r e e n i n g f u n d a m e n t a l s m a y b e g a i n e d f r o m t h e u s e o f h i g h s p e e d c i n e - p h o t o g r a p h y . Slot velocity (m/s) F i g u r e 1 3 E f f e c t s o f S l o t V e l o c i t y a n d F i b r e T y p e o n P e r m e a b i l i t y Slot velocity (m/s) F i g u r e 14 E f f e c t s o f S l o t V e l o c i t y a n d U p s t r e a m V e l o c i t y o n P e r m e a b i l i t y 5 6 F i g u r e 1 5 E f f e c t s o f S l o t V e l o c i t y a n d S l o t W i d t h o n P e r m e a b i l i t y 57 F i g u r e 16 E f f e c t o f E n t r y L e n g t h o n P e r m e a b i l i t y 5 8 V i s u a l o b s e r v a t i o n c a n r e v e a l h o w f i b r e s a r e d i s t r i b u t e d a c r o s s t h e c h a n n e l , how t h e y a r e o r i e n t e d i n t h e c h a n n e l , a n d h o w t h e y m o v e w h e n t h e y a p p r o a c h a n d i n t e r a c t w i t h t h e s l o t . T h r e e f i l m s w e r e a n a l y z e d i n t h i s s t u d y : F i l m 1 i n v o l v e d u p s t r e a m a n d s l o t v e l o c i t i e s o f 7 . 2 a n d 3 . 2 m / s r e s p e c t i v e l y , a n d 0 . 2 3 0 mm d i a m e t e r s h i v e - l i k e n y l o n f i b r e s . F i l m 2 i n v o l v e d t h e s a m e f l o w c o n d i t i o n s , b u t m o r e f l e x i b l e ( 0 . 0 4 3 mm d i a m e t e r ) n y l o n f i b r e s . F i l m 3 a l s o i n v o l v e d 0 . 0 4 3 mm f i b r e s , b u t a s l o t v e l o c i t y o f 7 . 1 m / s . D e t a i l s o f 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 a r e g i v e n i n T a b l e V . S o m e t y p i c a l f i l m f r a m e s f r o m F i l m 1 a r e s h o w n i n F i g u r e 1 7 . A s d i s c u s s e d i n C h a p t e r 4 , t h e f i l m i m a g e s w e r e d i g i t i z e d f o r a n a l y s i s , a n d e x a m p l e s o f c o m p u t e r - g e n e r a t e d t r a j e c t o r i e s a r e s h o w n i n F i g u r e 1 8 . A w e l l - d e f i n e d e x i t l a y e r , s u c h a s t h a t s h o w n i n F i g u r e 3 , w a s e v i d e n t i n a l l t h r e e f i l m s . T h e s e o b s e r v a t i o n s w e r e b a s e d o n t h e m o t i o n o f s m a l l d e b r i s i n t h e f l o w w h i c h a c t e d a s f l o w t r a c e r s . A n a l y s i s o f f i b r e l o c a t i o n i n t h e f i l m s r e v e a l e d t h a t f i b r e c o n c e n t r a t i o n i n t h e e x i t l a y e r i s l o w e r t h a n i n t h e m a i n s t r e a m . T h e c a u s e o f t h i s e f f e c t i s u n c e r t a i n . I t m a y b e a c o n s e q u e n c e o f c o l l i s i o n s b e t w e e n t h e f i b r e s a n d t h e w a l l ; o r t h e v e l o c i t y g r a d i e n t a d j a c e n t t h e w a l l m a y c a u s e f i b r e s t o m i g r a t e a w a y f r o m t h e w a l l . T h e r o l e o f t h i s " w a l l e f f e c t " i n s c r e e n i n g m a y b e s i g n i f i c a n t i f t h e c o n c e n t r a t i o n g r a d i e n t d e c r e a s e s f o r f i b r e s o f i n c r e a s i n g 5 9 s t i f f n e s s o r s i z e . T h e r e w o u l d t h e n b e r e l a t i v e l y f e w e r s h i v e s i n t h e f l o w e n t e r i n g t h e s c r e e n a p e r t u r e , a n d t h u s s c r e e n i n g w o u l d o c c u r s i m p l y b y f l o w b i f u r c a t i o n . A s u m m a r y o f t h e f i l m d a t a i s g i v e n i n T a b l e V . F o r t h e s a k e o f a n a l y s i s , t h e z o n e n e a r t h e s c r e e n p l a t e i s d i v i d e d i n t o l a y e r s , a s d e f i n e d i n T a b l e I V . T h e n o m i n a l e x i t l a y e r t h i c k n e s s i s s e t e q u a l t o t h e c h a n n e l h e i g h t m u l t i p l i e d b y t h e r a t i o o f f e e d a n d a c c e p t f l o w s . T h i s t h i c k n e s s i s l e s s t h a n t h e c o m b i n e d t h i c k n e s s e s o f L a y e r s I a n d I I f o r e a c h o f t h e f i l m s . T h e o b s e r v e d f i b r e t r a j e c t o r i e s w e r e c l a s s i f i e d i n t o t h e i n t o t h e f i v e " m o t i o n t y p e s " l i s t e d i n T a b l e I I I . T h e r e l a -t i v e i n c i d e n c e o f v a r i o u s m o t i o n t y p e s i s g i v e n i n T a b l e V . T h e t o t a l i n c i d e n c e o f M o t i o n T y p e s D a n d E i s e q u a l t o p e r m e a b i l i t y . A c o m p a r i s o n o f F i l m s 2 a n d 3 s h o w s t h a t i n c r e a s e d s l o t v e l o c i t y c a u s e s a n i n c r e a s e i n t h e s e m o t i o n t y p e s , c o n s i s t e n t w i t h t h e p e r m e a b i l i t y m e a s u r e m e n t s s h o w n i n F i g u r e 1 3 . T h e c o r r e l a t i o n b e t w e e n t h e m o t i o n o f a f i b r e a n d i t s l o c a t i o n a n d o r i e n t a t i o n i s s h o w n i n F i g u r e s 1 9 , 2 0 a n d 2 1 . A l l f i b r e s t h a t i n t e r a c t e d w i t h t h e s l o t ( M o t i o n T y p e s B , C , D a n d E ) w e r e w i t h i n t h e t h r e e l a y e r s a d j a c e n t t o t h e s l o t t e d p l a t e a t t h e p l a n e o f i n t e r e s t ( 1 . 7 5 mm u p s t r e a m o f t h e s l o t ) . S t a p l i n g a n d s l o t c o n t a c t ( M o t i o n T y p e s C a n d D) o c c u r r e d i n F i l m 2 , b u t o n l y f o r f i b r e s w i t h n e g a t i v e f i b r e a n g l e s . P a s s a g e w i t h o u t s l o t c o n t a c t ( M o t i o n T y p e E ) w a s 6 0 F i g u r e 17 M o t i o n o f F i b r e s Near a S l o t ( C i n e - F i l m ) 61 iLIST 2 RUN*- aLOAD11 4SAUE" 5C0NT** F i g u r e 18 M o t i o n o f F i b r e s N e a r a S l o t ( C o m p u t e r i z e d I m a g e s ) 6 2 T a b l e I I I : F i b r e M o t i o n T y p e s T y p e M o t i o n T h e f i b r e m o v e s p a s t t h e s l o t w i t h o u t e i t h e r e n d e n t e r i n g t h e s l o t o r t o u c h i n g a s l o t w a l l . O n e e n d o f t h e f i b r e e n t e r s t h e s l o t a n d t o u c h e s o n e o f t h e w a l l s , b u t i s t h e n s w e p t o u t o f t h e s l o t a n d b a c k i n t o t h e m a i n s t r e a m . O n e e n d o f t h e f i b r e e n t e r s t h e s l o t a n d t h e f i b r e i s i m m o b i l i z e d - b a l a n c e d o n t h e d o w n s t r e a m e d g e o f t h e s l o t . T h i s i s c o m m o n l y c a l l e d " s t a p l i n g " . T h e f i b r e p a s s e s t h r o u g h t h e s l o t a f t e r c o n t a c t i n g o n e ( o r b o t h ) o f t h e s l o t w a l l s . E T h e f i b r e p a s s e s t h r o u g h t h e s l o t w i t h o u t c o n t a c t i n g e i t h e r s l o t w a l l . C h a n n e l L a y e r D e f i n i t i o n s B o u n d a r i e s F r o m t h e s u r f a c e o f t h e s l o t t e d p l a t e t o a p l a n e 1 / 8 a f i b r e l e n g t h a b o v e t h e s u r f a c e . F r o m a p l a n e 1 / 8 a f i b r e l e n g t h a b o v e t h e p l a t e s u r f a c e t o a p l a n e 1 / 4 a f i b r e l e n g t h a b o v e t h e s u r f a c e . F r o m a p l a n e 1 / 4 a f i b r e l e n g t h a b o v e t h e p l a t e s u r f a c e t o a p l a n e 1 / 2 a f i b r e l e n g t h a b o v e t h e s u r f a c e . F r o m a p l a n e 1 / 2 a f i b r e l e n g t h a b o v e t h e p l a t e s u r f a c e t o a p l a n e 1 f i b r e l e n g t h a b o v e t h e s u r f a c e . F r o m a p l a n e 1 f i b r e l e n g t h a b o v e t h e s u r f a c e t o t h e c h a n n e l c e n t r e l i n e ( o r t o a p l a n e 1 f i b r e l e n g t h b e l o w t h e t o p o f t h e f i l m f r a m e , i f t h e c e n t r e l i n e a n d t o p o f t h e f i l m f r a m e a r e l e s s t h a n 1 f i b r e l e n g t h a p a r t ) . F r o m t h e c h a n n e l c e n t r e l i n e ( o r p l a n e 1 f i b r e l e n g t h b e l o w t h e t o p o f t h e f i l m f r a m e ) t o t h e e d g e o f t h e f i l m f r a m e . 64 T a b l e V : F i l m D a t a S u m m a r y F i l m 1 2 3 E x p e r i m e n t a l C o n d i t i o n s : u p s t r e a m v e l o c i t y ( m / s ) 7 . 2 7 . 9 7 . 1 s l o t v e l o c i t y ( m / s ) 3 . 2 3 . 1 7 . 1 n y l o n f i b r e l e n g t h 3 . 1 3 . 1 3 . 1 f i b r e d i a m e t e r (mm) 0 . 2 3 0 0 . 0 4 3 0 . 0 4 3 s l o t w i d t h (mm) 0 . 5 0 . 5 0 . 5 n u m b e r o f f i b r e s o b s e r v e d 2 9 8 6 9 5 8 2 7 m e a s u r e d p e r m e a b i l i t y 0 . 0 1 0 . 0 9 0 . 8 6 e x i t l a y e r t h i c k n e s s (mm) 0 . 2 3 0 . 2 0 0 . 5 3 R e l a t i v e C o n c e n t r a t i o n s : l a y e r I (0 - 0 . 3 8 mm) 0 . 3 2 0 . 3 3 0 . 1 2 l a y e r I I ( 0 . 3 8 - 0 . 7 5 mm) 0 . 3 2 0 . 5 8 0 . 4 6 l a y e r I I I ( 0 . 7 5 - 1 . 5 0 mm) 0 . 9 0 1 . 0 1 1 . 1 7 l a y e r I V ( 1 . 5 0 - 3 . 0 0 mm) 0 . 9 9 1 . 0 6 1 . 0 9 l a y e r V ( 3 . 0 0 - 8 . 7 5 mm) 1 . 0 0 1 . 0 0 1 . 0 0 l a y e r V I * d i s r e g a r d e d * D i s t r i b u t i o n o f M o t i o n T y p e s : A s i m p l e m o v e m e n t 9 7 . 3 % 9 7 . 2 % 9 4 . 8 % d o w n s t r e a m B s l o t c o n t a c t t h e n 2 . 7 1 . 8 1 . 2 m o v e m e n t d o w n s t r e a m C i m m o b i l i z a t i o n a t n i l 0 . 9 2 . 5 t h e s l o t D s l o t p a s s a g e w i t h n i l 0 . 1 0 . 6 s l o t w a l l c o n t a c t E s l o t p a s s a g e w i t h o u t n i l n i l 0 . 8 s l o t w a l l c o n t a c t t o t a l 1 0 0 . 0 1 0 0 . 0 1 0 0 . 0 65 £ 1.50 E £ 1.25 o 1.00 <o 0.75 E o 0.50 £ 0.25 h C/> Q 01 2 O o -o o o o o ® o o o o <8> <8> o o ® o o Motion types 0 ® 9 0 f A B C D E ® 0 <8> •1.0 -0.5 0 0.5 1.0 Angle (radians) a . J 1=1 <D O - J r-H k_ <D >* O n " 2 F i g u r e 1 9 C o r r e l a t i o n o f F i b r e M o t i o n , F i b r e P o s i t i o n , a n d F i b r e O r i e n t a t i o n f o r F i l m 1 E E CD O CD CD O CO E o 1.50 1.25 1.00 0.75 Z. 0.50 CD O 0.25 o co Q ^ 0 ® o o ® o o ® •o-o o ^ o o ocP°° o „ o ° o o c ? ° § 8 ( 3D° OO O °oo oo° 0 3 OO ° ° 0 * ®f • • o o® o ® Motion types o®oot A B C DE 9 ® ® O © ® - f -1.0 -0.5 0 0.5 1.0 Angle (radians) u 2 F i g u r e 2 0 C o r r e l a t i o n o f F i b r e M o t i o n , F i b r e P o s i t i o n , a n d F i b r e O r i e n t a t i o n f o r F i l m 2 67 e £ O Q . CD CD 1.50 1.25 1.00 o co 0.75 E o 0.50 <D 9- 0.25 to 5 0 TT 2 •O- •o-o o ® (9(2) o 0 o o ° 0 ° o o u o 3 o § o o Qo<3 ® o O n ® <* (3)0 ° A * V Motion types A B C DE * 3 3 -1.0 -0.5 0 0.5 1.0 Angle (radians) 3 O CD >. O - I CD TT 2 F i g u r e 2 1 C o r r e l a t i o n o f F i b r e M o t i o n , F i b r e P o s i t i o n , a n d F i b r e O r i e n t a t i o n f o r F i l m 3 68 o b s e r v e d i n F i l m 3 a n d f o u n d t o b e r e s t r i c t e d t o f i b r e s w i t h n e g a t i v e a n g l e s - A n a l y s i s o f F i l m s 1 , 2 a n d 3 a l s o p r o v i d e s s o m e g e n e r a l i n f o r m a t i o n o n t h e v e l o c i t y a n d o r i e n t a t i o n o f f i b r e s u p s t r e a m o f t h e s l o t . T h e d a t a p r e s e n t e d i n T a b l e V I s h o w t h a t : 1 ) T h e r e i s a v e l o c i t y g r a d i e n t a c r o s s t h e c h a n n e l , a n d t h e a x i a l v e l o c i t y n e a r t h e w a l l ( i . e . i n L a y e r I ) i s a b o u t 25% l e s s t h a n t h e m i d s t r e a m v e l o c i t y ( L a y e r V ) . 2 ) T h e f i b r e v e l o c i t i e s i n L a y e r s I V a n d V a r e i n f a i r a g r e e m e n t w i t h t h e b u l k v e l o c i t i e s l i s t e d i n T a b l e V , f o r a l l t h r e e f i l m s . B u l k v e l o c i t y m e a s u r e m e n t s w e r e m a d e b y t i m i n g t h e f l o w i n t o a c o n t a i n e r a n d a r e i n d e p e n d e n t o f t h e f i b r e v e l o c i t y m e a s u r e m e n t s . 3 ) T h e o b s e r v e d t r a n s v e r s e v e l o c i t y c o m p o n e n t ( a r i s i n g f r o m t u r b u l e n c e ) i s 3 - 5 % t h e a x i a l m a i n s t r e a m v e l o c i t y . 4) F i b r e s n e a r t h e c e n t r e o f t h e c h a n n e l h a v e a s l i g h t d e g r e e o f a x i a l o r i e n t a t i o n . F i b r e s c l o s e t o t h e w a l l m u s t , o f g e o m e t r i c n e c e s s i t y , b e a l i g n e d p a r a l l e l t o t h e w a l l . 5 . 3 A M o d e l f o r F i b r e P a s s a g e A m o d e l f o r f i b r e p a s s a g e i s s u g g e s t e d b y t h e e x p e r i m e n t a l f i n d i n g s o f t h i s t h e s i s . A c c o r d i n g t o t h i s m o d e l , f i b r e p e r m e a b i l i t y a t a s l o t i s d e t e r m i n e d b y t w o f a c t o r s : a " w a l l e f f e c t " a n d a n " e n t r y e f f e c t " . O n l y f i b r e s i n t h e e x i t l a y e r a r e c a n d i d a t e s t o p a s s t h r o u g h t h e s l o t . T a b l e V I F i b r e V e l o c i t y a n d O r i e n t a t i o n F i l m I V x ( m / s ) 1 6 . 1 2 5 . 2 3 4 . 8 V y ( m / s ) 1 - 0 . 2 2 - 0 . 3 3 - 0 . 7 u ( r a d / s ) 1 - 9 7 2 - 4 6 2 3 - 4 3 9 a n g l e d i s t r i b u t i o n : - TT - 3 TT 1 — 2 8 2 -3 -- 3 TT - TT 1 -8 4 2 -3 -— TT — Tf 1 -4 8 2 -3 -- TT - 0 1 0 . 3 3 8 2 0 . 4 3 3 0 . 8 3 0 - TT 1 0 . 3 3 8 2 0 . 5 7 3 0 . 1 7 Tf - TT 1 -8 4 2 -3 -TT — 3 Tf 1 0 . 3 3 4 8 2 -3 -3 TT - Tf 1 -8 2 2 -3 -t o t a l 1 1 . 0 0 2 1 . 0 0 3 1 . 0 0 L a y e r I I I I I I V V 6 . 6 6 . 5 6 . 9 7 . 4 6 . 0 6 . 6 7 . 1 7 . 3 6 . 1 6 . 3 6 . 6 7 . 0 - 0 . 4 - 0 . 2 - 0 . 1 - 0 . 1 - 0 . 2 - 0 . 2 - 0 . 1 - 0 . 1 - 0 . 3 - 0 . 4 - 0 . 3 - 0 . 2 - 1 8 2 8 3 3 3 2 - 1 4 0 - 2 7 2 - 2 1 5 - 2 0 0 6 3 - 3 2 1 - 3 4 7 - 4 5 - 9 3 0 . 0 8 - 0 . 0 5 0 . 0 4 0 . 0 7 - 0 . 0 3 0 . 0 6 0 . 0 9 - - 0 . 1 0 0 . 1 0 0 . 0 5 0 . 0 5 0 . 0 8 0 . 1 1 - 0 . 0 5 0 . 0 5 0 . 1 2 - 0 . 2 2 0 . 0 8 0 . 1 3 0 . 1 1 0 . 0 8 0 . 0 9 0 . 1 6 0 . 1 1 0 . 0 8 0 . 1 3 0 . 1 5 0 . 6 7 0 . 2 6 0 . 1 2 0 . 1 9 0 . 2 6 0 . 2 5 0 . 1 9 0 . 1 4 0 . 3 3 0 . 2 3 0 . 2 1 0 . 1 8 - 0 . 3 0 0 . 2 0 0 . 1 4 0 . 4 7 0 . 3 2 0 . 2 3 0 . 1 5 0 . 5 0 0 . 3 1 0 . 2 5 0 . 1 3 0 . 3 3 0 . 2 2 0 . 2 8 0 . 1 5 0 . 0 5 0 . 1 6 0 . 2 0 0 . 1 5 0 . 0 6 0 . 2 3 0 . 1 3 0 . 1 4 - - 0 . 1 6 0 . 1 2 0 . 0 5 0 . 0 6 0 . 1 1 0 . 1 4 - 0 . 0 3 0 . 1 1 0 . 1 1 - - 0 . 0 6 0 . 1 0 - 0 . 0 3 0 . 0 6 0 . 0 8 - 0 . 0 5 0 . 0 6 0 . 0 7 1 . 0 0 1 . 0 0 1 . 0 0 1 . 0 0 1 . 0 0 1 . 0 0 1 . 0 0 1 . 0 0 1 . 0 0 1 . 0 0 1 . 0 0 1 . 0 0 7 0 T h u s t h e p e r m e a b i l i t y a t a s l o t c a n b e s h o w n a s t h e p r o d u c t o f t w o p e r m e a b i l i t y c o m p o n e n t s : P P e w e ( 5 . 1 ) C u H e r e , P = p e r m e a b i l i t y ; P e = t h e p e r m e a b i l i t y c o m p o n e n t a s s o c i a t e d w i t h t h e e n t r y e f f e c t ; P w = t h e p e r m e a b i l i t y c o m p o n e n t a s s o c i a t e d w i t h t h e w a l l e f f e c t ; C s = t h e f i b r e c o n c e n t r a t i o n i n t h e f l o w t h r o u g h t h e s l o t ( i . e . t h e a c c e p t s t r e a m ) ; C e = t h e f i b r e c o n c e n t r a t i o n i n t h e e x i t l a y e r ; a n d C u = t h e a v e r a g e u p s t r e a m f i b r e c o n c e n t r a t i o n . F o r t h e t h r e e f i l m s a n a l y z e d i n t h i s t h e s i s , t h e c o n c e n t r a t i o n o f f i b r e s i n t h e e x i t l a y e r w a s a b o u t 33% t h a t i n t h e f e e d f l o w ; t h a t i s , P w h a d a v a l u e o f a b o u t 0 . 3 3 . I n F i l m 2 , t h e o v e r a l l p e r m e a b i l i t y , P , w a s 0 . 0 9 . H e n c e , b y a p p l y i n g E q u a t i o n 5 . 1 , o n e c a n c a l c u l a t e t h a t o n l y 27% o f t h e f i b r e s i n t h e e x i t l a y e r p a s s e d t h r o u g h t h e s l o t ( i . e . P e = 0 . 2 7 ) . T h e n a t u r e o f t h e w a l l e f f e c t h a s b e e n d e s c r i b e d i n t h e p r e v i o u s s e c t i o n a n d w i l l n o t b e d i s c u s s e d f u r t h e r . T h e e n t r y e f f e c t c a n b e e x p l a i n e d i n t h e f o l l o w i n g w a y . G i v e n t h a t a f i b r e m u s t b e i n t h e e x i t l a y e r t o b e a c a n d i d a t e f o r p a s s a g e , a n d t h a t t h e t h i c k n e s s o f t h i s l a y e r i s m u c h l e s s t h a n a f i b r e l e n g t h , t h e n a n y f i b r e t h a t i s e l i g i b l e f o r 7 1 p a s s a g e m u s t b e a l i g n e d a l m o s t p a r a l l e l t o t h e s c r e e n p l a t e . T h e r e f o r e , t o p a s s t h r o u g h t h e s l o t , m o s t f i b r e s m u s t t u r n s u b s t a n t i a l l y a t t h e s l o t e n t r y . F l e x i b l e f i b r e s c a n b e n d d u r i n g t u r n i n g a n d f o l l o w t h e f l o w t h r o u g h t h e s l o t . H o w e v e r , r i g i d f i b r e s m u s t r o t a t e i n o r d e r t o p a s s t h r o u g h t h e s l o t . D u r i n g r o t a t i o n , t h e f i b r e may b e c a r r i e d f o r w a r d b y t h e m a i n f l o w t o a n e x t e n t t h a t i t c o n t a c t s t h e d o w n s t r e a m e d g e o f t h e s l o t , a n d r e t u r n s t o t h e m a i n f l o w . F i b r e s t h a t a p p r o a c h t h e s l o t c l o s e t o t h e w a l l , w i t h n e g a t i v e f i b r e a n g l e s , a r e m o s t l i k e l y t o p a s s t h r o u g h t h e s l o t ( a s n o t e d i n t h e p r e v i o u s s e c t i o n ) . T h i s i s r e a s o n a b l e s i n c e t h e c l o s e r t h e f i b r e i s t o t h e w a l l , t h e l e s s i t m u s t t r a v e l t o e n t e r t h e s l o t ; a n d t h e m o r e f a v o u r a b l e t h e a n g l e , t h e l e s s t h e f i b r e n e e d s t o r o t a t e t o b e a l i g n e d w i t h t h e s l o t . T h i s m o d e l o f f i b r e m o t i o n a t a s l o t e n t r y c a n b e u s e d t o e x p l a i n w h y c e r t a i n f i b r e , f l o w , a n d s l o t v a r i a b l e s a f f e c t p e r m e a b i l i t y a s t h e y d o . S h o r t f i b r e s h a v e h i g h e r p e r m e a -b i l i t i e s t h a n l o n g f i b r e s ( s e e F i g u r e 1 1 ) , b e c a u s e w h e n a s h o r t , r i g i d f i b r e t i p s i n t o a s l o t , l e s s o f t h e f i b r e i s e x p o s e d t o d r a g f o r c e s i n t h e m a i n s t r e a m w h i c h c o u l d p u l l t h e f i b r e f r o m t h e s l o t . F l e x i b l e f i b r e s w o u l d b e e x p e c t e d t o h a v e h i g h e r p e r m e a b i l i t i e s ( s e e F i g u r e 1 2 ) , b e c a u s e t h e y c a n c o n f o r m t o t h e s t r e a m l i n e s p a s s i n g i n t o t h e s l o t , r a t h e r t h a n h a v i n g t o r o t a t e a n d s t r a d d l e t h e m a i n s t r e a m a n d s l o t f l o w s . 7 2 I n c r e a s e d s l o t v e l o c i t y p r o m o t e s f i b r e p a s s a g e ( F i g u r e 1 5 ) f o r t w o r e a s o n s : 1 ) T h e d r a g f o r c e s t h a t c a u s e t h e f i b r e t o m o v e i n t o t h e s l o t i n c r e a s e ; a n d 2 ) T h e e x i t l a y e r t h i c k n e s s i n c r e a s e s , a n d w i t h i t t h e c o n c e n t r a t i o n o f f i b r e s i n t h e e x i t l a y e r . D e c r e a s e d m a i n s t r e a m v e l o c i t i e s c a u s e i n c r e a s e d p e r m e a b i l i t i e s ( F i g u r e 1 4 ) f o r s i m i l a r r e a s o n s : T h e m a i n s t r e a m d r a g f o r c e s o n t h e f i b r e d e c r e a s e , a n d t h e e x i t l a y e r t h i c k n e s s i n c r e a s e s . I n c r e a s e d s l o t w i d t h i s a s s o c i a t e d w i t h h i g h e r p e r m e a b i l i t i e s ( s e e F i g u r e 1 5 ) , b e c a u s e w i d e r s l o t s a l l o w m o r e t i m e f o r a f i b r e t o r o t a t e a n d m o v e i n t o t h e s l o t . F i b r e s t a p l i n g ( M o t i o n T y p e C i n T a b l e I I I ) c a n a l s o b e d i s c u s s e d i n t e r m s o f t h e a b o v e m o d e l . C e r t a i n f i b r e s w i l l e n t e r t h e s l o t , r o t a t e , s t r i k e t h e d o w n s t r e a m e d g e o f t h e s l o t a n d b e i m m o b i l i z e d t h e r e . T h e d r a g e x e r t e d o n t h e f i b r e b y t h e s l o t f l o w i s b a l a n c e d b y t h e d r a g e x e r t e d b y t h e m a i n s t r e a m f l o w a n d s o t h e r e i s n o f u r t h e r f i b r e m o t i o n . A c c u m u l a t i o n s o f f i b r e s w i l l r e s t r i c t t h e f l o w t h r o u g h a s c r e e n p l a t e a p e r t u r e , a n d g r o w t o t h e p o i n t t h a t f i b r e s c a n n o t p a s s t h r o u g h t h e s c r e e n p l a t e . A l l p u l p s c r e e n s h a v e s o m e m e a n s o f b a c k f l u s h i n g t h e s c r e e n p l a t e a p e r t u r e s t o k e e p t h e m c l e a r . N o n e t h e l e s s , s t a p l i n g r e m a i n s a s a s u b j e c t o f i n d u s t r i a l c o n c e r n . 7 3 6. SUMMARY AND C O N C L U S I O N S T h i s t h e s i s i s c o n c e r n e d w i t h f i b r e p a s s a g e t h r o u g h s l o t s , a n d t h e a p p l i c a t i o n o f t h i s k n o w l e d g e t o p r e s s u r i z e d p u l p s c r e e n i n g . A s u m m a r y o f t h e w o r k , a n d t h e p r i n c i p a l f i n d i n g s a r e a s f o l l o w s . 1 . We e s t i m a t e d t h e f l o w v e l o c i t i e s n e a r a n a p e r t u r e i n a n i n d u s t r i a l p r e s s u r e s c r e e n u s i n g s i m p l e e n g i n e e r i n g a s s u m p t i o n s . T y p i c a l l y , t h e b u l k v e l o c i t y p a r a l l e l t o t h e f e e d s i d e o f a s c r e e n p l a t e i s 6 m / s , a n d t h e b u l k v e l o c i t y t h r o u g h a s c r e e n p l a t e a p e r t u r e i s 1 m / s . T h e s e v e l o c i t i e s w e r e u s e d a s g u i d e l i n e s i n o u r e x p e r i m e n t a l s t u d y o f p u l p s c r e e n i n g . 2 . We d e r i v e d t h e t w o e f f i c i e n c y - r e j e c t r a t e e q u a t i o n s g i v e n b e l o w . T h e s e e q u a t i o n s h a v e b e e n r e p o r t e d e l s e w h e r e i n t h e l i t e r a t u r e , a n d E q u a t i o n 2 . 1 i s i n w i d e s p r e a d u s e . O u r a n a l y s i s r e v e a l e d t h a t t h e e q u a t i o n s a r e b a s e d o n t w o d i f f e r e n t a s s u m p t i o n s c o n c e r n i n g t h e a m o u n t o f m i x i n g a d j a c e n t t o t h e s c r e e n p l a t e i n a p r e s s u r e s c r e e n . M o r e o v e r , t h e c o n s t a n t s i n t h e s e e q u a t i o n s ( ' C a n d ' Q ' ) c a n b e u s e d t o r e l a t e t h e r e l a t i v e p e r m e a b i l i t y o f p u l p f i b r e s a n d s h i v e s a t a s i n g l e a p e r t u r e , t o i n d u s t r i a l s c r e e n p e r f o r m a n c e . 7 4 T h e p l u g f l o w " e q u a t i o n i s : E R ( 2 . 1 ) 1 - Q + QR T h e " m i x e d f l o w " e q u a t i o n i s : E = R c ( 2 . 2 ) 3 . We b u i l t a n e x p e r i m e n t a l f l o w l o o p t h a t c o n t a i n e d a p l e x i g l a s c h a n n e l w i t h a s i n g l e s l o t , a n d c o n d u c t e d t e s t s a t v e l o c i t i e s c o m p a r a b l e t o t h o s e i n c o m m e r c i a l p r e s s u r e s c r e e n s . F o r p u l p f i b r e s a n d s h i v e - l i k e n y l o n f i b r e s i n a d i l u t e s u s p e n s i o n , p e r m e a b i l i t i e s w e r e o b t a i n e d w h i c h g a v e a v a l u e o f C = 0 . 0 2 ( s e e E q u a t i o n 2 . 1 ) . T h i s v a l u e o f ' C c o r r e s p o n d s t o e x c e l l e n t p e r f o r m a n c e i n a n i n d u s t r i a l p u l p s c r e e n . T h i s e x a m p l e i l l u s t r a t e s h o w p e r m e a b i l i t y m e a s u r e m e n t s a t a s i n g l e s l o t may b e r e l a t e d t o i n d u s t r i a l s c r e e n p e r f o r m a n c e t h r o u g h E q u a t i o n 2 . 1 ( o r E q u a t i o n 2 . 2 ) . M o r e o v e r , b e c a u s e t h e s u s p e n s i o n w a s d i l u t e , o n e may c o n c l u d e t h a t s i g n i f i c a n t f i b r e i n t e r a c t i o n i s n o t a p r e r e q u i s i t e f o r s c r e e n i n g . 4 . We m e a s u r e d t h e e f f e c t o f f i b r e , f l o w , a n d s l o t v a r i a b l e s o n p e r m e a b i l i t y . R e d u c e d f i b r e s t i f f n e s s a n d l e n g t h c a u s e d a n i n c r e a s e i n p e r m e a b i l i t y , a s d i d i n c r e a s e d s l o t w i d t h a n d i n c r e a s e d f l o w v e l o c i t y t h r o u g h t h e s l o t . 7 5 T h e s e f i n d i n g s a r e q u a l i t a t i v e l y c o n s i s t e n t w i t h i n d u s t r i a l e x p e r i e n c e , a n d p r o v i d e q u a n t i t a t i v e i n f o r m a t i o n n o t p r e v i o u s l y a v a i l a b l e . 5 . We o b s e r v e d t h e m o t i o n o f f i b r e s a t a s l o t e n t r y u s i n g h i g h s p e e d c i n e - f i l m s , a n d a n a l y s e d t h e f i b r e t r a j e c -t o r i e s u s i n g c u s t o m c o m p u t e r p r o g r a m m e s . T h e o b s e r v a t i o n s s u g g e s t e d t h a t t h e s c r e e n i n g o f f i b r e s o c c u r s b y t w o d i s t i n c t m e c h a n i s m s : i ) W a l l E f f e c t V i r t u a l l y a l l o f t h e f i b r e s p a s s i n g i n t o t h e s l o t c o m e f r o m a t h i n " e x i t l a y e r " a d j a c e n t t o t h e s c r e e n p l a t e . T h i s l a y e r h a s f e w e r f i b r e s t h a n t h e m a i n s t r e a m f l o w , d u e t o a c o n c e n t r a t i o n g r a d i e n t p r e s e n t a t t h e s c r e e n p l a t e . I f c o n c e n t r a t i o n g r a d i e n t s v a r y a c c o r d i n g t o f i b r e s t i f f n e s s a n d l e n g t h , s h i v e s a n d p u l p f i b r e s w o u l d b e s c r e e n e d f r o m o n e a n o t h e r b y f l o w b i f u r c a t i o n . i i ) E n t r y E f f e c t A s n o t e d a b o v e , a f i b r e m u s t b e i n t h e e x i t l a y e r i n o r d e r t o b e a c a n d i d a t e f o r p a s s a g e t h r o u g h t h e s l o t . B e c a u s e t h e e x i t l a y e r t h i c k n e s s i s t y p i c a l l y m u c h l e s s t h a n a f i b r e l e n g t h , f i b r e s i n t h i s l a y e r m u s t b e o r i e n t e d n e a r l y p a r a l l e l t o t h e s c r e e n p l a t e . S i n c e s l o t w i d t h i s a l s o m u c h s m a l l e r t h a n f i b r e l e n g t h , s o m e f i b r e s h a v e t o t u r n 9 0 d e g r e e s t o p a s s t h r o u g h t h e s l o t . I n t h e c a s e o f s t i f f f i b r e s , t h e e n t i r e f i b r e m u s t r o t a t e . B e f o r e t h e f i b r e t u r n s a n d e n t e r s t h e s l o t , t h e m a i n f l o w may c a r r y t h e f i b r e f o r w a r d t o t h e e x t e n t t h a t i t c o n t a c t s t h e 76 d o w n s t r e a m e d g e o f t h e s l o t a n d r e t u r n s t o t h e m a i n f l o w . M o r e f l e x i b l e f i b r e s c a n b e n d d u r i n g w h i l e t u r n i n g a n d p a s s i n t o t h e s l o t w i t h m u c h l e s s c h a n c e o f r e - e n t e r i n g t h e m a i n f l o w . T h u s p u l p f i b r e s a r e m o r e l i k e l y t o p a s s t h r o u g h a s c r e e n p l a t e t h a n s h i v e s , s i n c e s h i v e s a r e g e n e r a l l y s t i f f e r a n d l o n g e r . P e r m e a b i l i t y c o m p o n e n t s may b e a s s o c i a t e d w i t h e a c h o f t h e s e t w o e f f e c t s , a n d t h e i r p r o d u c t i s t h e o v e r a l l f i b r e p e r m e a b i l i t y . 77 7 . R E C O M M E N D A T I O N S FOR F U T U R E WORK P u l p s c r e e n i n g i s a n a r e a o f r e s e a r c h t h a t c a n p r o v i d e i m m e d i a t e a n d s u b s t a n t i a l b e n e f i t s t o i n d u s t r y . T h i s t h e s i s h a s e l u c i d a t e d v a r i o u s a s p e c t s o f p u l p s c r e e n i n g a n d p r o v i d e d a b a s i s f o r f u t u r e w o r k , w h i c h c o u l d t a k e o n e o f s e v e r a l d i r e c t i o n s : 1 . H i g h e r P u l p C o n s i s t e n c i e s . I n d u s t r i a l p u l p s c r e e n i n g i n v o l v e s m u c h h i g h e r c o n s i s t e n c i e s t h a n w e r e c o n s i d e r e d i n t h i s t h e s i s ; a n d c o n s i s t e n c y i s k n o w n t o h a v e a n i m p o r t a n t e f f e c t o n p u l p s c r e e n p e r f o r m a n c e . T h u s t h e r e i s , a c l e a r n e e d t o s u p p l e m e n t t h e f i n d i n g s o f t h i s t h e s i s w i t h a s t u d y o f p u l p s c r e e n i n g a t h i g h e r c o n s i s t e n c i e s . T h i s w o u l d r e q u i r e a m e a n s o f b a c k f l u s h i n g t h e s l o t o f o u r l a b o r a t o r y f l o w c h a n n e l t o k e e p i t c l e a r o f f i b r e s . 2 . F i b r e S t a p l i n g . I n n o r m a l s c r e e n o p e r a t i o n , f i b r e s a c c u -m u l a t e w i t h i n t h e s c r e e n s l o t u n t i l t h e y a r e f l u s h e d a w a y b y a r o t o r - i n d u c e d p u l s e . A k n o w l e d g e o f how t h e s t a p l e s f o r m , h o w t h e y a f f e c t s c r e e n p e r f o r m a n c e , a n d how s t a p l i n g c a n b e a v o i d e d m i g h t b e u s e d t o i n c r e a s e s c r e e n c a p a c i t y a n d p e r f o r m a n c e . N o v e l s c r e e n p l a t e p r o f i l e s w o u l d a l s o b e e x a m i n e d h e r e . 7 8 3 . P u l p S c r e e n M o d e l l i n g . A b e t t e r u n d e r s t a n d i n g o f t h e f l o w s w i t h i n a p r e s s u r e s c r e e n c o u l d l e a d t o i m p r o v e d s c r e e n d e s i g n s . I n t h i s t h e s i s , a s i m p l e e n g i n e e r i n g m o d e l o f a p r e s s u r e s c r e e n w a s p r o p o s e d . T o i m p r o v e o n t h i s m o d e l , c e r t a i n k e y a s p e c t s o f p u l p s c r e e n o p e r a t i o n s h o u l d b e m e a s u r e d , s u c h a s t h e e x t e n t o f m i x i n g i n t h e " s c r e e n i n g z o n e " b e t w e e n t h e r o t o r a n d s c r e e n p l a t e . I t w o u l d b e u s e f u l t o g a t h e r i n f o r m a t i o n o n a v a r i e t y o f i n d u s t r i a l p u l p s c r e e n s i n o r d e r t o d e v e l o p a m o d e l w h i c h w i l l b e o f g e n e r a l i n t e r e s t . 79 N O M E N C L A T U R E s c r e e n p l a t e o p e n a r e a c r o s s - s e c t i o n a 1 a r e a o f t h e a n n u l a r s c r e e n i n g z o n e o v e r a l l f i b r e w i d t h s c r e e n i n g i n d e x f i b r e c o n c e n t r a t i o n i n t h e e x i t l a y e r a d j a c e n t t o t h e s l o t t e d p l a t e ( e ) , i n t h e ( a c c e p t ) f l o w t h r o u g h t h e s l o t ( s ) , a n d i n t h e f l o w u p s t r e a m o f t h e s l o t ( u ) c o n c e n t r a t i o n o f p u l p f i b r e s i n t h e f e e d ( f . p ) , a c c e p t ( a . p ) , a n d r e j e c t ( r . p ) s t r e a m s o f a p u l p s c r e e n c o n c e n t r a t i o n o f s h i v e s i n t h e f e e d ( f . s h ) , a c c e p t ( a . s h ) , a n d r e j e c t ( r . s h ) s t r e a m s o f a p u l p s c r e e n a v e r a g e c o n c e n t r a t i o n o f p u l p a t a p l a n e l o c a t e d a d i s t a n c e " Z " f r o m t h e e n t r y t o t h e a n n u l a r s c r e e n i n g z o n e o u t e r d i a m e t e r o f t h e a n n u l a r s c r e e n i n g z o n e d e b r i s r e j e c t e f f i c i e n c y o r m o d u l u s o f e l a s t i c i t y h e i g h t o f t h e a n n u l a r s c r e e n i n g z o n e i n a p r e s s u r e s c r e e n m o m e n t o f i n e r t i a m o m e n t o f i n e r t i a o f a s h i v e c o m p r i s i n g " n " f i b r e s c o n s t a n t s o f p r o p o r t i o n a l i t y n u m b e r o f f i b r e s i n a s h i v e 8 0 p e r m e a b i l i t y , t h e r a t i o o f f i b r e c o n c e n t r a t i o n i n t h e s l o t f l o w a n d u p s t r e a m f l o w . " e n t r y e f f e c t " p e r m e a b i l i t y c o m p o n e n t p e r m e a b i l i t y o f p u l p f i b r e s p e r m e a b i l i t y o f s h i v e s " w a l l e f f e c t " p e r m e a b i l i t y c o m p o n e n t " s c r e e n i n g q u o t i e n t " , a n i n d e x o f s c r e e n p e r f o r m a n c e p r e s s u r e s c r e e n f e e d ( f ) , a c c e p t ( a ) , a n d r e j e c t f l o w r a t e ( r ) a x i a l f l o w r a t e i n t h e a n n u l a r s c r e e n i n g z o n e r e j e c t r a t e i n a p r e s s u r e s c r e e n ( b a s e d o n m a s s f l o w ) s l i p f a c t o r f i b r e w a l l t h i c k n e s s , o r t h i c k n e s s o f s l o t t e d p l a t e a v e r a g e r a d i a l v e l o c i t y a t t h e s c r e e n p l a t e s u r f a c e t i p s p e e d o f a p u l p s c r e e n r o t o r b u l k v e l o c i t y t h r o u g h a s c r e e n p l a t e a p e r t u r e c i r c u m f e r e n t i a l v e l o c i t y c o m p o n e n t w i t h i n t h e a n n u l a r s c r e e n i n g z o n e o f a p u l p s c r e e n ( t ) , a x i a l v e l o c i t y c o m p o n e n t ( z ) , a n d t h e r e s u l t a n t o f t h e p r e c e d i n g t w o v e l o c i t y c o m p o n e n t s (u ) l o c a l f i b r e v e l o c i t y p a r a l l e l t o t h e s l o t t e d p l a t e i n t h e e x p e r i m e n t a l t e s t c h a n n e l ( x ) , a n d p e r p e n d i c u l a r t o t h e s l o t t e d p l a t e ( y ) s l o t w i d t h 8 1 e x i t l a y e r t h i c k n e s s a x i a l d i s t a n c e f r o m t h e e n t r y t o t h e a n n u l a r s c r e e n i n g z o n e t o s o m e p o i n t o f i n t e r e s t f i b r e r o t a t i o n r a t e i n a p l a n e p e r p e n d i c u l a r t o t h e s l o t t e d p l a t e a n d p a r a l l e l t o t h e f l o w i n t h e e x p e r i m e n t a l c h a n n e l 82 BIBLIOGRAPHY A l A n d e r s s o n , 0 . , a n d W. B a r t o k . " A p p l i c a t i o n o f F e e d - b a c k t o F i b r e C l a s s i f i e r s . " S v e n s k P a p p e r s t i d n i n g , 5 8 ( 1 9 5 5 ) , 3 6 7 - 3 7 3 . B l B a d g e r , W . L . , a n d J . T . B a n c h e r o . I n t r o d u c t i o n t o  C h e m i c a l E n g i n e e r i n g . New Y o r k : M c G r a w - H i l l , 1 9 5 5 , p p . 6 1 8 - 6 3 6 . B 2 B r e r e t o n , T . " P r o b a b i l i t y S c r e e n i n g a n d t h e E f f e c t s o f M a j o r O p e r a t i n g V a r i a b l e s . " F i l t r a t i o n a n d S e p a r a t i o n , 1 2 ( 1 9 7 5 ) , 6 9 2 - 6 9 6 . B 3 B r o w n i n g , B . H . , a n d J . R . P a r k e r . T h e C h a r a c t e r i z a t i o n o f  O f f s e t L i n t a n d t h e T e s t i n g o f O f f s e t P a p e r s . P r o c . o f t h e S y m p o s i u m o n M e c h a n i c a l P u l p , E O C E P A , 1 9 7 0 , p p . 6 7 - 8 1 . C I C h o l l e t , J . , M . D u f f y , a n d 0 . S e p a l l . " S t u d i e s o f D i r t i n S u l p h i t e P u l p . " P u l p a n d P a p e r M a g a z i n e o f C a n a d a , 6 0 , N o . 4 ( 1 9 5 9 ) , T 1 2 3 - T 1 2 8 . C 2 C l a r k e - P o u n d e r , I . J . P i p e l i n e S c r e e n i n g . P r o c . o f t h e 5 6 t h A n n u a l M e e t i n g , C P P A , 1 9 7 0 , p p . D 1 1 6 - D 1 2 3 . F l F r i t h , M . D . , a n d D . J . F i s h e r . T h e E f f e c t o f  C o n s i s t e n c y o n S c r e e n i n g o f T M P a t P o w e l l R i v e r . M a c M i l l a n B l o e d e l R e s e a r c h L t d . I n t e r n a l R e p o r t . O c t o b e r , 1 9 7 8 . H I H o g l u n d , H . , E . J o h n s s o n , a n d G . T i s t a d . " S h i v e s i n M e c h a n i c a l P u l p . P a r t 2 . A n O p t i c a l M e t h o d o f D e t e r m i n i n g T h e i r L e n g t h D i s t r i b u t i o n . " S v e n s k  P a p p e r s t i d n i n g , 7 9 ( 1 9 7 6 ) , 4 1 1 - 4 1 7 . H2 H o p k i n s , R . M . , R . M a c P h e r s o n , a n d L . J . M o r i n . " A n a l y s i s o f t h e E f f e c t s o f C e n t r i f u g a l P u l p C l e a n e r s a n d P r e s s u r e S c r e e n s o n N e w s p r i n t R u n n a b i 1 i t y . " P u l p a n d P a p e r  M a g a z i n e o f C a n a d a , 6 3 , N o . 1 2 ( 1 9 6 2 ) , T 5 6 3 - T 5 7 0 . H3 H u m b e r , D . F . " P r a c t i c a l E x p e r i e n c e s w i t h S e v e r a l S c r e e n s . " U n p u b l i s h e d N o t e s . J a n u a r y 1 9 8 1 . K l K e l l o g g , R . M . , a n d F . F . W a n g a a r d . " V a r i a t i o n i n t h e C e l l - W a l l D e n s i t y o f W o o d . " W o o d a n d F i b r e , 1 , N o . 2 ( 1 9 6 9 ) , 1 8 0 - 2 0 4 . 83 K2 Kubat, J . , and B. Steenberg. "Screening at Low P a r t i c l e C o n c e n t r a t i o n s . " Svensk P a p p e r s t i d n i n g , 58 (1955), 319-324. K3 K e r e k e s , R.J., R.M. S o s z y n s k i , and P.A. Tarn Doo. The  F l o c c u l a t i o n of P u l p F i b r e s . 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A P P E N D I X I E X P E R I M E N T A L DAT Table VII High Speed Cine-Films f i l m # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 s l o t width (mm) 3.2 1.5 It 0.5 II 0.5 f i b r e type dyed shives •t shives lx.043 mm nylon lx.043 mm nylon 3x.200 mm nylon 3x.043 mm nylon lx.043 mm nylon 3x.043 mm nylon p!4.r28 k r a f t suspending medium 1% k r a f t pulp water water feed v e l o c i t y (m/s) 0.3 1.1 0.9 6.5 6.9 II 7.6 II 7.4 II 7.2 7.2 7.9 6.9 7 .1 accept v e l o c i t y (m/s) 1.0 2.1 0.6 2.6 5.1 5.5 5.5 3.2 3.1 3.1 7.1 3.0 00 <Ti Table VIII Permeability Measurements sst # s l o t width f i b r e type feed cone. feed v e l o c i t y accept v e l o c i t y permeability noti (mm) (fibres/1) (m/s) (m/s) 1 3 . 2 k r a f t shives _ 6. 9 2. 6 0.75 2 M •I .064 6. 9 2.0 0.32 2 3 II " .042 3. 5 1. 0 0.34 2 4 .082 1. 9 4. 3 1.27 2 5 .052 6. 9 0. 6 0.37 2 6 " lx.043 mm nylon 60 6. 8 1. 9 0.52 7 " 80 6. 5 2. 0 0.63 8 1. 5 " 150 7 . 6 5. 1 0. 58 3 9 k r a f t shives 280 7.6 5. 1 0.03 3 10 " II 140 7. 6 4. 4 0.07 3 11 " k r a f t pulp 350 7. 6 4. 4 0.28 3 12 0.5 lx.043 mm nylon 80 7. 4 5. 5 1.05 13 k r a f t shives 130 7. 4 5 . 5 0.09 14 " k r a f t pulp 170 7. 4 5. 5 0.55 15 3x.400 mm nylon 180 7. 2 3. 2 0.01 16 ii 3x.043 mm nylon 820 7 . 9 3. 1 0.09 17 " lx.043 mm nylon 900 6. 9 3. 1 0. 50 18 II pl4.r28 k r a f t 1650 7 . 3 3. 1 0.40 19 0.25 lx.043 mm nylon 1430 6. 8 13. 2 0.91 20 " 1340 6. 5 3. 7 0.57 21 lx.043 mm nylon 1260 6. 5 6. 6 0.67 22 0.5 " 2320 6. 4 3. 3 0.78 23 I I " 1910 6. 2 1. 9 0.47 24 " 1930 6. 3 5. 8 1.03 25 1.00 n 1750 6.5 2.8 0.78 26 II " 1580 6. 5 5. 9 1.09 27 " I I 1350 6.5 1. 6 0. 62 28 0.5 " 1390 6. 3 3. 2 0.76 4 notes; 1. Unless otherwise indicated, f i b r e counts were made manually. 2. Concentration measurement based on mass instead of a f i b r e count. Feed cone, u n i t s are g/1, not f i b r e s / 1 . 3. Three holes, aligned perpendicular to the flow, were used instead of a s l o t . 4. The distance from the channel entry to the s l o t was equal to 2 equivalent channel diameters. Table VIII Permeability Measurements (continued) test # s l o t width f i b r e type feed cone. (mm) (fib r e s / 1 ) 29 0.5 lx.043 mm nylon 1360 30 " " 1170 31 " 3x.043 mm nylon 1360 32 " " 1320 33 " " 1320 34 " " 1220 3 5 36 " " 2000 37 " pl4.r28 k r a f t 2320 38 " " 1110 39 40 41 0.25 3x.043 mm nylon 1640 42 43 44 1.00 " 1540 4 5 46 1.00 3x.043 mm nylon 47 0.5 " 1350 4 8 4 9 50 " " 1330 51 52 53 " lx.012 mm rayon 1360 5 4 55 56 " lx.020 mm rayon 800 notes: 5. The distance from the channel entry to the s l o t feed v e l o c i t y accept v e l o c i t y permeability notes (m/s) (m/s) 6.4 3 . 2 0.64 6.3 3.4 0.75 6.5 3 . 3 0.21 6.4 5.9 0.78 6.3 1.9 0.03 6.3 8.4 1.00 6.3 4.9 0.56 7.1 7 . 1 0.86 7.0 3.0 0.67 6.4 2.0 0.47 6.4 1.3 . 0.28 6.4 3.4 0.74 6.4 0.9 0.01 6.3 3.7 0.11 6.2 1.8 0.02 6.3 0.9 0.04 6.4 2.7 0.53 6.4 1.6 0.18 3.6 1.2 0.06 3.7 4.8 0.99 3.6 3.2 0.53 1.8 1. 1 0.02 1.8 2.2 0.74 1.8 4.0 1.04 6.5 3.4 0.84 6.2 1.9 0.52 6.3 0.9 0. 30 6.2 0.9 0.27 was equal to 14 equivalent channel diameters. oo oo Table VIII Permeability Measurements (continued) test # s l o t width f i b r e type feed cone. feed v e l o c i t y accept v e l o c i t y permeability notes (mm) (fibres/1) (m/s) (m/s) 57 0.5 lx.020 mm rayon 800 6.3 2.2 0. 57 58 II II 6.4 3.4 0. 81 59 II p l 0 . r l 4 k r a f t 1010 6.4 3.4 0. 66 60 " II II 6.3 1.9 0. 32 61 II I I II 6.3 0.9 0. 11 62 II pl4.r28 k r a f t 830 6.4 3.4 0. 67 63 II II II 6.3 1.9 0. 38 64 " II II 6.3 0.9 0. 18 65 II k r a f t pulp 63900 6.4 3 .1 0. 61 6 66 II II 6.4 3 .1 0. 42 6 67 II II 6.4 2.0 0. 45 6,7 68 II II 6.4 0.9 0. 25 6 69 II CTMP 132400 6.4 3.1 0. 58 6,7 70 II II II 6.4 1.9 0. 55 6,8 71 II II II 6.4 0.9 0. 39 6 72 " .043 mm d i a . nylon 40600 6.4 3.2 0.47 6,9 73 11 I I 6.4 1.9 0. 38 6 74 It " 6.4 0.9 0. 26 6 75 II k r a f t pulp .074 6.4 2.6 0. 31 2,8 76 II II 6.4 1.8 0. 14 2 77 II II 6.4 0.9 0. 09 2 78 II CTMP .055 6.3 2.9 0. 65 2,9 79 " n 6.3 1.8 0. 48 2, 10 80 " M 6.3 0.9 0. 35 2 notes: 2. Concentration measurement based on mass instead of a f i b r e count. Feed cone, u n i t s are g / l , not f i b r e s / 1 . 6. Fi b r e count made using the Kajaani FS-100. Permeability l i s t e d as a fu n c t i o n of f i b r e length below. 7. Accept l i n e pulsed at the rate of 8 pulses per minute during t h i s t e s t . 8. Accept l i n e pulsed at the rate of 10 pulses per minute during t h i s t r i a l . 9. Accept l i n e pulsed at the rate of 17 pulses per minute during t h i s t r i a l . 10. Accept l i n e pulsed at the rate oF 6 pulses per minute during t h i s t r i a l . Table IX Tests 65-68 F i b r e Length/Permeability Data f i b r e length f i b r e cone. permeability permeability p e r m e a b i l i t y permeability (mm) (fi b r e s / 1 ) (test 65) (test 66) (t e s t 67) (tes t 68) 0.00-0.20 4100 0. 79 0.73 0.78 0.78 0.20-0.41 5900 0.84 0.76 0.79 0.59 0.41-0.61 8000 0.82 0.67 0.69 0.45 0.61-0.82 4300 0.74 0.58 0.63 0.30 0.82-1.02 3700 0.73 0.48 0.57 0.25 1.02-1.23 3300 0.68 0.43 0.48 0.21 1.23-1.44 3100 0.63 0.40 0.46 0.18 1.44-1.64 3100 0.57 0.38 0.39 0. 16 1.64-1.85 2800 0. 54 0. 34 0.36 0.11 1.85-2.05 2800 0.54 0.31 0.33 0.09 2.05-2.26 2700 0.51 0.29 0.29 0.07 2.26-2.47 2500 0.50 0.25 0.25 0.06 2.47-2.67 2400 0.46 0.21 0.21 0.06 2.67-2.88 2200 0.46 0.19 0.21 0.06 2.88-3.08 2100 0.45 0.18 0.20 0.06 3.08-3.29 1800 0.43 0.17 0.19 0.06 3.29-3.50 1700 0.43 0.17 0.19 0.05 3.50-3.70 1400 0.40 0.18 0.17 0.04 3.70-3.91 1300 0. 38 0.18 0.16 0.03 3.91-4. U 1100 0.33 0.17 0.14 0.03 Table IX Tests 65-68 Fibre Length/Permeability Data (continued) f i b r e length f i b r e cone. permeability permeability permeability permeability (mm) (fibr e s / 1 ) (test 65) (test 66) (t e s t 67) (tes t 68) 4.11-4. 32 1000 0. 30 0.16 0.13 0.03 4.32-4. 52 800 0.25 0.13 0.12 0.03 4.52-4. 73 700 0.24 0.11 0.12 0.03 4.73-4. 94 500 0.25 0.08 0.13 0.02 4.94-5 . 14 400 0.29 0.09 0.12 0.01 5.14-5. 35 200 0. 36 0.10 0.11 0.01 5.35-5. 55 200 0.35 0.09 0.10 0.02 5.55-5. 76 100 0. 32 0.08 0.08 0.02 5.76-5. 97 100 0.29 0.08 0.08 0.01 5.97-6. 17 100 0.23 0.08 0.09 0.00 6.17-6. 38 50 0.21 0.11 0.06 0.00 6.38-6. 58 30 0.16 0.22 0.06 0.00 6.58-6. 79 20 0.20 0.14 0.08 0.00 6.79-7. 00 10 0.00 0.00 0.00 0.00 7.00 + 300 0.21 0.00 0.00 0.00 T r i a l conditions: f i b r e type k r a f t pulp k r a f t pulp k r a f t pulp k r a f t pulp s l o t width (mm) 0.5 0.5 0.5 0.5 feed v e l o c i t y (m/s) 6.4 6.4 6.4 6.4 accept v e l o c i t y (m/s) 3.1 1.8 2.0 0.9 p u l s a t i o n rate (pulses per min. . ) 0 0 8 0 Table X Tests 69-71 Fibre Length/Permeability Data f i b r e length f i b r e cone. permeability permeability permeability (mm) (fibres/1) (test 69) (t e s t 70) (tes t 71) 0.00-0.20 14400 0.65 0.75 0.79 0.20-0.41 22400 0.70 0.78 0.63 0.41-0.61 26900 0.67 0.71 0.44 0.61-0.82 16100 0. 57 0.51 0.32 0.82-1.02 12500 0.53 0.45 0.28 1.02-1.23 9500 0.50 0.40 0.23 1.23-1.44 7300 0.50 0.38 0.18 1.44-1.64 5500 0.48 0.33 0.14 1.64-1.85 4100 0.46 0.29 0.12 1.85-2.05 3300 0.40 0.23 0.09 2.05-2.26 2400 0.35 0.20 0.08 2.26-2.47 1900 0.31 0.17 0.06 2.47-2.67 1500 0. 30 0.17 0.06 2.67-2.88 1100 0.32 0.17 0.05 2.88-3.08 900 0.32 0.15 0.05 3.08-3.29 700 0.32 0.11 0.03 3.29-3.50 600 0.31 0.11 0.02 3.50-3.70 400 0.30 0.12 0.01 3.70-3.91 300 0.31 0.11 0.01 3.91-4.11 200 0.36 0.11 0.03 Table X Tests 69-71 Fibre Length/Permeability Data (continued) f i b r e length f i b r e cone. permeability permeabilitry permeability (mm) (fibres/1) (t e s t 69) (t e s t 70) (t e s t 71) 4.11-4.32 100 0.43 0.15 0.06 4.32-4.52 80 0.48 0.19 0.07 4.52-4.73 80 0.42 0.15 0.04 4.73-4.94 60 0.26 0.12 0.00 4.94-5.14 50 0.17 0.07 0.00 5.14-5.35 30 0.00 0.00 0.00 5.35-5.55 30 0.00 0.00 0.00 5.55-5.76 10 0.28 0.00 0.00 5.76-5.97 10 0.83 0.00 0.00 5.97-6.17 10 1.79 0.00 0.00 6.17-6.38 0 - - -6.38-6.58 0 - - -6.58-6.79 0 6.79-7.00 0 - - -7.00 + 10 2.61 0.00 0.00 T r i a l conditions: f i b r e type CTMP CTMP CTMP s l o t width (mm) 0.5 0.5 0.5 feed v e l o c i t y (m/s) 6.4 6.4 6.4 accept v e l o c i t y (m/s) 3.1 1.9 0.9 pul s a t i o n rate (pulses per min.) 8 10 0 Table XI Tests 72-74 Fibre Length/Permeability Data f i b r e length f i b r e cone. permeability permeability p e r m e a b i l i t y (mm) (fibres/1) (test 72) (t e s t 73) (t e s t 74) 0.00-0.20 5700 0.36 0.37 0. 35 0.20-0.41 3800 0.64 0.70 0.58 0.41-0.61 3900 0.79 0.77 0.53 0.61-0.82 2000 0.65 0.78 0.49 0.82-1.02 2800 0.62 0.55 0.32 1.02-1.23 3000 0. 59 0.45 0.25 1.23-1.44 2700 0.56 0.39 0.20 1.44-1.64 2900 0.47 0.24 0.13 1.64-1.85 2800 0.42 0.17 0.09 1.85-2.05 2400 0.41 0.15 0.09 2.05-2.26 900 0. 38 0.17 0.06 2.26-2.47 300 0.42 0.28 0.10 2.47-2.67 200 0.39 0.28 0.14 2.67-2.88 300 0.21 0.07 0.08 2.88-3.08 500 0.17 0.04 0.04 3.08-3.29 1300 0.15 0.03 0.01 3.29-3.50 1900 0.15 0.02 0.01 3.50-3.70 1700 0.16 0.02 0.01 3.70-3.91 1000 0.17 0.02 0.02 3.91-4.11 200 0.25 0.03 0.06 Table XI Tests 72-74 Fibre Length/Permeability Data (continued) f i b r e length f i b r e cone. permeability permeability permeability (mm) (fibres/1) (test 72) ( t e s t 73) (tes t 74) 4.11-4.32 100 0.24 0.04 0.06 4.32-4.52 50 0.25 0.06 0.06 4.52-4.73 30 0.24 0.06 0.06 4.73-4.94 0 - - -4.94-5.14 0 5.14-5.35 0 - - -5.35-5.55 0 - - -5.55-5.76 < 10 0.74 0.00 0.00 5.76-5.97 < 10 0.25 0.00 0.00 5.97-6.17 < 10 0.00 0.00 0.00 6.17-6.38 < 10 0.00 0.00 0.00 6.38-6.58 < 10 0.00 0.72 0.00 6.58-6.79 < 10 0.00 0.90 0.00 6.79-7.00 < 10 0.00 0.84 0.00 7.00 + 60 0.00 0.00 0.00 T r i a l conditions! f i b r e type nylon nylon nylon s l o t width (mm) 0.5 0.5 0.5 feed v e l o c i t y (m/s) 6.4 6.4 6.4 accept v e l o c i t y (m/s) 3.2 1.9 0.9 puls a t i o n rate (pulses per min.) 17 0 0 A P P E N D I X I I C O M P U T E R P R O G R A M M E S 9 7 10 ' 20 ' D i g i t i z i n g F i b r e - S l o t Films 30 * Robert Gooding 40 ' May 1984 50 • 60 ' This program records and displays the p o s i t i o n , o r i e n t a t i o n and 65 ' curvature of f i b r e s in a s e r i e s of f i l m frames. The data is i n s t a l l e d 70 ' in a f i l e that bears the f i l m number (e.g. FILrt.l). Other programmes 80 ' i n t e r p r e t the data and determine the p r o b a b i l i t y a f i b r e w i l l assume 90 ' a given p o s i t i o n or o r i e n t a t i o n . 100 ' 110 ' V a r i a b l e s : 120 ' FRN frame number 130 * FRA frame counter 140 * NFRA FRA plus one 150 ' FRAM FRN for f i b r e ' s f i r s t appearance 160 ' CUT f i b r e sequence counter 170 ' FIB f i b r e counter 180 ' CHEK =1 i f FIB counter i s in use; =0 otherwise 190 * CX1,CY1,CX2,CY2 c a l i b r a t i o n coordinates (s l o t corners) 200 ' TRX,TRY,LRX,LRY frame image coordinates 210 ' TLX, TLY ,LLX, LLY 220 ' TOP,BOT,RIT,LEFT length of frame sides 230 ' PX1,PY1,PX2,PY2 plate end coordinates 240 ' MSX1,MSY1,MSX2,MSY2 mid-slot corner coordinates 250 ' MSX3,MSY3,MSX4,MSY4 260 ' AX1,AY1,AX2,AY2 s l o t e x i t coordinates 270 * CX1A,CY1A arrays of o r i g i n coordinates 290 ' AX,AY,BX,BY,CX,CY arrays of f i b r e end, middle and end coordinates 300 * DF$ data storage f i l e 310 ' DAT$ date of analysis 320 ' NAM$ analyst 330 ' Z button l a b e l (=1,2 or 4) 340 * CAL c a l i b r a t i o n length ( i . e . s l o t width) 350 ' Q,R multipurpose counters 360 • 370 CLS 380 OPEN "coml:9600,n,8,l,rs,cs,ds,cd" AS #1 390 PRINT f1,CHR$ (32),CHR$(66) 400 ' 410 ' Sketch a screen p l a t e . 420 SCREEN 2 430 CLS 440 LINE (559,27)-(80,172),,B 450 LINE (80,150)-(310,150) 460 LINE -(310,160) 470 LINE -(300,160) 480 LINE -(300,172) 490 LINE (559,150)-(330,150) 500 LINE -(330,160) 510 LINE -(340,160) 520 LINE -(340,172) 530 * 540 PRINT "Check alignment by lo c a t i n g the four corners of the frame image with the blue button - following the prompt." 550 CIRCLE (559,27),15 560 INPUT #1,TRX,TRY,Z 570 IF Z O l THEN 560 580 CIRCLE (559,27),15,0 590 CIRCLE (559,172),15 600 INPUT #1,LRX,LRY,Z 610 IF Z O l THEN 600 620 CIRCLE (559,172) ,15,0 9 8 630 CIRCLE (80,172),15 640 INPUT #l,LLX,LLY,Z 650 IF Z O l THEN 640 660 CIRCLE (80,172),15,0 670 CIRCLE (80,27),15 680 INPUT #1,TLX,TLY,Z 690 IF Z O l THEN 680 700 * 710 ' Now check to see i f opposing sides have approximately equal lengths. 720 TOP=SQR((TRX—TLX)"2 +(TRY-TLY)*2) 730 BOT=SQR((LRX-LLX)"2+(LRY-LLY)*2) 740 RIT=SQR((TRX-LRX)"2+(TRY-LRY)~2) 750 LEFT=SQR((TLX-LLX)"2+(TLY-LLY)*2) 760 PRINT "TOP=",TOP,"BOT=",BOT 770 PRINT "RIT=",RIT,™LEFT=",LEFT 780 PRINT "TRX=",TRX,"TRY=",TRY 790 PRINT "LRX=",LRX,"LRY=",LRY 800 PRINT "LLX=",LLX,"LLY=",LLY 810 PRINT "TLX=",TLX,"TLY=",TLY 820 CK1=ABS(RIT-LEFT)/RIT 830 CK2=ABS(T0P-B0T)/T0P 840 IF CK2>CK1, THEN CK1=CK2 850 IF CK1>.05, GOTO 540 860 PRINT "Alignment co r r e c t to",CK1*100,"%" 870 ' 880 PRINT "Locate other key points on the screenplate." 890 CIRCLE (80,150),15 900 INPUT #1,PX1,PY1,Z 910 CIRCLE (80,150) ,15,0 920 CIRCLE (310,150),15 930 INPUT #1,CX1,CY1,Z 940 IF Z O l THEN 930 950 CIRCLE (310,150) ,15,0 960 CIRCLE (330,150),15 970 INPUT #1,CX2,CY2,Z 980 IF Z O l THEN 970 990 CIRCLE (330,150),15,0 1000 CIRCLE (559,150),15 1010 INPUT #1,PX2,PY2,Z 1020 IF Z O l THEN 1010 1030 CIRCLE (559,150) ,15,0 1040 CIRCLE (300,160),15 1050 INPUT #1,MSX1,MSY1,Z 1060 IF Z O l THEN 1050 1070 CIRCLE (300,160),15,0 1080 CIRCLE (310,160),15 1090 INPUT #1,MSX2,MSY2,Z 1100 IF Z O l THEN 1090 1110 CIRCLE (310,160),15,0 1120 CIRCLE (330,160),15 1130 INPUT tl,MSX3,MSY3,Z 1140 IF Z O l THEN 1130 1150 CIRCLE (330,160),15,0 1160 CIRCLE (340,160),15 1170 INPUT #1,MSX4,MSY4,Z 1180 IF Z O l THEN 1170 1190 CIRCLE (340,160),15,0 1200 CIRCLE (300,172),15 1210 INPUT I1,AX1,AY1,Z 1220 IF Z O l THEN 1210 1230 CIRCLE (300,1721,15,0 1240 CIRCLE (340,172),15 1250 INPUT #1,AX2,AY2,Z 9 9 L260 IF Z O l THEN 1250 1270 CIRCLE (340,172),15,0 1280 ' 1290 ' Preliminary information: L300 INPUT "Data f i l e name",DF$ 1310 OPEN DF$ AS #2 LEN=32 1330 INPUT "S t a r t i n g frame nuraber";FRN 1335 INPUT "S t a r t i n g sequence number";CNT 1350 INPUT "Date (day-month-year)",OAT$ 1360 INPUT "Analyst";NAM$ 1370 FIELD #2, 10 AS L$, 12 AS M$, 10 AS N$ 1380 RSET L$=DAT$ 1390 RSET M$=NAM$ 1400 RSET NS=DF$ 1410 PUT #2,1 1420 FIELD #2, 4 AS A$, 4 AS B$, 4 AS C$, 4 AS D$, 4 AS E$, 4 AS F$, 4 AS G$, 4 AS H$ 1430 RSET A$=MKS$(TRX):RSET B$=MKS$(TRY):RSET C$=MKS$(LRX):RSET D$=MKSS(LRY):R SET E$=MKS$(LLX):RSET F$=MKS$(LLY):RSET G$=MKS$(TLX):RSET H$=MKSS(TLY) 1440 PUT #2,2 1450 RSET A$=MKS$(PX1):RSET B$=MKS$(PY1):RSET C$=MKSS(PX2):RSET D$=MKS$(PY2):R SET ES=MKS$ (CXI):RSET F$=MKSS(CY1):RSET G$=MKS$(CX2):RSET H$=MKS$(CY2) 1460 PUT #2,3 1470 RSET A$=MKSS(MSX1):RSET BS=MKS$(MSY1):RSET C$=MKS$(MSX2):RSET D$=MKS$(MSY 2):RSET E$=MKS$(MSX3):RSET F$=MKS$(MSY3):RSET G$=MKS$(MSX4):RSET H$=MKS$(MSY4) 1480 PUT #2,4 1490 RSET A$=MKS$(AX1):RSET B$=MKS$(AY1):RSET C$=MKS$(AX2):RSET D$=MKS$(AY2) 1500 PUT #2,5 1505 CAL=SQR((PX2—PX1)"2+(PY2-PY1)~2)/10 1510 • 1520 ' Draw the image 1530 SCREEN 2 1540 LINE (0,0)-(639,199),0,BF 1550 LINE (TLX*.101 + 26.62,225—TLY*•0403) — (TRX*.101 + 26.62,225—TLY*. 0403) 1560 LINE -(LRX*. 101 + 26.62,225—LRY*.0403) 1570 LINE -(LLX*.101+26.62,225—LLY*.0403) 1580 LINE —(TLX*.101+26.62,225—TLY *.0403) 1590 LINE (PX1*.101+26.62,225-PY1*.0403)- (CXI*.101 + 26.62,225-CY1*.0403) 1600 LINE (CX2*. 101 + 26.62,225-CY2*.0 403)-(PX2 *.101 + 26.62,225-PY2*.0403) 1610 LINE (CXI*.101+26.62,225-CY1*.0403)- (MSX2*.101 + 26.62,225-MSY2*.0403) 1620 LINE -(MSX1*.101+26.62,225-MSY1*.0403) 1630 LINE -(AX1*.101+26.62,225-AYl*.0403) 1640 LINE (AX2 *.101 + 26.62,225—AY2 *.0403)- (MSX4 *.101 + 26.62,225-MSY4 * . 0 403 ) 1650 LINE - (MSX3*-101 + 26.62,225-MSY3*.0403) 1660 LINE -(CX2*.101+26.62,225-CY2*.0403) 1670 LPRINT "Film No.",DF$,"CAL=",CAL 1673 SA$=" REC ":SB$=" FRAM ":SC§=" FCNT ":SD$=" AX ":SE§=" AY ":SF$=" BX ":SG$=" BY ":SH$=" CX ":SI$=" CY 1676 LPRINT USING "\ \";SA$;SB$;SC$;SD$;SE$;SF$;SG$;SH$ ; SIS 1680 " 1690 ' Define each f i b r e by l o c a t i n g the end, middle and end of each with the b l ue button. 1700 DIM AX (15,15) ,AY(15,15) ,BX(15,15),BY(15,15),CX(15,15) ,CY(15,15) 1710 DIM CHEKU5) 1720 DIM FRAM(15),FCNT(15) 1730 DIM CXIA(15,15),CY1A(15,15) 1740 GOTO 2380 1810 ' 1820 ' Redefine the p l a t e coordinates for each frame. 1830 IF FRN=1 GOTO 2380 1840 FRN=FRN+1 1900 CIRCLE (CXI*.101+26.62,225-CY1*.0403),15 1910 INPUT #1,CX1N,CY1N,Z 1920 IF Z O l GOTO 1910 1 0 0 1930 CIRCLE (CXI *.101+ 26.62,225-CY1*.0403) ,15,0 1940 CX1=CX1N: CY1=CY1N 2000 ' 2010 ' Define the f i b r e s that appeared in the previous frame. 2020 FOR FIB=1 TO 15 2030 IF CHEK(FIB)<>1 GOTO 2350 2040 FOR Q=l TO 15 2050 FRA=16-Q 2060 IF AX (FRA,FIB)<>0 GOTO 2080 2070 NEXT Q 2080 CIRCLE (AX(FRA,FIB)*.101 + 26.62,225-AY(FRA,FIB)*.0403) ,5 2090 NFRA=FRA+1 2100 INPUT #1, AX(NFRA,FIB), AY(NFRA,FIB),Z 2110 CIRCLE (AX(FRA,FIB)*.101 + 26.62,225-AY(FRA,FIB)*.0403) ,5,0 2120 * If Z=2 (black button) then the f i b r e has disappeared. 2130 IF Z<>2 GOTO 2170 2140 AX(NFRA,FIB)=0: AY(NFRA,FIB)=0 2150 GOTO 2750 2160 ' If Z=4 (red button) then the session has concluded 2170 IF Z=4 GOTO 3160 2180 IF Z O l GOTO 2100 2190 CIRCLE (BX(FRA,FIB)*.101 + 26.62,225-BY(FRA,FIB)*.0403) ,5 2200 INPUT #1, BX(NFRA,FIB), BY(NFRA,FIB),Z 2210 IF Z O l GOTO 2200 2220 CIRCLE (BX(FRA,FIB)*.101+26.62,225-BY(FRA,FIB)*.0403) ,5,0 2230 CIRCLE (CX(FRA,FIB)*.101 + 26.62,225—CY(FRA,FIB)*.0403) ,5 2240 INPUT #1, CX(NFRA,FIB), CY(NFRA,FIB),Z 2250 IF Z O l GOTO 2240 2260 CIRCLE (CX(FRA,FIB)*.101+26.62,225-CY(FRA,FIB)*.0403),5,0 2290 CX1A(NFRA,FIB)=CX1 2300 CY1A(NFRA,FIB)=CY1 2330 LINE (AX(NFRA,FIB)*.101+26.62,225-AY(NFRA,FIB)*.0403)-(BX(NFRA,FIB)*.101+ 26.62,225-BY (NFRA,FIB)*.0403) 2340 LINE (BX(NFRA,FIB)*.101+26.62,225-BY(NFRA,FIB)*.0403)-(CX(NFRA,FIB)*.101+ 26.62,225-CY(NFRA,FIB)*.0403) 2350 NEXT FIB 2360 ' 2370 ' Define the f i b r e s that have appeared for the f i r s t time. 2380 FRA=1 2390 FOR FIB=1 TO 15 2400 IF CHEK(FIB)<>0 GOTO 2710 2410 CIRCLE (50,50),25 2420 INPUT *1,AX(FRA,FIB),AY(FRA,FIB),Z 2430 CIRCLE (50,50),25,0 2440 ' If Z=2 (black button) then there are no more new f i b r e s . 2450 IF Z<>2 GOTO 2490 2460 AX(FRA,FIB)=0: AY (FRA,FIB)=0 2470 GOTO 1840 2480 ' If Z=4 (red button) then the session has concluded 2490 IF Z=4 GOTO 3160 2500 IF Z O l GOTO 2420 2510 CIRCLE (300,50),25 2520 INPUT #1,BX(FRA,FIB),BY(FRA,FIB),Z 2530 IF Z O l GOTO 2520 2540 CIRCLE (300,50),25,0 2550 CIRCLE (600,50),25 2560 INPUT #1, CX(FRA,FIB),CY(FRA,FIB),Z 2570 IF Z O l GOTO 2560 2580 CIRCLE (600,50) , 25,0 2590 CHEK(FIB)=1 2600 FRAM(FIB)=FRN 2610 FCNT(FIB)=CNT 2620 CNT=CNT+1 2650 CXIA(FRA,FIB)=CXl 1 0 1 2660 CY1A(FRA,FIB)=CY1 2690 LINE (AX(FRA,FIB)*.101+26.62,225-AY(FRA,FIB)*.0403)-(BX(FRA,FIB) *.101 + 26. 6 2,2 25-BY(FRA,FIB)*.0403) 2700 LINE (BX(FRA,FIB)*.101 + 26.62,2 25-BY(FRA,FIB)*.040 3)-(CX(FRA,FIB)*.101+26. 62,225-CY(FRA,FIB)*.0403) 2710 NEXT FIB 2720 GOTO 1840 2730 1 2740 ' Store the locations of a f i b r e that has disappeared. 2750 FOR FRA=1 TO FRA 2770 * Transform coordinates: 2780 TX=AX(FRA,FIB) 2790 TY=AY(FRA,FIB) 2800 GOSOB 3060 2805 TXA=TX:TYA=TY 2810 RSET A$=MKS$(TX) 2820 RSET BS=MKS$(TY) 2830 TX=BX(FRA,FIB) 2840 TY=BY(FRA,FIB) 2850 GOSUB 3060 2855 TXB=TX:TYB=TY 2860 RSET C$=MKS$(TX) 2870 RSET D$=MKS$(TY) 2880 TX=CX(FRA,FIB) 2890 TY=CY(FRA,FIB) 2900 GOSOB 3060 2905 TXC=TX:TYC=TY 2910 RSET E$=MKS$(TX) 2920 RSET F$=MKS$(TY) 2925 LPRINT OSING "####.###";LOC(2)+1;FRAM (FIB);FCNT(FIB);TXA;TYA;TXB;TYB;TXC; TYC 2930 RSET G$=MKS$(FRAM(FIB)) 2940 RSET H$=MKS$(FCNT (FIB)) 2950 POT #2 2960 LINE (AX(FRA,FIB)*.101 + 26.62,2 25-AY(FRA,FIB)*.0403)-(BX(FRA,FIB)*. 101 + 26. 62,2 2 5-BY(FRA,FIB)*.0403),0 2970 LINE (BX(FRA,FIB)*.101+26.62,2 25-BY(FRA,FIB)*.0403)-(CX(FRA,FIB)*.101+26. 62,22 5-CY(FRA,FIB)*.0403),0 2980 NEXT FRA 2981 LPRINT " " 2990 CHEK(FIB)=0 3000 FOR Q=l TO FRA 3010 AX(Q,FIB)=0: AY(Q,FIB)=0: BX(Q,FIB)=0: BY(Q,FIB)=0: CX(Q,FIB)=8: CY(Q,FIB )=0 3020 NEXT Q 3030 GOTO 2350 3040 ' 3050 ' This subroutine transforms pad coordinates to frame coordinates. Slot width is taken as the unit of distance. 3060 TX=(TX-CX1A(FRA,FIB))/CAL 3070 TY=(TY-CY1A(FRA,FIB))/CAL 3080 RAD=SQR(TX"2+TY"2) 3085 IF TX<0 THEN RAD=-RAD 3090 ANG1=ATN(TY/TX) 3100 ANG2=ATN((PY1-CY1)/(PX1-CX1)) 3110 TX=RA0*C0S(ANG1-ANG2) 3120 TY=RAD*SIN(ANG1-ANG2) 3130 RETORN 3140 * 3150 ' We conclude the session by p r i n t i n g the f i n a l record and frame number. 3160 LPRINT "End of Session for Film Number";DF$ 3170 LPRINT " F i n a l Frame Number =";FRN 3180 LPRINT " F i n a l Record Number =";L0C(2) 3190 END 1 0 2 10 • 20 * D i s p l a y i n g / L i s t i n g Fibre T r a j e c t o r i e s 30 ' Robert Gooding 40 * May 1984 50 ' 60 ' Given a f i l e number ( f i l m number) and the addresses of f i b r e sequences, 70 ' ( i n i t i a l record numbers) t h i s programme draws the f i b r e positions of 80 ' those sequences, or p r i n t s the coordinates of the points that define 90 ' the f i b r e p o s i t i o n s . 100 ' 110 • 120 ' Variables: 130 ' DFS data storage f i l e 140 ' NAM$ analyst 150 1 DAT$ date of analysis 160 ' TRX,TRY,LRX,LRY frame image corner coordinates 170 * TLX,TLY,LLX,LLY 180 ' PX1,PY1,PX2,PY2 pl a t e end coordinates 190 ' MSX1,MSY1,MSX2,MSY2 mid-slot coordinates 200 * MSX3,MSY3,MSX4,MSY4 210 ' SEQ number of sequences for display 220 ' RNM array of s t a r t i n g record numbers 230 * RN record number 240 ' IND$ d i s p l a y / l i s t indicator 250 ' Q,R,U multipurpose counters 260 ' FCNT f i b r e sequence counter 270 1 FCNTM f i b r e sequence counter for previous record 280 ' FRA frame counter 290 ' FRAM frame number 300 ' 310 CLS 320 INPUT "Data f i l e narae",DF$ 330 OPEN DF$ AS #2 LEN=32 340 DIM RNM(15),FCNT(15),AX(15,15),AY (15,15) ,BX (15,15),BY(15,15),CX(15,15),CY (15,15) 350 * 360 ' Load preliminary data 370 FIELD #2, 10 AS L$, 12 AS M$, 10 AS N$ 380 GET #2,1 390 DF$=N$ 400 NAM$=M$ 410 DAT$=L$ 420 PRINT DFS,NAM$,DAT$ 430 FIELD #2, 4 AS A$, 4 AS B$, 4 AS C$, 4 AS D$, 4 AS E$, 4 AS F$, 4 AS G$, 4 AS H$ 440 GET #2,2 450 TRX=CVS(A$):TRY=CVS(B$):LRX=CVS(C$):LRY=CVS(D$):LLX=CVS(E$):LLY=CVS(F$):T LX=CVS(G$):TLY=CVS(H$) 460 GET #2,3 470 PX1=CVS(A$):PY1=CVS(B$):PX2=CVS(C$):PY2=CVS(D$):CX1=CVS(ES):CY1=CVS(F$):C X2=CVS(G$):CY2=CVS(H$) 480 GET #2,4 490 MSX1=CVS(A$):MSY1=CVS(B$):MSX2=CVS(C$):MSY2=CVS(D$):MSX3=CVS(E$):MSY3=CVS (F$):MSX4=CVS(GS):MSY4=CVS(HS) 500 GET #2,5 510 AX1=CVS(A$):AY1=CVS(B$):AX2=CVS(C$):AY2=CVS(D$) 520 ' 530 ' Interogate operator 540 INPUT "Number of f i b r e sequences";SEQ 550 IF SEQ=0 GOTO 1570 560 FOR U=l TO SEQ 570 INPUT "Give a sequence record number";RNM(U) 580 NEXT U 1 0 3 590 INPUT " d i s p l a y , l i s s t ot ceel ";IND$ 600 IF IND$="display" GOTO 650 610 IF INDS="lisst" GOTO 650 611 IF IND$="reel" GOTO 650 620 GOTO 590 630 ' 640 ' Consider each f i b r e sequence. 650 FOR U=l TO SEQ 660 RN=RNM(U) 670 GET #2,RN 680 FCNT(U)=CVS(H$) 690 IF RN=6 GOTO 780 700 ' 710 ' Search for the s t a r t of the f i b r e sequence and load the data. 720 RN=RN-1 730 GET *2,RN 740 FCNTM=CVS(H$) 750 IF FCNT(U)=FCNTM GOTO 720 760 RN=RN+1 770 GET #2,RN 780 FRAM=CVS(G$) 800 ' 810 ' Load data for each sequence 820 FCNTM=FCNT(U) 830 FRA=1 840 AX(FRA,0)=CVS(AS):AY(FRA,U)=CVS (B$):BX(FRA,U)=CVS(CS):BY(FRA,U)=CVS(D$):C X(FRA,U)=CVS(ES):CY(FRA,U)=CVS(F$) 850 GET #2 860 FCNTM=CVS (H$) 870 IF FCNT (U) OFCNTM GOTO 900 880 FRA=FRA+1 890 GOTO 840 900 NEXT U 910 IF IND$="lisst" GOTO 1500 920 * 930 * Draw the screen p l a t e and d i s p l a y the f i b r e sequences. 940 SCREEN 2 950 CLS 960 LINE (0,0)-(639,199) ,0,BF 970 LINE (TLX*.101 + 26.62,225-TLY*.0403)-(TRX*.101+26.62,225-TLY*. 0403) 980 LINE -(LRX*.101+26.62,225-LRY*.0403) 990 LINE -(LLX*.101+26.62,225-LLY*.0403) 1000 LINE -(TLX*.101+26.62,225-TLY*.0403) 1010 LINE (PX1*.101 + 26.62,225-PY1*.0403)-(CXI *.101+26.62,225-CY1*. 0403) 10 20 LINE (CX2*.101 + 26.62, 225-CY2*.0403)- (PX2*.101 + 26.62,225-PY2*.0 403) 10 30 LINE (CXI*.101+26.62,225-CY1*.0403)-(MSX2*.101+26.62,225-MSY2*.0403) 1040 LINE -(MSX1*.101+26.62,225-MSY1*.0403) 1050 LINE -(AX1*.101+26.62,225-AY1*.0403) 1060 LINE (AX2*.101 + 26.62,225-AY2*.0 403)-(MSX4 *.101 + 26.62,2 25-MSY4 *.0403) 1070 LINE -(MSX3*.101+26.62,225-MSY3*.0403) 1080 LINE -(CX2*.101+26.62,225-CY2*.0403) 1090 ' 1100 ' Transform coordinates. 1110 CAL=SQR( ( P X 2 - P X 1 ) ' 2 +(PY2 - P Y 1 )*2 ) / 1 0 1120 FOR U=l TO SEQ 1130 FOR Q=l TO FRA 1140 R=AX(Q,U) 1150 S=AY(Q,U) 1160 GOSOB 1370 1170 AX(Q,0)=R 1180 AY(Q,0)=S 1190 R=BX(Q,0) 1 2 0 0 S=BY(Q,0) 1 0 4 L210 GOSUB 1370 L220 BX(Q,U)=R L230 BY (Q,U)=S 1240 R=CX (Q,0) 1250 S=CY(Q,U) 1260 GOSUB 1370 1270 CX (Q,U)=R 1280 CY(Q,U)=S 1290 LINE (AX(Q,U) ,AY(Q,U))-(BX(Q,U),BY <Q,U) ) 1300 LINE (BX(Q,U),BY(Q,U))-(CX(Q,U),CY(Q,U)) 1310 NEXT Q 1311 PRINT"Stact of f i b r e sequence";FCNT(U);" at record number";RN;"frame numbe r";FRAM 1320 NEXT U 1322 IF IND$<>"reel" GOTO 540 1323 RNM(1)=RN+FRA 1324 INPUT ZX$ 1325 GOTO 650 1340 ' 1350 * This subroutine transforms frame coordinates to pad coordinates 1360 ' and then to screen coordinates. 1370 R=R*CAL+CX1 1380 S=S*CAL+CY1 1390 RAD=SQR(R"2+S"2) 1400 IF R<0 THEN RAD=-RAD 1410 ANG1=ATN(S/R) 1420 ANG2=ATN((PY1-CY1)/(PX1-CX1)) 1430 R=RAD*C0S(ANG1+ANG2) 1440 S=RAD*SIN(ANG1+ANG2) 1450 R=R*.101+26.62 1460 S=225-S*.0403 1470 RETURN 1480 ' 1490 ' L i s t the coordinates of the points that define the f i b r e t r a j e c t o r y 1500 FOR U=l TO SEQ 1510 FOR Q=l TO FRA 1520 PRINT "Frarae";Q;"Fibre";FCNT(U) 1530 PRINT "AX=";AX(Q,U);"AY=";AY(Q,U);"BX="; BX(Q,U);"BY=";BY(Q,U);"CX=" ;cx(Q, 0);"CY =";CY(Q,U) 1540 NEXT Q 1550 NEXT U 1560 GOTO 540 1570 END 1 0 5 10 • 20 ' DIGINT.Al 30 * Interpreting D i g i t i z e d Films 40 * *** This programme only considers f i b r e s that appear in any 15th frame *** 50 ' Robert Gooding 60 ' June 1984 70 * 80 ' This programme takes data stored in f i l e "Film.A" and determines the 90 ' d i s t r i b u t i o n of f i b r e centre distances (with respect to the wall) at 100 ' a plane 1.75 mm before the leading edge of the s l o t . 110 • 120 * V a r i a b l e s : 130 ' AS,B$,C$,D$ record locations of f i b r e p o s i t i o n and counters 140 * ES,F$,G$,HS 150 ' AX,AY,CX,CY arrays of f i b r e end points 160 ' N frame counter (within a sequence) 170 ' FCNT sequence number 180 * PS p o s i t i o n r e g i s t e r array 190 ' X,Y arrays of f i b r e mid-point coordinates 200 ' YL lo c a t i o n of f i b r e mid-point ahead of the s l o t 210 ' 220 CLEAR 230 CLS 240 OPEN "c:FILM.A" AS #1 LEN=32 250 FIELD #1, 4 AS A$, 4 AS B$, 4 AS C$, 4 AS D$, 4 AS E$, 4 AS F$, 4 AS G$, 4 AS H$ 260 DIM AX(15),AY(15),CX(15),CY(15),X(15),Y(15),PS(2,6) ,P(15) 270 DIM Q(15),R(15),S(15),DD(3,15),AS(20),BS(20),CS(20),DS(20),HS(20) 275 LENTOT=0:NTOT=0 280 GET #1,49 290 N=l 300 FLAG=0 310 AX(N)=CVS(A$):AY(N)=CVS(B$):CX(N)=CVS(E$):CY(N)=CVS(F$):FRAM=CVS(G$):FCNT =CVS(H$) 320 IF LOC(l)=3399 GOTO 440 330 IF (((N+FRAM-6)/15)-FIX((N+FRAM-6)/15))=0 THEN FLAG=1 340 GET #1 350 PRINT L0C(1),CVS(A$),CVS(H§) 360 GOTO 1750 370 IF FCNTOCVS (H$) GOTO 430 380 N=N+1 390 GOTO 310 400 ' 410 1 F i t a s p l i n e to the f i b r e p o s i t i o n s and determine the l o c a t i o n of the 420 ' midpoint ahead of the s l o t . 430 IF FLAG O l GOTO 290 440 FOR 1=1 TO N 450 X(I)=(AX(I)+CX(I))/2 460 Y(I)=(AY(I)+CY(I))/2 470 NEXT I 480 GOSUB 910 490 FOR 1=1 TO N 500 IF X(I)>-.7563 GOTO 520 510 NEXT I 520 IF 1=1 GOTO 540 530 1=1-1 540 YL=Y(I)+Q(I)*(-.7563-X(I))+R(I)*(-.7563-X(I))"2+S(I)*(-.7563-X(I))"3 550 IJ=6 560 IF YL<3.7813 THEN IJ=5 570 IF YL<1.2965 THEN IJ=4 580 IF YL<-6482 THEN IJ=3 590 IF YL<.3241 THEN IJ=2 600 IF YL-C.1621 THEN IJ = 1 1 0 6 610 615 616 620 630 640 650 660 ' 670 ' 680 690 700 710 720 725 727 730 740 ' 750 ' 760 ' 770 ' 780 " 790 ' 800 1 810 ' 820 ' 830 ' 840 ' 850 ' 860 ' 870 ' 880 ' 890 ' 900 ' 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 LENGTH=SQR ( (AX (I) -CX (I) ) "2+ (AY (I) -CY (I) ) ~2) LENTOT=LENTOT+LENGTH NT0T=NT0T+1 IF LENGTH>.6482 THEN IK=1 ELSE IK=2 PS(IK,IJ)-PS (IK,IJ)+1 IF LOC(l)=3399 GOTO 680 GOTO 290 L i s t the d i s t r i b u t i o n of f i b r e centres. FOR 1=1 TO 6 FOR J=l TO 2 LPRINT "I=",I,"J = ",J,"NUMBER=",PS(J,I) NEXT J NEXT I LAVE=LENT0T*2.314/NTOT LPRINT "Average Length=",LAVE END Subroutine SPLINE This subroutine f i t s a cubic s p l i n e of the form: F(X) = Y(I) + Q(I)*(X-X(I)) + R(I)*(X-X(I))**2 + S(I)*(X-X(I))**3 to an array of N coordinate p a i r s . Input: coordinate vectors number of coordinate points X,Y N Output: Q,R,S V a r i a b l e s : I,IP,IPP DD,A4,B4,AS BS,CS,DS,HS vectors of i n t e r p o l a t i o n c o e f f i c i e n t s counters matrix elements Ose d i v i d e d d i f f e r e n c e s to f i n d A4 and B4 NM=N-1 FOR 1=1 TO 3 IP=I+1 DD(1,I) = (Y(IP)-Y(I) )/(X(IP)-X(D) NEXT I FOR 1=1 TO 2 IP=I+1 IPP=I+2 DD(2,I)=(DD(1,IP)-DD(1,I))/(X(IPP)-X(I)) NEXT I A4=(DD(2,2)-DD(2,1))/(X(4)-X(1)) t FOR J=l TO 3 I=N-4+J IP=I+1 DD(1,I) = (Y(IP)-Y(I))/(X(IP)-X(D) NEXT J FOR J=l TO 2 I=N-4+J IP=I+1 IPP=I+2 DD(2,I) = (DD(1,IP)-DD(1,I))/(X(IPP)-X(I) ) NEXT J B4=(DD(2,N-2)-DD(2,N-3))/(X(N)-X(N-3)) • FOR 1=1 TO NM IP=I+1 HS(I)=X(IP)-X(I) NEXT I 1 0 7 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320 1330 1340 1350 1360 1370 1380 1390 1400 1410 1420 1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 1630 1640 1650 1660 1670 1680 1690 1700 1710 1720 1730 1740 1750 1760 1770 1780 1790 1800 1810 1820 ' Find the c o e f f i c i e n t s of the tr i d i a g o n a l equations. BS(1)=-HS (1) CS(1)=HS(1) DS(1)=3*A4*HS (1) "2 FOR 1=2 TO NM IP=I+1 IM=I-1 AS(I)=HS(IM) BS(I)=2*(HS(IM)+HS(I)) CS(I)=HS(I) DS(I)=3*((Y(IP)-Y(I))/HS(I)-(Y(I)-Y(IM))/HS(IM)) NEXT I AS (N) =HS (NM) BS(N)=—HS(NM) DS (N)=-3*B4*HS(NM)"2 GOSOB 1580 * Determine Q(I) and S(I) FOR 1=1 TO NM IP=I+1 Q(I)=(Y(IP)-Y(I))/HS(I)-HS(I)*(2*R(I)+R(IP))/3 S(I)=(R(IP)-R(I))/(3*HS(I)) NEXT I RETURN i ' Subroutine TDMA i ' This subroutine solves a t r i d i a g o n a l matrix. ' Input: ' AS,BS,CS,DS matrix c o e f f i c i e n t s number of matrix rows Output: Variables N R P,Q,DEN sol u t i o n vector matrix variables P(1)=-CS(1)/BS(1) Q(1)=DS(1)/BS(1) FOR 1=2 TO N IM=I-1 DEN=AS(I)*P(IM)+BS(I) P(I)=-CS(I)/DEN Q(I)=(DS(I)-AS(I)*Q(IM))/DEN NEXT I R(N)=Q(N) FOR 11=1 TO NM I=N-II IP=I+1 R(I)=P(I)*R(IP)+Q(I) NEXT II RETURN This subroutine i n s t r u c t s the program to overlook c e r t a i n sequences. IF (LOC(l)>69) AND (LOCQX72) GOTO 340 IF LOC(l)=261 GOTO 340 IF LOC(1)=310 GOTO 340 IF (LOC(l)>688) AND (LOC(l)<726) GOTO 340 IF LOC(l)=743 GOTO 340 IF LOC(l)=762 GOTO 340 IF (LOC(l)>841) AND (LOC(l)<848) GOTO 340 IF (LOC(l)>947) AND (LOC(l)<954) GOTO 340 1 0 8 1830 IF (L0C(1)>1150) AND (LOC(l)<1166) GOTO 340 1840 IF (LOC(l)>1171) AND (LOCUK1174) GOTO 340 1850 IF LOC(l)=1218 GOTO 340 1860 IF (LOC(l)>1334) AND (LOCUX1342) GOTO 340 1870 IF LOC(l)=1361 GOTO 340 1880 IF <L0C(1)>1425) AND (LOC(l)<1428) GOTO 340 1890 IF LOC(l)=1468 GOTO 340 1900 IF (LOC(l)>1486) AND (LOC(l)<1492) GOTO 340 1910 IF (LOC(l)>1511) AND (LOC(l)<1566) GOTO 340 1920 IF LOC(l)=1655 GOTO 340 1930 IF (LOC(l)>1912) AND (LOCUX1994) GOTO 340 1940 IF LOC(1)=2059 GOTO 340 1950 IF (LOC(l)>2112) AND (LOC(l)<2119) GOTO 340 1960 IF (LOC(1)>2198) AND (LOC(l)<2202) GOTO 340 1970 IF LOC(l)=2236 GOTO 340 1980 IF (LOC(l)>2342) AND (LOC(l)<2345) GOTO 340 1990 IF LOC(l)=2488 GOTO 340 2000 IF (LOC(1)>2612) AND (LOC(l)<2618) GOTO 340 2010 IF (LOC(l)>2652) AND (LOC(l)<2655) GOTO 340 2020 IF LOC(l)=2745 GOTO 340 2030 IF (LOC(l)>2800) AND (L0C(1X2823) GOTO 340 2040 IF (LOC(l)>2837) AND (LOC(l)<2840) GOTO 340 2050 IF (LOC(l)>2927) AND (LOCQX2930) GOTO 340 2060 IF (LOC(1)>3008) AND (LOC(1X3014) GOTO 340 2070 IF LOC(l)=3125 GOTO 340 2080 IF (LOC(l)>3345) AND (L0C(1)<3349) GOTO 340 2090 IF (LOC(l)>3367) AND (L0C(1X3372) GOTO 340 2100 GOTO 370 1 0 9 i a • 15 ' DIGINT.A3 20 ' Interpreting D i g i t i z e d Films 30 ' Robert Gooding 40 ' September 1984 50 ' 60 ' This programme takes sequences olNfibre positions from f i l e "Film.A" 70 ' and determines the d i s t r i b u t i o n of: 80 ' - f i b r e angle (ranging from -pi/2 to pi/2) 90 ' - a x i a l f i b r e v e l o c i t y (m/s) 100 ' - transverse f i b r e v e l o c i t y (m/s) 110 ' - angular v e l o c i t y (rad/s) 120 ' A l l v a r i a b l e s are evaluated at a distance upstream of the s l o t 130 ' corresponding to the distance between s l o t s i n an i n d u s t r i a l screen 140 ' (assuming 12% open area) 150 ' 160 ' Var i a b l e s : 170 ' A$,B$,C$,D$ record locations of f i b r e p o s i t i o n s and counters 180 ' E$,F$,G$,HS 190 * AX,AY,CX,CY vectors of f i b r e end points 200 ' N frame counter (within a sequence) 210 ' FRAM frame number 220 ' FCNT sequence number 230 ' X,Y vectors of f i b r e mid-point coordinates 240 ' ANG vector of f i b r e angles 250 ' VX,VY vectors of f i b r e a x i a l and transverse v e l o c i t i e s 260 ' ROT vector of f i b r e r o t a t i o n a l v e l o c i t y ( i n plane) 270 ' SOLN vector of X,Y,ANG,VX,VY,ROT for given FCNT 280 ' M vector of zone counters 285 ' RES,RESQ arrays of zone counters 286 ' MANG array of zone/angle counters 290 ' 300 CLEAR 310 CLS 320 OPEN " c : f i l m . a " AS #1 LEN=32 330 FIELD #1,4 AS A$,4 AS BS,4 AS C$,4 AS D$,4 AS E$,4 AS F$,4 AS G$,4 AS H$ 340 DIM AX(15),AY(15),CX(15),CY(15),X(15),Y(15),ANG(15),VX(15),VY(15),ROT(15 ),S0LN(5),M(6),RES(6,5),RESQ(6,5),MANG(6,8) 345 LPRINT " FCNT"," Y"," ANG"," VX"," VY"," ROT" 347 FAC=2.314 350 GET #1,6 360 N=l 370 AX(N)=CVS(A$):AY(N)=CVS(BS):CX(N)=CVS(E$):CY(N)=CVS(F$):FRAM=CVS(G$):FCN T=CVS(H$) 380 IF LOC(l)=3399 GOTO 470 390 GET #1 400 PRINT LOC(1),CVS(A$),CVS(H$) 410 GOTO 1060 420 IF FCNTOCVS(H$) GOTO 470 430 N=N+1 440 GOTO 370 450 • 460 ' Determine f i b r e angle and p o s i t i o n for each appearance in the sequence. 470 FOR 1=1 TO N 480 X(I)=(AX(I)+CX(I))*FAC/2 490 Y(I)=(AY(I)+CY(I))*FAC/2 500 ANG(I)=ATN((AY(I)-CY(I))/(AX(I)-CX(I)) ) 510 NEXT I 520 ' 530 ' Determine v e l o c i t i e s 540 TIME=l/(1363.22+2.80919*FRAM-1.59357E-03*FRAM*2+3.8719E-07*FRAM"3-3.7037 7E-11*FRAM"4) 110 550 FOR 1=2 TO N 560 IM=I-1 570 VX(IM)=(X(I)-X(IM))/TIME 580 VY(IM)=(Y(I)-Y(IM))/TIME 590 ROT(IM)=(ANG(I)-ANG(IM)J/TIME 600 NEXT I 610 1 620 * Locate the i n t e r v a l of int e r e s t 630 FOR 1=1 TO N 640 IM=I-1 650 IF X(I)>-1.75 GOTO 690 660 NEXT I 665 GOTO 1030 670 ' 680 ' Interpolate and c o l l e c t data for each wall zone 690 IF 1=1 GOTO 1030 • 700 FRAC=(-1.75-X(IM))/(X(I)-X(IM)) 710 SOLN(1)=Y(IM)+(Y(I)-Y(IM))*FRAC 720 SOLN(2)=ANG(IM)+(ANG(I)-ANG(IM))*FRAC 730 SOLN(3)=VX(IM) 740 SOLN(4)=VY(IM) 750 SOLN(5)=ROT(IM) 770 LPRINT USING "###I######.tFCNT,SOLN(1),SOLN(2),SOLN(3),SOLN(4),SOLN(5 ) 780 ' 790 ' Analyze the data in each of the f i v e "wall distance' zones 820 IF SOLN(l)<8.75 THEN J=5 ELSE J=6 825 IF SOLN(1)<3 THEN J=4 830 IF SOLNQX1.5 THEN J = 3 840 IF SOLNQX.75 THEN J=2 850 IF SOLNUX.375 THEN J=l 855 L=FIX((SOLN(2)+1.5708)*2.5465)+1 856 MANG(J,L)=MANG(J,L)+1 860 M(J)=M(J)+1 870 FOR K=l TO 5 880 RES(J,K)=RES (J,K)+SOLN(K) 890 RESQ (J,K)=RESQ (J,K)+SOLN(K)~2 900 NEXT K 910 IF LOC(l)=3399 GOTO 950 920 GOTO 360 930 ' 940 ' Present the r e s u l t s 950 LPRINT "Zone","Variable","Average","Variance" 960 FOR J=l TO 6 965 LPRINT J,M(J) 970 FOR K=l TO 5 980 AV=RES(J,K)/M(J) 990 VAR=(RESQ(J,K)—RES(J,K)*2/M(J))/(M(J)-l) 1000 LPRINT J,K,AV,VAR 1010 NEXT K 1020 NEXT J 1022 FOR L=l TO 8 1024 LPRINT MANG(1,L),MANG(2,L),MANG(3,L),MANG(4,L),MANG(5,L),MANG(6,L) 1026 NEXT L 1030 END 1040 * 1050 ' This subroutine i n s t r u c t s the program to overlook c e r t a i n sequences 1060 IF (LOC(l)>69) AND (LOC(l)<72) GOTO 390 1065 IF (LOC(l)>45) AND (LOCQX49) GOTO 390 1067 IF (LOC(l)>57) AND (LOC(l)<62) GOTO 390 1070 IF LOC(l)=261 GOTO 390 1080 IF LOC(1)=310 GOTO 390 1090 IF (LOC(l)>688) AND (LOCUX726) GOTO 390 I l l 1100 IF LOC(l)=743 GOTO 390 1110 IF LOC(l)=762 GOTO 390 1120 IF (LOC(l)>841) AND (LOC(l)<848) GOTO 390 1130 IF (LOC(l)>947) AND (L0C(1X954) GOTO 390 1140 IF (LOC(l)>1150) AND (LOCUK1166) GOTO 390 1150 IF (LOC(l)>1171) AND (LOC(l)<1174) GOTO 390 1160 IF LOC(l)=1218 GOTO 390 1170 IF (LOC(l)>1334) AND (LOC (1 K1342) GOTO 390 1180 IF LOC(l)=1361 GOTO 390 1190 IF (LOC(l) >1425) AND (LOCUK1428) GOTO 390 1200 IF LOC(l)=1468 GOTO 390 1205 IF (LOC(l)>1486) AND (LOC(l)<1492) GOTO 390 1210 IF (LOC(l)>1511) AND (LOC(l)<1566) GOTO 390 1220 IF LOC(l)=1655 GOTO 390 1230 IF (LOC(l)>1912) AND (LOC(l)<1994) GOTO 390 1240 IF LOC(1)=2059 GOTO 390 1250 IF (LOC(l)>2112) AND (LOC(l)<2119) GOTO 390 1260 IF (LOC(l)>2198) AND (LOC(1)<2202) GOTO 390 1270 IF LOC(l)=2236 GOTO 390 1280 IF (LOC(l)>2342) AND (LOC(l)<2345) GOTO 390 1290 IF LOC(l)=2488 GOTO 390 1300 IF (LOC(l)>2612) AND (LOC(l)<2618) GOTO 390 1310 IF (LOC(l)>2652) AND (LOC(l)<2655) GOTO 390 1320 IF LOC(l)=2745 GOTO 390 1330 IF (LOC(1)>2800) AND (LOC(l)<2823) GOTO 390 1340 IF (LOC(l)>2837) AND (LOC(1)<2840) GOTO 390 1350 IF (LOC(l)>2927) AND (LOC(1)<2930) GOTO 390 1360 IF (LOC(l)>3008) AND (LOC(1)<3014) GOTO 390 1370 IF LOC(l)=3125 GOTO 390 1380 IF (LOC(l)>3345) AND (LOC(l)<3349) GOTO 390 1390 IF (LOC(l) >3367) AND (L0C(1X3372) GOTO 390 1400 GOTO 420 A P P E N D I X I I I D E T A I L S OF E X P E R I M E N T A L A P P A R A T U S 1 1 3 T h i s a p p e n d i x i s a n a d j u n c t t o C h a p t e r 3 , a n d d e t a i l s 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 a r e l i s t e d h e r e i n . P l u m b i n g D e t a i l s : P u m p : P a r a m o u n t M o d e l 1 . 5 V - 6 ; 6 " d i a m e t e r o p e n i m p e l l e r ; c e n t r i f u g a l ; m a n u f a c t u r e d b y P u m p s a n d P o w e r L t d . , V a n c o u v e r , B . C . ; 1 7 2 5 r p m , 0 . 5 h p m o t o r ; m e a s u r e d s h u t - o f f p r e s s u r e = 1 8 p s i ; n o r m a l r u n n i n g p r e s s u r e = 1 3 p s i ; n o r m a l o p e r a t i n g c a p a c i t y = 3 6 U S g p m . P i p e : 1 . 5 " S c h e d u l e 8 0 P V C ; l e n g t h o f s t r a i g h t a w a y u p s t r e a m o f p l e x i g l a s c h a n n e l = 3 3 " ; l e n g t h o f s t r a i g h t a w a y d o w n s t r e a m o f c h a n n e l = 3 0 " . T u b i n g : 0 . 9 6 m l e n g t h o f 8 mm i . d . T y g o n R - 3 6 0 3 f l e x i b l e t u b i n g . V a l v e s : F o u r 1 . 5 " P V C b a l l v a l v e s ; o n e P V C 3 - w a y v a l v e ( m o d i f i e d t o p r e v e n t w a t e r h a m m e r ) ; 1 . 5 " P V C - s t e e l - n e o p r e n e d i a p h r a g m v a l v e . A c c e p t f l o w c o n t r o l l e d b y i n s e r t i n g d i f f e r e n t , c u s t o m m a d e , t i p s i n t o t h e o u t l e t o f t h e t u b i n g . R e s e r v o i r s : Two 2 0 . 7 5 " x 2 0 . 7 5 " x 1 2 " ( d e e p ) p l a s t i c t u b s . S y s t e m : M a x i m u m c a p a c i t y = 8 0 l i t r e s ; n o r m a l o p e r a t i n g c a p a c i t y = 6 0 l i t r e s ; n o r m a l w a t e r t e m p e r a t u r e = 2 0 C . P l e x i g l a s c h a n n e l d e t a i l s : M a t e r i a l : 0 . 2 5 " t h i c k p l e x i g l a s 0 . 5 0 " t h i c k p l e x i g l a s f o r f l a n g e s ; f o r c h a n n e l w a l l s , j o i n t s c l o s e d w i t h 1 1 4 d i c h l o r o e t h a n e . I n t e r n a l D i m e n s i o n s : F e e d / r e j e c t c h a m b e r - 1 2 " l o n g , 0 . 7 5 " d e e p , 0 . 7 5 " h i g h . F i t t i n g s : F e e d / r e j e c t p o r t s - 1 . 5 " p i p e f l a n g e s w i t h n e o p r e n e g a s k e t s ; a c c e p t p o r t - 0 . 3 7 5 " F P T p l e x i g l a s f i t t i n g . P h o t o g r a p h i c D e t a i l s : C a m e r a : H y c a m M o d e l N o . K 2 0 S 4 E m a n u f a c t u r e d b y R e d L a k e L a b o r a t o r i e s I n c . S a n t a C l a r a , C a l i f o r n i a ; n o m i n a l f r a m i n g r a t e = 3 0 0 0 p i c t u r e s p e r s e c o n d ; a c t u a l f r a m i n g r a t e g i v e n b y t h e f o l l o w i n g e q u a t i o n : F R = 1 3 6 3 + 2 . 8 0 9 * F N - 1 . 5 9 4 * 1 0 ~ 2 * F N 2 + 3 . 8 7 2 * 1 0 ~ 6 * F N 3 - 1 0 4 - 3 . 7 0 4 * 1 0 * F N w h e r e F R = f r a m i n g r a t e , a n d F N = f r a m e n u m b e r . T h e a b o v e e q u a t i o n w a s d e t e r m i n e d u s i n g a t i m i n g l i g h t w h i c h m a r k e d t h e e d g e o f t h e f i l m 1 0 0 t i m e s p e r s e c o n d . T h e n u m b e r o f f r a m e s b e t w e e n m a r k s w a s m e a s u r e d m a n u a l l y , e q u a t i o n s o f v a r i o u s o r d e r w e r e f i t t e d t o t h e d a t a , a n d t h e n t h e a b o v e e q u a t i o n w a s c h o s e n . F u r t h e r d e t a i l s : 1 / 5 0 s h u t t e r ; f 5 . 6 a p e r t u r e ; S u n - D i o n a r 16 Z o o m l e n s w i t h 2 0 mm e x t e n s i o n ; 5 5 - 6 0 mm z o o m . F i l m : 16 mm E a s t m a n E k t a c h r o m e v i d e o n e w s f i l m ; h i g h s p e e d 7 2 5 0 t u n g s t e n , 4 0 0 A S A ; 1 0 0 f o o t r e e l . 1 1 5 L i g h t i n g : F o u r Q E J - 3 0 G e n e r a l E l e c t r i c b u l b s i n a c u s t o m m o u n t ; 1 2 0 0 w a t t s t o t a l p o w e r ; l i g h t d i f f u s e d b y 1 / 8 " t h i c k ( w h i t e ) p l a s t i c s h e e t . F i b r e l e n g t h a n a l y z e r d e t a i l s : K a j a a n i F S - 1 0 0 F i b r e L e n g t h A n a l y z e r m a n u f a c t u r e d b y K a j a a n i O y E l e c t r o n i c s , K a j a a n i , F i n l a n d ; 0 . 2 mm d i a m e t e r c a p i l l a r y t u b e ; 5 0 0 k g / c m 2 v a c u u m . F i l m a n a l y z i n g a r r a n g e m e n t : P r o j e c t o r : P h o t o O p t i c a l D a t a A n a l y z e r M o d e l 2 2 4 A Mk I V m a n u f a c t u r e d b y L - W I n t e r n a t i o n a l , W o o d l a n d H i l l s , C a l i f o r n i a ; K o d a k E k t a n a r l e n s , 2 " , f l 6 . D i g i t i z i n g P a d : M o d e l MM 1 2 0 1 D i g i t i z e r ; 1 1 . 7 x 1 1 . 7 " a c t i v e a r e a ; 5 0 0 l i n e s p e r i n c h r e s o l u t i o n ; + / - 0 . 0 2 5 " r a t e d a c c u r a c y ; m a n u f a c t u r e d b y S u m m a r g r a p h i c s C o r p . , F a i r f i e l d , C o n n e c t i c u t . C o m p u t e r : I B M P e r s o n a l C o m p u t e r ; N E C M o d e l N o . J B - 1 2 0 1 M m o n i t o r , 6 4 0 p o i n t s ( h o r i z o n t a l ) x 2 0 0 p o i n t s ( v e r t i c a l ) r e s o l u t i o n . 116 A P P E N D I X I V F I B R E L E N G T H D I S T R I B U T I O N S Table XII Length D i s t r i b u t i o n of lx.043 mm Nylon F i b r e s ( r e p l i c a t e d ) f i b r e length d i s t r i b u t i o n (mm) 0.00 - 0. 07 0.64 0.12 0.07 - 0. 14 0.32 0.27 0.14 - 0. 21 0.16 0.12 0.21 - 0. 28 0.56 0.19 0.28 _ 0. 35 0.37 0.12 0.35 - 0. 42 0.21 0.13 0 . 42 - 0. 49 0.16 0.19 0.49 - 0. 56 0.32 0.41 0.56 _ 0. 63 0.58 0.69 0.63 - 0. 70 1.75 1.57 0.70 - 0. 77 3.18 3.43 0.77 - 0. 84 7 . 50 8.33 0.84 _ 0. 91 10.91 12.61 0.91 - 0.98 14.64 15.53 0.98 - 1. 05 15.44 15.31 1.05 - 1. 12 13.93 13.27 1.12 - 1. 20 11.62 11.45 1. 20 - 1. 27 7.22 7.24 1.27 - 1. 34 5.14 4.84 1. 34 - 1. 41 2.24 1.78 f i b r e length d i s t r i b u t i o n (mm) 1.41 - 1.48 1.42 1.11 1.48 - 1.55 0.53 0. 36 1.55 - 1.62 0.46 0.28 1.62 - 1.69 0.29 0.16 1.69 - 1.76 0.19 0.12 1.76 - 1.83 0.08 0.06 1.83 - 1.90 0.08 0.05 1.90 - 1.97 0.05 0.04 1.97 - 2.04 0.03 0.04 2.04 - 2.11 0.00 0.04 2.11 - 2. 18 0.00 0.04 2.18 - 2.25 0.00 0.03 2.25 - 2.32 0.00 0.03 2.32 - 2.40 0.00 0.02 2.40 + 0.16 0.04 f i r s t d e c i l e 0.72 0.72 f i r s t q u a r t i l e 0.83 0.82 second q u a r t i l e 0.95 0.94 t h i r d q u a r t i l e 1.08 1.07 ninth d e c i l e 1.20 1.19 average 0.96 0.95 weighted average 1.00 0.99 Table XIII Length D i s t r i b u t i o n of 1.5X.043 mm Nylon F i b r e s ( r e p l i c a t e d ) f i b r e length d i s t r i b u t i o n f i b r e length d i s t r i b u t i o n (mm) (mm) 0.00 - 0. 11 0.65 2.35 - 2.47 0.23 0.11 - 0. 23 0.86 2.47 - 2.58 0.14 0.23 - 0. 35 0.83 2.58 - 2.70 0.13 0.35 - 0. 47 0.18 2.70 - 2.82 0.10 0.47 - 0. 58 0.26 2.82 - 2.94 0.10 0. 58 - 0. 70 0.29 2.94 - 3.05 0.08 0.70 - 0. 82 0.31 3.05 - 3.17 0.08 0.82 - 0. 94 0.37 3.17 - 3.29 0.09 0.94 - 1. 05 0.47 3.29 - 3.41 0.11 1.05 - 1. 17 0.65 3.41 - 3.52 0.09 1.17 - 1. 29 1.16 3.52 - 3.64 0.05 1.29 - 1. 41 5.91 3.64 - 3.76 0.02 1.41 - 1. 52 10.51 3.76 - 3.88 0.02 1.52 - 1. 64 19.28 3.88 - 4.00 0.02 1.64 - 1. 76 23.78 4.00 + 0.04 1.76 - 1. 88 19. 57 1.88 - 2. 00 10.85 f i r s t d e c i l e 1.25 mm 2 .00 - 2. 11 1.55 f i r s t q u a r t i l e 1.42 2 .11 - 2. 23 0.96 second q u a r t i l e 1.57 2.23 - 2. 35 0.31 t h i r d q u a r t i l e 1.70 ninth d e c i l e 1.81 average 1. 55 weighted average 1.61 Table XIII Length D i s t r i b u t i o n of 1.5x.043 mm Nylon F i b r e s (continued) f i b r e length d i s t r i b u t i o n f i b r e length d i s t r i b u t i o n (mm) (mm) 0.00 - 0.07 0.25 1.41 - 1.48 13.87 0.07 - 0.14 0.45 1.48 - 1.55 18.27 0.14 - 0.21 0.29 1.55 - 1.62 18.72 0.21 - 0.28 0.21 1.62 - 1.69 13.74 0.28 - 0.35 0.22 1.69 - 1.76 8. 30 0.35 - 0.42 0.21 1.76 - 1.83 2.05 0.42 - 0.49 0.11 1.83 - 1.90 1.23 0.49 - 0.56 0.15 1.90 - 1.97 0.33 0.56 _ 0.63 0.14 1.97 - 2.04 0.25 0.63 - 0.70 0.18 2.04 - 2.11 0.14 0.70 - 0.77 0.11 2.11 - 2.18 0.12 0.77 - 0.84 0.14 2.18 - 2.25 0.10 0.84 _ 0.91 0.18 2.25 - 2.32 0.09 0.91 - 0.98 0.31 2.32 - 2.40 0.08 0.98 - 1.05 0.39 2.40 + 0. 37 1.05 - 1.12 0.82 1.12 - 1.20 1.16 f i r s t d e c i l e 1.22 mm 1.20 - 1.27 2.99 f i r s t q u a r t i l e 1.35 1.27 - 1.34 4.48 second q u a r t i l e 1.46 1.34 - 1.41 9.92 t h i r d q u a r t i l e 1.56 nint h d e c i l e 1.64 average 1.44 weighted average 1.47 Table XIV Length D i s t r i b u t i o n of 3x.043 mm Nylon Fi b r e s ( r e p l i c a t e d ) f i b r e length (mm) 0, ,00 - 0.20 0, ,20 - 0.41 0, ,41 - 0.61 0.61 - 0.82 0, ,82 - 1.02 1. ,02 - 1.23 1. .23 - 1.44 1, .44 - 1.64 1, .64 1.85 1, .85 - 2.05 2, .05 - 2.26 2, .26 2.47 2 , .47 _ 2.67 2 , 67 - 2.88 2. ,88 - 3.08 3, .08 - 3.29 3, .29 - 3.50 3. .50 - 3.70 3. .70 - 3.91 3, .91 - 4.11 d i s t r i b u t i o n 8.51 5.18 7.80 2.90 2.62 1.38 0.64 0.98 0.71 0.91 0.59 0.79 0.47 0.83 0.47 0.60 0.40 0.45 0.31 0.24 0.19 0.19 0.41 0.46 0.59 0.73 6.51 7.07 12.28 13.16 18.18 19.72 18.31 20.20 12.57 14.02 6.69 7.37 ,0.58 0.57 f i b r e length (mm) 4.11 - 4.32 4.32 - 4.52 4.52 - 4.73 4.73 - 4.94 4.94 - 5.14 5.14 - 5.35 5.35 - 5.55 5.55 - 5.76 5.76 - 5.97 5.97 - 6.17 6.17 - 6.38 6.38 - 6.58 6.58 - 6.79 6.79 - 7.00 7.00 + f i r s t d e c i l e f i r s t q u a r t i l e second q u a r t i l e t h i r d q u a r t i l e ninth d e c i l e average weighted average d i s t r i b u t i o n 0.34 0.43 0.11 0.27 0.11 0.25 0.07 0.20 0.04 0.18 0.01 0.11 0.02 0.07 0.05 0.13 0.06 0.25 0.05 0.24 0.02 0.12 0.05 0.00 0.09 0.00 0.14 0.00 0.14 0.13 0.03 0.52 mm 2.51 2.71 2.96 3.02 3.24 3.28 3.47 3.50 2.69 2.88 3.11 3.14 O Table XV Length D i s t r i b u t i o n of lx.012 mm Rayon Fi b r e s ( r e p l i c a t e d ) f i b r e length d i s t r i b u t i o n (mm) 0.00 - 0.07 6.37 3.81 0.07 - 0.14 3.64 2.94 0.14 - 0.21 2.76 2.06 0.21 - 0.28 2.60 2.97 0.28 _ 0.35 2.52 3.12 0.35 - 0.42 2.97 3.45 0.42 - 0.49 3.17 3.24 0.49 - 0.56 3.29 3.15 0.56 - 0.63 3.34 3.20 0.63 - 0.70 4.32 4; 34 0.70 - 0.77 5.61 5.51 0.77 - 0.84 7.52 7.70 0.84 _ 0.91 8.98 9.46 0.91 - 0.98 9.44 10.14 0.98 - 1.05 9.08 9.60 1.05 - 1.12 6.95 7. 30 1.12 _ 1.20 5.19 5.54 1.20 - 1.27 2.76 3.07 1.27 - 1.34 2.10 2.37 1.34 - 1.41 1. 30 1.40 f i b r e length d i s t r i b u t i o n (mm) 1.41 - 1.48 1.17 1.14 1.48 - 1.55 0.91 0.77 1.55 - 1.62 0.80 0.67 1.62 - 1.69 0.60 0.53 1.69 - 1.76 0. 52 0. 50 1.76 - 1.83 0.42 0.42 1.83 - 1.90 0.40 0. 38 1.90 - 1.97 0. 32 0.31 1.97 - 2.04 0.25 0.28 2.04 - 2.11 0.17 0.21 2.11 - 2.18 0.16 0.17 2.18 - 2.25 0.13 0.11 2.25 - 2. 32 0.12 0.09 2.32 - 2.40 0.11 0.08 2.40 + 0.22 0.15 f i r s t d e c i l e 0.07 0.16 mm f i r s t q u a r t i l e 0.44 0.49 second q u a r t i l e 0.79 0.81 t h i r d q u a r t i l e 0.98 0.99 ninth d e c i l e 1.18 1.18 average 0.81 0.81 weighted average 0.97 0.97 Table XVI Length D i s t r i b u t i o n of lx.020 mm Rayon Fi b r e s ( r e p l i c a t e d ) f i b r e length d i s t r i b u t i o n (mm) 0. 00 - 0.07 0.15 0.42 1. 39 0. 07 - 0.14 0.20 0.00 0.03 0. 14 - 0.21 0.10 0.23 0.09 0. 21 - 0.28 0.05 0.06 0.16 0. 28 _ 0.35 0.17 0.10 0.20 0. 35 - 0.42 0.22 0.14 0.19 0. 42 - 0.49 0.18 0.17 0.14 0. 49 - 0. 56 0.17 0.13 0.12 0. 56 _ 0.63 0.13 0.12 0.16 0. 63 - 0.70 0.25 0.12 0.28 0. 70 - 0.77 0.37 0.19 0.58 0. 77 - 0.84 1.19 0.45 1. 59 0. 84 - 0.91 1.88 0.70 2.53 0. 91 - 0.98 4. 68 2.07 5.90 0. 98 - 1. 05 6.82 3.21 8.52 1. 05 - 1.12 13.07 8. 54 14.86 1. 12 - 1.20 17 .19 12.75 18. 58 1. 20 - 1.27 18.04 17.39 17.64 1. 27 - 1.34 14.77 17.83 12.98 1. 34 - 1.41 8.67 14.36 6.21 f i b r e length d i s t r i b u t i o n (mm) 1.41 -1.48 5.85 10.45 4.12 1.48 - 1.55 2.29 4.82 1.46 1.55 -1.62 1.56 3.10 0.91 1.62 -1.69 0.62 1.03 0.30 1.69 - 1.76 0.41 0.68 0.25 1.76 - 1.83 0.20 0.25 0.17 1.83 - 1.90 0.20 0.18 0.14 1.90 - 1.97 0.14 0.10 0.12 1.97 - 2.04 0.08 0.09 0.13 2.04 - 2.11 0.06 0.08 0.11 2.11 - 2.18 0.09 0.08 0.07 2.18 - 2.25 0.09 0.07 0.03 2.25 - 2.32 0.06 0.06 0.02 2. 32 - 2.40 0.03 0.05 0.02 2.40 + 0. 30 0.45 0.54 f i r s t d e c i l e 0.92 1.00 0.87 min f i r s t q u a r t i l e 1.03 1.10 1.00 second q u a r t i l e 1.14 1.21 1.10 t h i r d q u a r t i l e 1.24 1. 32 1.21 ninth d e c i l e 1. 36 1.42 1.31 average 1. 14 1.21 1. 10 weighted average 1.17 1 i 24 1.14 Table XVII Length D i s t r i b u t i o n of p l 0 . r l 4 K r a f t Pulp F i b r e s ( r e p l i c a t e d ) f i b r e length d i s t r i b u t i o n (mm) 0.00 - 0. 20 2.04 1.20 0.20 - 0. 41 1.33 1.29 0.41 - 0.61 2.35 2.49 0.61 - 0.82 1.33 1.33 0.82 - 1. 02 1.17 1.38 1.02 - 1. 23 1.36 1.45 1.23 - 1. 44 1.70 1.78 1.44 - 1.64 2.31 2.35 1.64 _ 1. 85 3.15 3.27 1.85 - 2 . 05 3.73 4.26 2.05 - 2. 26 4.48 4.57 2.26 - 2 . 47 5.03 5.42 2.47 _ 2 . 67 5.81 5.92 2.67 - 2. 88 6.50 7.13 2.88 - 3. 08 6.92 7.42 3.08 - 3 . 29 7.59 7.60 3.29 _ 3 . 50 7.84 7.49 3.50 - 3. 70 7.36 6.71 3.70 - 3. 91 6.63 6.05 3.91 - 4. 11 5.22 4.88 f i b r e length d i s t r i b u t i o n (mm) 4.11 - 4.32 4.54 4.37 4.32 - 4.52 3.26 3.31 4.52 - 4.73 2.66 2.77 4.73 - 4.94 1.70 1.81 4.94 - 5.14 1.34 1.40 5.14 - 5.35 0.81 0.80 5.35 - 5.55 0.65 0.59 5.55 - 5.76 0. 38 0.32 5.76 - 5.97 0.27 0.24 5.97 - 6.17 0.14 0.13 6.17 - 6.38 0. 13 0.10 6.38 - 6.58 0. 10 0.06 6.58 - 6.79 0.10 0.05 6.79 - 7.00 0.09 0.04 7 .00 + 0. 13 0.12 f i r s t d e c i l e 1.08 1.12 mm f i r s t q u a r t i l e 2.06 2.04 second q u a r t i l e 2.90 2.84 t h i r d q u a r t i l e 3.59 3.56 ninth d e c i l e 4.21 4.21 average 2.84 2.79 weighted average 3.31 3.27 Table XVIII Length D i s t r i b u t i o n of pl4.r28 K r a f t Pulp F i b r e s ( r e p l i c a t e d ) f i b r e length d i s t r i b u t i o n (mm) 0.00 - 0.20 0.79 0.91 0.20 - 0.41 1.02 1.30 0.41 - 0.61 1.55 1.38 0.61 - 0.82 0.68 1.15 0.82 _ 1.02 1.32 1.25 1.02 - 1.23 2.28 1.87 1.23 - 1.44 3.55 3.36 1.44 - 1.64 5.18 5.27 1.64 _ 1.85 7.14 7.42 1.85 - 2.05 8.90 9.23 2.05 - 2.26 9.46 9.33 2.26 - 2.47 9.34 9.08 2.47 _ 2 .67 8.97 8.46 2.67 - 2.88 8.25 8.16 2.88 - 3.08 7.44 7.59 3.08 - 3.29 5.91 6.14 3.29 _ 3.50 5.20 5.26 3.50 - 3.70 3.85 3.75 3.70 - 3.91 3.20 3.11 3.91 - 4.11 2.00 1.98 f i b r e length d i s t r i b u t i o n (mm) 4.11 - 4.32 1.45 1.48 4.32 - 4.52 0.78 0.78 4.52 - 4.73 0.64 0.58 4.73 - 4.94 0.38 0.33 4.94 - 5.14 0.24 0.28 5.14 - 5.35 0.10 0.18 5.35 - 5.55 0.10 0.13 5.55 - 5.76 0.08 0.07 5.76 - 5.97 0.07 0.07 5.97 - 6.17 0.04 0.05 6.17 - 6.38 0.04 0.03 6. 38 - 6.58 0.02 0.01 6.58 - 6.79 0.02 0.00 6.79 -7.00 0.01 0.00 7.00 + 0.08 0.00 f i r s t d e c i l e 1.16 1.16 mm f i r s t q u a r t i l e 1.68 1.67 second q u a r t i l e 2.23 2.22 t h i r d q u a r t i l e 2.85 2.86 ninth d e c i l e 3.45 3.45 average 2.29 2.28 weighted average 2.64 2.64 i t * Table XIX Length D i s t r i b u t i o n of K r a f t Pulp F i b r e s f i b r e length d i s t r i b u t i o n f i b r e length d i s t r i b u t i o n (mm) (mm) 0.00 - 0. 20 7.5 4.11 - 4.32 1.7 0.20 - 0. 41 9.2 4.32 - 4.52 1.3 0.41 - 0. 61 13.0 4.52 - 4.73 1.0 0.61 - 0. 82 6.5 4.73 - 4.94 0.6 0.82 - 1. 02 5.5 4.94 - 5.14 0.5 1.02 - 1. 23 5.1 5.14 - 5.35 0.4 1.23 - 1. 44 4.9 5.35 - 5.55 0.3 1.44 - 1. 64 4.7 5.55 - 5.76 0.2 1.64 - 1. 85 4.6 5.76 - 5.97 0.2 1.85 - 2. 05 4.3 5.97 - 6.17 0.1 2.05 - 2. 26 4.0 6.17 - 6.38 0.1 2.26 - 2.47 3.7 6.38 - 6.58 0.0 2.47 - 2. 67 3.5 6.58 - 6.79 0.0 2.67 - 2. 88 3.3 6.79 - 7.00 0.0 2.88 -3.08 3.0 7 .00 + 0.0 3.08 - 3. 29 2.6 3.29 - 3. 50 2.5 f i r s t d e c i l e 0.05 mm 3.50 - 3.70 2.1 f i r s t q u a r t i l e 0.32 3.70 - 3. 91 2.0 second q u a r t i l e 1.10 3.91 - 4. 11 1.8 t h i r d q u a r t i l e 2.31 ninth d e c i l e 3.43 average 1.56 weighted average 2.61 Table XX Length D i s t r i b u t i o n of CTMP Pulp F i b r e s ( r e p l i c a t e d ) f i b r e length d i s t r i b u t i o n (mm) 0.00 - 0.20 7. 83 8.13 0.20 - 0.41 15. 49 16.83 0.41 - 0.61 20. 30 21.33 0.61 - 0.82 11. 68 11.50 0.82 _ 1.02 9. 60 8.99 1.02 - 1.23 7. 54 6.92 1.23 - 1.44 5. 84 5.47 1.44 - 1. 64 '' 4. 40 4.14 1.64 _ 1.85 3. 30 3.20 1.85 - 2.05 2. 73 2.74 2.05 - 2.26 2. 11 2.20 2.26 - 2.47 1. 74 1.75 2.47 _ 2.67 1. 31 1.33 2.67 - 2.88 1.04 1.01 2.88 - 3.08 0.96 0.91 3.08 - 3.29 0. 78 0.72 3.29 _ 3.50 0. 68 0.64 3.50 - 3.70 0. 53 0.49 3.70 - 3.91 0. 49 0.42 3.91 - 4.11 0. 38 0.29 f i b r e length d i s t r i b u t i o n (mm) 4.11 - 4. 32 0.31 0.22 4.32 - 4.52 0.20 0.15 4.52 - 4.73 0.16 0.14 4.73 - 4.94 0.12 0.12 4.94 - 5.14 0.12 0.11 5.14 - 5.35 0.10 0.09 5.35 - 5. 55 0.07 0.07 5.55 - 5.76 0.05 0.04 5.76 - 5.97 0.05 0.02 5.97 - 6.17 0.04 0.01 6.17 - 6. 38 0.03 0.00 6.38 - 6.58 0.01 0.00 6.58 - 6.79 0.01 0.01 6.79 - 7.00 0.01 0.01 7.00 + 0.08 0.02 f i r s t d e c i l e 0.02 0.02 f i r s t q u a r t i l e 0.22 0.20 second q u a r t i l e 0. 52 0.47 t h i r d q u a r t i l e 1.11 1.07 ninth d e c i l e 1.97 1.92 average 0.88 0.84 weighted average 1.78 1.71 

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