UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1986_A7 G66.pdf [ 7.63MB ]
Metadata
JSON: 831-1.0058886.json
JSON-LD: 831-1.0058886-ld.json
RDF/XML (Pretty): 831-1.0058886-rdf.xml
RDF/JSON: 831-1.0058886-rdf.json
Turtle: 831-1.0058886-turtle.txt
N-Triples: 831-1.0058886-rdf-ntriples.txt
Original Record: 831-1.0058886-source.json
Full Text
831-1.0058886-fulltext.txt
Citation
831-1.0058886.ris

Full Text

THE PASSAGE  OF FIBRES THROUGH SLOTS IN PULP  SCREENING  by ROBERT WILLIAM B. E n g . , M c G i l l  GOODING  University,  1977  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR  THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY Department  We  accept to  OF GRADUATE  of Chemical  this  thesis  the required  THE UNIVERSITY  Engineering  as c o n f o r m i n g standard  OF BRITISH COLUMBIA  September ©  STUDIES  Robert W i l l i a m  1986 Gooding,  1986  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree at the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may department or by h i s o r her  be granted by the head o f representatives.  my  It i s  understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be  allowed without my  permission.  Department of  CJ^r^-(CaJ^  <£*^C^&ZJT^IC^  The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3  Date  »V  acX^>6^C  written  i i  ABSTRACT  The is of  an  screening  important  "accept"  plate,  and  plate.  The  fibre were  the  was  a mechanism  t r a j e c t o r i e s that  effect"  causes  which  effect", enough  to  be  which and  mechanism  deplete favours  flexible  and pass  through  which a  of a  and  layer of  large  enough  to  the screen  slotted on  the  variables  on  findings  commercial-scale  pressure  was  high  that  of  follow  and  fibres  based  speed  components:  flow  plate  proposed  using  fibres,  the passage  or  These  two  of  the passage  fibres  slot  thesis.  observed has  involves  coarser  flow,  in this  suspension  perforated  of screening  were  the  i n aqueous  larger,  fibre,  to the operation  Also  slot  of  measured  This  turn  of  fibres  through  retention  photography.  the  pulp  process  fibres  influence  related  fibre  industrial  pulp  passage  screen.  o f wood  1)  passes 2)  cine"wall  through an  "entry  are  short  the streamlines  that  slot.  that  a  on  i i i  DEDICATION  To  my  father,  Edward  Gooding  i v  TABLE  OF C O N T E N T S  Page ABSTRACT  ii  LIST  OF  TABLES  LIST  OF  FIGURES  vi  vii  ACKNOWLEDGEMENTS  ix  1.  INTRODUCTION  1  2.  LITERATURE REVIEW  4  2.1 2.2 2.3 2.4 2.5  3.  5.  Physical Properties of P u l p Fibres Shives Screen Design Screen Performance Flow Near a Screen A p e r t u r e M o t i o n of F i b r e s in S c r e e n i n g S i t u a t i o n s  5 7 10 15 15  ANALYSIS 3.1 3.2 3.3  4.  The and Pulp Pulp The The  18  Shive Stiffness The F l o w F i e l d at a S c r e e n P l a t e A p e r t u r e The E f f i c i e n c y - Reject Rate Relationship  .. ..  18 22 25  E X P E R I M E N T A L WORK  35  4.1 4.2 4.3  35 38 44  Fibre Suspensions Flow Loop Cine-Photography  RESULTS 5.1 5.2 5.3  AND D I S C U S S I O N  Permeability Measurements Fibre Trajectories Near a A Model for Fibre Passage  49  Slotted  Plate  ....  49 53 69  V  Page 6. SUMMARY  AND  CONCLUSIONS  7. RECOMMENDATIONS  FOR  73  FUTURE  WORK  77  NOMENCLATURE  79  BIBLIOGRAPHY  82  APPENDIX  I:  Experimental  Data  85  APPENDIX  II:  Computer  APPENDIX  III:  Experimental  Apparatus  APPENDIX  IV:  Fibre  Distributions  Programmes  Length  96  Details  112  116  vi  LIST  OF  TABLES  Page I  Physical  Properties  of Pulp  II  Physical  Properties  of Experimental  III  Fibre  IV  Channel  V  Film  VI  Fibre  VII  High  VIII  Permeability  IX  T e s t s 65-68 F i b r e Measurements  Length/Permeability  T e s t s 69-71 F i b r e Measurements  Length/Permeability  T e s t s 72-74 F i b r e Measurements  Length/Permeability  X  XI  Motion  Fibres  ..  6  ....  36 62  Definitions  63  Summary  Velocity Speed  and S h i v e s  Types  Layer  Data  Fibres  64  and O r i e n t a t i o n  69  Cine-Films  86  Measurements  87  90  92  94  XII  Length  D i s t r i b u t i o n of lx.043  mm  Nylon  XIII  Length  D i s t r i b u t i o n o f 1.5x.043  XIV  Length  D i s t r i b u t i o n o f 3x.043  mm  Nylon  Fibres  120  XV  Length  D i s t r i b u t i o n of lx.012  mm  Rayon  Fibres  121  XVI  Length  D i s t r i b u t i o n of lx.020  mm  Rayon  Fibres  122  XVII  Length  Distribution of pl0.rl4  Kraft  Fibres  123  XVIII  Length  D i s t r i b u t i o n of pl4.r28  Kraft  Fibres  124  XIX  Length  Distribution of Kraft  XX  Length  D i s t r i b u t i o n o f CTMP  mm  Pulp Pulp  Fibres  Nylon  Fibres Fibres  Fibres  117 118  125 126  vi i  LIST  OF  FIGURES  Page 1.  Centrisorter-type  2.  Screen  3.  Streamlines  Pressure  Performance  Slotted  Screen  9  Curves  a t a Flow  12  Bifurcation  in a  Plate  4.  Idealized  5.  Relationship  6.  Flow  Fibre  Adjacent  Pressure  15 and S h i v e  Between  Shive  to a Screen  Cross-Sections Stiffness Plate  19  and S i z e  ..  in a  Screen  25  7.  Flow  Loop  Schematic  8.  Flow  Loop  and P l e x i g l a s  9.  Plexiglas  Channel  39 Channel  and High  Speed  40 Cine-Camera  ...  Film  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 on Permeability 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  50 51  E f f e c t s of Slot Permeability  Velocity  54  E f f e c t s of Slot Permeability  Velocity  E f f e c t s of S l o t Permeability  Velocity  16.  Effect  of Entry  Length  17.  Motion  of Fibres  Near  a Slot  (Cine-Film)  18.  Motion  of Fibres  Near  a Slot  (Computerized  19.  C o r r e l a t i o n of F i b r e Motion, F i b r e Fibre Orientation f o r Film 1  13.  14.  15.  Equipment  41  10.  12.  Analyzing  21  46  and F i b r e  Type  and Upstream  on  Velocity  on 55  and S l o t  Width  on 56  on P e r m e a b i l i t y  Position  57 60 Image)  61  and 65  vi i i  20.  21.  C o r r e l a t i o n of F i b r e Motion, F i b r e Fibre Orientation for Film 2  Position  C o r r e l a t i o n of F i b r e Motion, F i b r e Fibre Orientation for Film 3  Position  and 66 and 67  i x  ACKNOWLEDGEMENTS  I  wish  tolerance and  thank  during  the  organizations  financial *  My  *  The  *  My  *  The  thesis  past  have  of  Prof.  faculty  few  to  thesis  John  Grace  Robert  and  of  *  Mr.  *  National  Science  *  Mr.  Sven  Smeds,  *  Mr.  Ted  *  Messrs. Rand  Mark  Frith,  Hooper, Doug  Miss  and and  S.W.  Young  Georgina  and  Bob  individuals  technical  and  William  Branion Tam  of  Doo  Chemical  Columbia  Bloedel  and  Mr.  of  Canada  and  its  White Ltd.  Research  Automation  Hooper  Peter  Institute  Engineering  Kajaani  Richard  and  British  MacMillan  and  Kerekes  Department  Research  other  committee,  Prof.  the  Paper  especially  Richard  and  The  Many  patience  work:  Soszynski  staff  support,  important  advisory  U n i v e r s i t y of  and  made  this  Engineering, Pulp  her  years.  Prof.  my  colleagues,  for  also  supervisor,  members  staff,  *  Sonya  contributions  Holmes,  *  to  Council  of  Canada  Ltd.  Co.  Pederson,  Ltd. Canadian  Ingersoll-  Ltd.  Messrs.  Peter  Flynn  and  Bob  Nichols,  Bird  Machine  Co.  Inc.  1  1.  INTRODUCTION  Wood c o n s i s t s m a i n l y to  one a n o t h e r  mechanical These that  and bonded  means  fibres  c a n be  produces  them  mechanical  pulping,  fibre  Both small  high-quality  for  this  also  Shives  and must  paper.  i s great  Chemical into  or  fibres.  and t h e  process pulping  the f i b r e s .  In  to divide  not n e c e s s a r i l y  10% o f t h e p u l p  that  processes  which  are  along  the strength  pulp  i n order  while  their  efficiency.  t o 0.5%.  optical  to  produce  pulp  a r e commonly  used  thesis.  the c a p a c i t y of  consumption, A pressure  fed to i t i n order 1.0%  and  Pressurized  increase power  of  i t i s i n aqueous  shives.  screens",  produce  bundles  are the subject of t h i s  their  from  pulping  removed  i n c e n t i v e to  may  fibre  be  to reduce  concentration  lower  "pressure  to increase  the  though  parallel  Chemical  liberate  of removing  especially  shive  to  Screening  called  screens,  reject  pulp,  pulping.  "shives",  p u r p o s e , and t h e y  There pressure  of  i s a means  screens,  called  and m e c h a n i c a l  fibres.  of paper  suspension  lignin.  t o d i v i d e wood  lignin  pieces,  quantities  quality  with  aligned  boundaries.  chemical  unseparated  fibres  f o r c e s a r e a p p l i e d t o t h e wood  fibre-size  natural  used  is called  dissolving  into  together  are collectively  involves  it  of t u b u l a r  To  screen  t o reduce the  reclaim  i s i n a d v e r t e n t l y r e j e c t e d , the  and  some o f  "rejects" are  2  passed  to secondary  Despite removal,  the widespread  l i t t l e  fundamental pulp. the  and t e r t i a r y  has  Also,  screen  However,  the apertures  t h e minimum  plate  i s not a  understanding apertures  The what  and t r i a l  how  aperture  specific fibre,  likelihood aperture; from  fibres  i n a pressure  The various  pulp  that and  this  plate  in a  must  pass.  are  larger  pulp plate  shives.  Thus  the The  screen  screen lack  through  design  to  of the  rely  on  of  this  thesis  of f i b r e s * are  was  to  a  slot;  though  segregated  from  understand that i s ,  shives  at  an  screen. were  and s c r e e n  fibres  next,  screen  screen  from  inspection of  do n o t g e n e r a l l y p a s s  objectives  flow,  an  a  error.  objective  the passage  p r o v i d e s  to a l l shives.  pressure  and  from  the accept  many  f o r shive  are segregated  i s a  typical  of  shives  caused  general  know  in a  diameter  o f why  controls  which  screens  that  shives  There  physical barrier  has  intuition,  to  through  how  i s apparent  equipment.  pressure  than  published  of  no e x p l a n a t i o n  screening  systems.  use of p r e s s u r e  been  understanding  screening  will  information.  The  plate pass  to predict  first,  to  determine  how  variables influence the through  pressure  specific  a  screen  screen  tasks  plate  performance  undertaken  were  to: 1. D e f i n e and  the mechanical  shives.  properties  o f wood  pulp  fibres  3  2.  Estimate a  3.  the  pressure  Construct  Measure passing feed  a  5.  Observe  flow at  a  the  *Note:  In  embracing shives  this all  that  a  slotted  channel  aperture  motion  go  in  rod-like  types  the  slot  is  particles,  to  and a  compare  "fibre"  fibres.  fibres  at  to  flow  including  the  that  flow  in  the  rates.  entry  using  trajectories  those  as  in  flow  slot  the  used  the  screen.  relative  fibres  and  through  of  fibre  of  simulating  pressure  slot,  various  thesis,  and s y n t h e t i c  and in a  the  cine-photography, fibres  at  concentration  for  the  loop slot  through  flow  conditions  screen.  conditions 4.  flow  a  that  do  general pulp  of not.  term,  fibres,  4  2.  Screening separating  large  principles P1,R1).  is  have  In  screening",  a  mesh  of  passing  size.  but  the  must  screening of  the  economic 2)  they  do  screening  is  different  from  and  a  not form  perhaps  somewhat  cleaned  pulp  to  3)  of  screening  is  be  must pulp  much  with  a  the 50%  less  to  "size chance  than  the  apertures  depend  not  a  only  on  or  on  v e l o c i t y ,  unique  any  and  have  while  fibres  and  in  in  the  a  pulp  or  is  in be  stiffness,  that  textile,  high  must  Pressurized  screening the  since,  treatment  shives  width  length.  probability  process  and  occur  in  processes  low,  simple  differences  differ  widespread  (B2).  a  and  may  particles  Here  somewhat  passage  geometrical  more  particle is  a  "positive  small  presented  particles is  permits  o r i e n t a t i o n ,  separation  according  a  are  necessity  suspension,  separated because  times,  other  of  (B1,M1,M2,  termed  presents  for  screening  reviews  screening".  aperture)  p a r t i c l e  with  throughput; aqueous  of  on  value  of  an  size  Particles  number  and  "probability  ( i . e . the  through  interaction  1)  is  alternate  method  general  screening,  but  separation"  Pulp  of  particles,  An  and  several  a l l large  of  size,  form  in  plate  screening  limited  particles,  perforated  through.  aperture  widespread  or  to  of  REVIEW  and  described  simplest  to  form  ancient small  been  barrier pass  an  and  the  LITERATURE  is  pulp quite  mineral  or  5  agricultural  industries.  of  fibre  screening  commercial 1960, its  i n the  installation  and  there  pressure  screen  assessed.  Some  fibres a  before  in dilute  this  how  topics  pulp  industry.  screen  methods  The  first  occurred  after  scientific  chapter  screen will  fibres  suspensions,  other  s t u d i e s of  or s i n c e .  of  and  related  paper  published  sections  p r o p e r t i e s of  and  unlike  pressure  no  works  i t is  and  the  be  the  motion  p a t t e r n at  a is  reviewed:  s h i v e s , the flow  how  performance  also  and  describe  a  of  slot  channel.  2.1  The  P h y s i c a l P r o p e r t i e s of  The  p r o p e r t i e s o f wood  publications, and  such  Sjostrom on  range  values  of  substantial tree  to  have  a  pulp  and  used  measure  Analyzer  The  are  for  from  can  the  Somerville (Hi) .  Other  are (M3),  fibre  to  of  screen  which  shives (Tl)  definitions  of  bear  most The  reflect  the  within a tree,  from  Shives  laboratory  the  do  not  definition.  i n a pulp and  (P2),  I.  geometric the  al.  in Table  species.  on  i n numerous et  properties  accepted,  amount  Panshin  that exists  based  Shives  described  summarized  species  be  F i b r e s and  properties  screening  p r e c i s e , widely definition  the  fibres  natural variation  tree,  Pulp  Macdonald  given  working to  as  (SI).  directly  as  a  have been  remaining  physical  pulp  of  operating principles The  in  Indeed  devices  sample, STFI  shives are  A  such  Shives  drawn  from  6  Table  I  : P h y s i c a l P r o p e r t i e s of Pulp  pulp length(mm) width(mm) wall  thickness(mm)  stiffness(xlO  -  1  mechanical chemical  Note:  The and  F i b r e s and  fibres  Shives  shives  2-4  3-6  .02-.04  .10-.60  .002-.008  not  applicable  Nm )  2  2  pulp  81  pulp  data given shives.  2  above  relate  to black  10 -10 4  not  spruce  7  estimated  fibres  7  publications that relate their  size  v a r i o u s problems caused by s h i v e s t o  (B3,CI,H2,LI,M4).  The  s h i v e dimensions  T a b l e I are based on a l l of these In t h i s  study,  both  be n e u t r a l l y buoyant. density walls  of  and  pulp  1.5  fill  fibres  g/cm the  and  fibres  sources. and  s h i v e s are c o n s i d e r e d t o  The w a l l s of p u l p f i b r e s 3  ( K l ) , but water w i l l  fibre  shives  given i n  lumens.  The  i n aqueous  have a b a s i c  s w e l l the  apparent  suspension  fibre  density  of  i s therefore  o n l y s l i g h t l y g r e a t e r than t h a t of water. Pulp f i b r e s t i f f n e s s has been measured i n r e c e n t work by Tam  Doo  and  included fibres  Kerekes  i n Table  are  stiffer  consequence pulp.  of  There  stiffness.  (T2),  I. than  chemical  no  pulp  from  their  that  mechanical  fibres,  l i g n i n content  published  of  discussed  simple,  i n Chapter  3.  work  is a  mechanical  measurements  of  be  beam-like f i b r e  are pulp  which  the  However, the s t i f f n e s s of s h i v e s may  by assuming s h i v e s t o be as  data  It i s evident  the h i g h e r are  and  shive  estimated composites,  Such s h i v e s t i f f n e s s  estimates  are shown i n Table I.  2.2  Pulp Screen  Design  There have been t h r e e generations of p u l p screen d e s i g n : 1)  flat  screens,  2)  atmospheric  screens.  Each of these screens  removal,  and  each has  screens,  3)  pressure  i s intended mainly  for shive  a screen p l a t e  and  which the accept  pulp  8  must  pass  their  operating  Flat  screens,  pulp, is,  through.  shive  diameter.  these  screens  plate The  higher of  screen  the  the  flat  several  but  the  that  a  being  and  times  find  and  (C2,L2,S2). for  wood  screening;  that  the  smallest  clean;  high only  mat  do  of  essential Figure  not  however  maintenance limited  then  by  use  in  radially  down  the  the  the  on  the  in  screen  this  average  the  use,  type shive It  feed  of  side  of but  screens. (H3)  efficiency  a  through.  passage  pressure  shives. they  are  Pressure and  higher  capacity.  a  typical  enters  the  annular  cylindrical  through  than  type)  screening with  apertures  forms  lower  f e a t u r e s of  passes  good  i n widespread  a higher  Pulp  rotary  g e n e r a l l y pass  impedes  are s t i l l  1.  plate  fibres  which  having  and  larger  replaced  (stationary)  passes  screens  used  than  and  It provides  compensate f o r t h e i r  e n e r g y demand by  tially,  now  screen  shives  screens  in  be  is perfectly  (centrifugal  are  Atmospheric  shown  i s smaller  screens  The  plate  The  to  positive  capacities  screen.  screen  screens  by  pulp  the  considerably  screen  pulp  of  mills.  believed  steadily  of  aperture  Flat  throughput.  diameter, is  from  atmospheric  succeeded  type  low  dynamics  differ  accept  have  requirements.  The  first  shives  screen  modern p u l p  principles  the  segregate  the  However, t h e  screen  screen  pressure  feed gap  chamber  between  plate.  plate,  screen  tangen-  the  Accept  whereas t h e  are  rotor pulp reject  Figure 1  C e n t r i s o r t e r - t y p e Pressure  Screen  10  pulp  continues Rotor  purpose  down t h e gap t o t h e r e j e c t  designs  vary  plate  apertures,  parallel  to the screen  Figure  i s studded  of  1  rotor  foils  Screen  plates  with  appropriate  for a  selections  involve  hole  plate  Some t y p i c a l  2.3  Chapter flow  Pulp The  3.  as  Screen  that  style  involve  are designed Since  i s made  by  to  screen  t o permit  screen  the aperture  cannot  trial  of the screen  and t h e p r o f i l e  be  plate  Other aperture  of the i n s i d e  surface  smooth o r c o n t o u r e d ) .  d i m e n s i o n s and t h r o u g h p u t s chapter,  inside  size  predicted  and e r r o r .  estimates  a pressure  are given  are also  made o f  screen.  Performance  two most common p a r a m e t e r s o f s c r e e n  stream.  shown i n  This  i s critical  application  (either  In t h a t  E, and " r e j e c t  the portion  reject  on i t s p e r i p h e r y .  changed.  screen  velocities  "efficiency",  rotor  u s e , as a r e r o t o r s  t h e shape  or s l o t ) ,  the screen  The drum-type  lugs  given  the choice  the  slurry  screens  readily  reliably,  in  and t o a c c e l e r a t e the pulp  configuration  and p u l p  t o be  (either  unplug  plate.  pulses  or p a d d l e s .  plate  performance,  pressure  but t h e i r  which  i s i n widespread  vertical  of  among s c r e e n m a n u f a c t u r e r s ,  i s t h e same: t o i n d u c e  screen  outlet.  of s h i v e s Similarly,  rate",  R.  Efficiency  i n the feed reject  rate  performance a r e  that  i s defined  passes  to the  i s the o v e r a l l  portion  11  of  the  Reject this  feed rates  thesis The  used  pulp may  high  be  reject  rate  screen  i n Figure  2.  efficiency  at  E  E  In  =  R  2.1  2.1  conforms  well  usefulness  and  a  and  E-R  curve at  E-R  i s one  rate  is  curve  is  having  i s , the  of good  i s determined various  fractions.  reject  typical  that  loss  mass  a  maximum  pulp.  experimentally,  reject  flow  rates).  Two  theoretical  efficiency  and  reject  settings equations  rate:  QR  (  -  2  1  }  (2.2)  Equation  2.  efficiency  t h e minimum  relate  are constant  Figure  the pulp  c  Equations  that  but i n  rate;  reject  - (A  1  =  basis,  reject  efficiency  which  volumetric  low  a  an  exist  (T3).  performance  industry,  also  on  stream  screen  In  f o r various  a  reject  Good  with  (i.e.  the  performance,  of shives  measuring  to  i s based between  removal  by  passes  c a l c u l a t e d on  relationship  to assess  shown  that  is  A of  and  2.2  'Q'  f o r a given the  to  one  and pulp  i n more  industrial  p u b l i c a t i o n this  equation  screen  performance  Nelson  attributed  'C  screen  plate.  widespread  use,  and i t  screening by  and  Nelson how  2.1  indices  f u r n i s h and  Q  measurements at  Equation  are screening  to a  data,  shown  (Nl) d e s c r i b e s  c a n be a  as  determined  single  colleague  flow named  in the from  setting. Bolton,  12  Figure  2  Screen Performance  Curves  13  but of  Nelson  gave no  i t s underlying Following  derive  single  aperture  similar, chapter  but  complete.  Hence "mixed  based  on  Kubat  screen  (K2).  series,  and  the  suspension  the  screening  adapted  to  This w i l l  be  This model,  a  and  field  of is  assumed  the  is  from In  the  the  screen  the  mixed  easier  e x p e r i m e n t a l l y . The  to  be  pulp  model  i n the  model  define,  be  and  referred  of  2.2  is  i n the  screen  act  mixing".  Thus  the  the  based  2.2  thus  the  end  as of  this  model i s  is  derived.  equation.  on  chosen  because  increases  "reject"  the  conditions  amount of m i x i n g  A  flat  screening  and  a  annular  Equation  Equation  was  by  the f o l l o w i n g  f o l l o w i n g chapter, and  a  a  to  large part,  flow  in  suspension  "feed"  in  aperture.  analysis  "back  to  instantaneous  apertures  "plug flow"  flow  that  subsequently  experimental plug  to  attempted  is rejected  equation.  no  i n the  i s , in  the  will  that  there  shives  called  to  Steenberg's  pressure  The  description  aperture  model, mixing  screening  and  zone.  accordingly. instead  flow"  2.1  each  t h a t what  considered  moves  thesis  or  (Wl)  i s offered  In t h i s  Equation  Wahren  back  derivation  is  that of  equation  that  and  recirculated  They  concentration  assuming  thesis.  the  in  by  simpler  zone  the  publication,  in p a r a l l e l ,  is  of t h i s  screening  as  2.1  acts  of  assumptions.  Nelson's  Equation  screen plate  to  derivation  plug  were for  flow  chosen  this  study  associated  easier  i n the annular  to  flow  model  screening  14  zone  may  well  plug  flow  2.4  The  model  Flow  Thomas directly a  be  and  recirculating  Thomas  and  to  present was  less  2.5  The In  where  that  Motion  t h e r e et  may  single  diameter This screening  be  to  the to  fibre,  i.e. to  thesis,  a  of  fibres  within  however,  suspensions  of  flow  a  flow  that  i s  flow  at  the  they  side  of  the  flow  found the  a  slot  t h a t in  the  flow the  p a s s i n g main  v e l o c i t y  rate  in  the  flow,  p r o f i l e  exit  layer  flow.  screened  fibre  the  conditions.  layer"  Screening  estimated  a  observed  flow  noted  "exit  s u b s t a n t i a l (K3)  They  the  the  in  is  date  mixing.  screening:  upstream  a l s o  main  Fibres  for  p a r t i c u l a r ,  Because  the  hundreds  equal  In  an  plate,  pulp  i s  a l .  from  pulp  plate.  according  in  of  industry,  Kerekes  adjacent  the  future  investigated  3.  p l a t e .  to  than  slotted  came  some  Aperture  Cornelius  the  next  a  at  account  pressurized  size  slot  to  (T4)  Figure  zone in  adjacent  a  in  changes  the  Screen  to  above  shown  through  a  and  adapted  Cornelius  relevant  pattern  there  may b e  Near  bifurcation  that  significant,  at  Situations consistencies  i n t e r a c t i o n that within  at  between  such the  s p h e r i c a l  of  1-4%,  f i b r e s .  c o n s i s t e n c i e s  volume volume  "swept" that  by  has  a  length. considers  which  are  the  simpler  sufficiently  problem dilute  of that  15  Figure  3  S t r e a m l i n e s at a Flow B i f u r c a t i o n in a S l o t t e d Plate  16  fibre  interaction  understanding  is insignificant.  industrial  concentration" concentration The  of  fibres  fibre  screening near  a screen  p l a t e a t normal  through  with  a  flow  rotate  a fibre  simple align  of r i g i d  parallel  be n e g l e c t e d .  flow,  adjacent effect  to a  a fibre  plate  to a  thus  screen  fibres plate  of  fibres  a screen  a  plate from  tend  The  i n v e s t i g a t e d the  tend  to  in to  velocity  might  have  plate  t o be  required plate  fibres  will  to a screen  be  along  expected  rigid  surface  would  and  Increased  an a p e r t u r e  (M5).  plate  parallel  through  A n d e r s o n and B a r t o k  that  the flow  screen  fluid  effect,  be  a  the aperture.  the o r i e n t a t i o n  of  that  through  could  over  (R2)  approaching  found  approaching  fibre.  et a l .  to the p l a t e .  and p r e d i c t e d  t o pass  They  that  the motion  Ries'e  passage  fibre  on t h e f l o w  screen:  with  of  to the screen  considered  substantially  maximum  by a s s u m i n g  the alignment  i n the d i r e c t i o n  pressure  could  increases  Accordingly,  shear  similar  the  fibres  incidence.  t o some d e g r e e as i t p a s s e s  gradient  suggest  aperture.  perpendicular  the p l a t e  parallel  Mason  "critical  i s calculated  suspension  the p r o b a b i l i t y  aperture.  to  interaction  plate  perforated  flow  Mason's  i s u l t i m a t e l y concerned  a dilute  align  step to  one f i b r e w i t h i n e a c h volume swept by a  considered  forces  is a first  screening.  used  concentration"  i s only Pulp  was  a t which  "critical  there  (M5)  pulp  This  a  in a  aligned  to  rotate  aperture. passage of f i b r e s  17  through  a  because which  mesh l i k e  has  surface. fibre on  a  Also,  like  s c r e e n i n g .  case  plate  of  pass  observed length  and  to  (or  mesh).  flowing zero  through that  component  the  the  on  and  through the  screen  p l a t e .  of  stiffness.  of  as  one  screen  a  dilute  relative  sides  of  represents plate, where  Anderson with  flow  interaction the  feed  a  screening  used  fibre  situation  increased  the  Bartok  and  a  represents  fibre  to  "permeability" accept  i n t e r e s t  considered  parallel  A permeability freely  particular  they  influence  the  permeability  increased  of  Anderson  defined  fibres  is  C o r n e l i u s ,  remove  of  of  work  Riese,  They  fibres  permeability  and  substantial  suspension  screen  Their  Thomas  concentration  can  (Al).  the  while no  and  decreased  a  a  fibre Bartok fibre  18  3.  Shive p l a t e  stiffness  a p e r t u r e  pressurized values the  of  these  shive  3.1  to  (i.e.  extent  in  wood  s e c t i o n .  of  of  fibres  are  wood  a l l and  in  to  screen  single  a  screen  v a r i a b l e s  chapter,  in  representative  order  to  simulate  establish i n d u s t r i a l  rate  performance  curve  to  fibre  is and  aperture.  the and  naturally-occurring  The  the  of  in  process)  in  bonded  s t i f f n e s s of  moment  a to  each of  elasticity of  inertia  a  presence  assumes  that  shives  in  c r o s s -  square fibre to  are  of  and  shive  simplify  assumed  to  the be  other. beam  (E), (I),  of  the  wood  bundle  size  and  Also,  4.  the  on  d e l i g n i f i c a t i o n  and of  depends  of  below  defects  shive  species,  degree  Figure  f i b r e s  modulus  the  wood  illustration  given  the  the  analysis  free  intimately  g e n e r a l ,  property,  this  key  efficiency-reject  pulping  schematic  a n a l y s i s ,  of  a  the  shive.  is  product  an  f i b r e s ,  cross-sections  In  a  be  estimated  dimensions,  the  A  identical  at  to  near  Stiffness  c o n s t i t u e n t  defects  conditions  required  industrial  stiffness  the  are  Also,  cross-sectional  the  In  conditions  permeabilities  The  flow  b e l i e v e d  variables  relate  Shive  the  screening.  screening.  derived  and  are  experimental  pressure  its  pulp  and  ANALYSIS  is  which which  equal is is  a a  to  the  material geometric  19  WOOD  FIBRE  NINE  WOOD  CROSS-SECTION  FIBRE  BUNDLE  CROSS-SECTION  Figure  4  Idealized  Fibre  and Shive  Cross-Sections  20  property. assessed  The moment o f i n e r t i a about  can  be  For  a single  z  where For  calculated  l  +  a nine-fibre  =  9  axis  (b~2t)t  standard  9I  1  +  3  thickness,  + 2  stiffness  in  Figure  5.  and b = o v e r a l l  fibre  width.  2  (3.2)  fibres,  2  + t b  + 3  2  n  1 2  to estimate  0 , 5  (4t)(b-t)b  (b-2t)t  +  + ... +  of a s i n g l e  I as EI = 81 x 1 0 ~ value  (3.1)  + 24b*t(b-t)  f  this  It  formulae (P3).  2  3  to  engineering  (b-2t)(b-t) t  f o r a b u n d l e o f "n" wood  Table  i t scentroid.  is  bundle,  n  The  and t h r o u g h  cross-section  fibre.  ^ll  =  using  t = f i b r e wall  I  And  i t sneutral  of a s h i v e  3  (b-2t)(b-t) t 2  +  0.5  (n  2  .  ^-V fibre  Equation  the s t i f f n e s s  For t h i s purpose,  ]  . _  undelignified Nm  [ r  2  (3.3)  i s given  3.3 may  of s h i v e s ,  f i b r e diameter  be  in  applied  as  shown  i s assumed t o  21  4x4  i  i  10°  i  1  10*  Number of fibre  Figure  5  1  I0  1  ' —  I0  4  •  6  cross-sections  R e l a t i o n s h i p Between S h i v e  Stiffness  and S i z e  S h i v e s t i f f n e s s may be p r e d i c t e d f r o m t h e s t i f f n e s s o f 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 o f t h i s t e c h n i q u e i s s u p p o r t e d by t h e a g r e e m e n t b e t w e e n t h e e s t i m a t e d s t i f f n e s s o f a 4x4 i n c h wood beam ( c i r c l e ) and t h e measured " t e x t b o o k " v a l u e ( s q u a r e ) .  22  be  30 m i c r o n s  check,  the s t i f f n e s s  (black to  spruce)  published  shown of  3.3  this  flow  and  screen  measurements  in estimating shive  at a Screen  plate,  bulk  share  V  =  aperture  s  this  Plate  that  of the accept  each  flow,  T h i s comparison i s  Q . a  supports  a  zone between t h e r o t o r plate aperture.  through hole  an a p e r t u r e ,  (or s l o t )  open  i s equal  area  t o 1.0  i . e . f o r Q =0.107 m/s,  the rotor  superimposed  a  lugs on  passes  V , s  an  Thus,  (3.4)  i s the total  conditions,  pressure  a r e made o f  a ~~A s  velocity  t h e use  typical  and e s t i m a t e s  and 2) w i t h i n a s c r e e n  by a s s u m i n g  compared  Aperture  within  of the flow  and  beam  stiffness.  1) i n t h e a n n u l a r  velocity  method  (M6).  As a  i n c h wood  Q  s  A  - by - 4  agreement  s e c t i o n , the flows  estimated  large  by  5, and t h e c l o s e  velocities:  The  where  inch  ( s e e F i g u r e 1) a r e a n a l y z e d ,  the  equal  4  be e s t i m a t e d  The F l o w F i e l d  screen  of a  stiffness  Equation  In  of  may  in Figure  3.2  is  and f i b r e w a l l t h i c k n e s s t o be 4 m i c r o n s .  past  an a p e r t u r e  the flow  through  of the screen m/s  plate.  for typical  and A =0.103 s  causes  flow  c i r c u m f e r e n t i a l d i s t a n c e between  screening  m.  Passage  2  pulses  the aperture.  The  t o be  Given  l u g s , t h e time  the  between  23  pulses  may  duration.  be  assumed  Thus,  as  a  to  be  f i r s t  much  greater  approximation,  than the  the  pulse  pulses  can  be  neglected. The  bulk  resultant  of  down  gap  the  rotor.  two  The  along  the  through  velocity  and  the  1  the  component,  as  plate.  (Q.  in  -  part  z  ,  the  gap  a x i a l  flow  V  of  annular  the  c i r c u m f e r e n t i a l  axis  screen  flow  components:  velocity  screen  =  the  velocity  axial  the  of  is  bulk  induced  is  flow by  decreases flow  the  the  linearly  drawn  off  Thus,  Z  Q )  (3.5)  z  where the  A  feed  zone,  that  and  pressure  rate, is  the  a x i a l  zone  to  V  V^the  in  may  be  wake  of  V  may  be  wake  taken  circumferential  m ,  expressed  a  of as  distance in  terms  lug.  at  a  between of  1.8  to  the  and  a  of a  the typi-  m/s,  given  Q =0.126  m /s. 3  a  V  t  ,  w i l l  f i r s t  vary  approxi-  estimated  distance  is  screening  For  0.3  m and  As  Qf  entry  component,  constant  cylinder  the  interest.  from  the  annulus,  annular  from  of  velocity  the  the  H=0.516  2  z  the  point  decreases  z  of  of  distance  the  c i r c u m f e r e n t i a l  location  area  height  A =0.068  3  the t  is  the  m /s,  f  in  H  screen,  Q =0.126  mation flow  Z  cross-sectional  screening  The with  the  flow  annular cal  is  z  from  equal  to  the half  lugs  (S3).  S p e c i f i c a l l y ,  tip  speed  of  the  rotor,  24  V ,  and  r  V  The  slip  =  f c  factor,  (1-S)  V  that  the  V =32  (3.6)  vector  velocity  m/s  r  S:  r  circumferential  given is  a  and  sum  of  component  S=0.85. the  has  The  a x i a l  a  value  resultant  and  of  4.8  m/s  velocity,  tangential  V  u  ,  v e l o c i t y  components:  V  A  =  u  (V  + V  2  z  reject  particle  screening  zone,  As  a  f i r s t  of  5  m/s  estimates of  these  3.3  flow"  and  0  -  (3.7)  5  traces  its  everywhere of  V  flows  are  Two  equations  the show  -  equation. one  the  the slot in  be  Figure  in  "mixed section  assumes  that  mixing  complete,  5.1  assumed  to  screening V  s  ,  and  the  annular  to  4.8  have  a  value  zone.  The  the  m/s.  direction  6.  Rate  given  down  from  velocity,  this  and  path  varies  annular  In  instantaneous  helical  may  u  Reject  were  performance:  V  in  and  u  a  velocity  approximation,  Efficiency  If is  t  thus  The  screen  )  2  Relationship Section  flow" both in the  the  2.3  to  describe  equation,  and  equations  are  annular  pulp  in  the  the  pulp "plug  derived.  screening reject  zone  stream  p =  v , c ,n, s  Figure  6  c  u  s  Flow in a  Adjacent Pressure  to a Screen Screen  Plate  26  will  be the same as the p u l p  i n the s c r e e n i n g  apertures  will  act in p a r a l l e l ,  aperture  will  be  representative  performance.  As  discussed  permeability,  Pp,  fibres  and what  happens  a t any  overall  screen  in the previous  i s the r e l a t i v e  on the two s i d e s  of  zone. A l l  chapter,  concentration  of a s c r e e n  plate.  of  Thus  pulp  f o r the  mixed flow model of s c r e e n i n g ,  P  ° -P C r.p  =  where C and  C  r >  which  a #  p  p  i s the c o n c e n t r a t i o n of pulp  i s the c o n c e n t r a t i o n of pulp  i s taken  annular  (3.8)  a  D p  as e q u a l  Q,C, f f.p  stream,  concentration  i n the  Cf^p, C  screen w i l l  of the flows  lead d i r e c t l y  a >  and Q p  to the mixed  (3.9)  v  a  into  equation.  Q C + Q C a a.p r r.p  where Qf, Q  accept  i n the r e j e c t  3.8, a m a t e r i a l balance  out of a pressure  flow s c r e e n i n g  and  stream  s c r e e n i n g zone.  Given Equation and  to the pulp  i n the accept  r  and C  are the feed, r >  accept  and r e j e c t  p are pulp c o n c e n t r a t i o n s  and r e j e c t streams. Equations  flows;  i n the feed,  analogous to 3.8 and 3.9  27  can  also  P  be  , sh  given  =  C  for  shive  concentration:  a.sh  (3.10)  — r. s h  Q  f  C  f . s h  =  Q  a  C  D e f i n i t i o n s expressed  a . s h  of  +  Q  r  C  r . s h  (  e f f i c i e n c y  and  r e j e c t  Q  r  C  r . s h  Q  f  C  f . s h  r  C  f  Dividing  f  1  }  can  u a.sh a.p  C sh r.sh P C p r.p  (3.13)  n  Equation  Substituting  P  1  (3.12)  r . p Q C t f. p  C  '  algebraically:  Q  c  rate  3  3.11  by  Equation  3.9  Q^C. , - Q C , f f.sh r r.sh Q.C. - Q C f f . p r r . p  in  Equation  Q  C  f f.sh QfC. f f. p F  F  3.8  -  Q  - Q  r r  and  C  C  r.sh r.p  3.10:  be  28  Substituting  _ P  Equations  0  _ ,C , sh r.sh P C p r . p  C  r  out  like  3.12  r.sh E  Q C ^ r r . p  Cancelling  p  in  -  and  3.13  Q C , r r.sh „ - Q C r r.p n  —  terms:  sh  4- -  1  P  ~~D  1  Rearranging:  sh P  1  P  E  P  P  R  (  sh  +  _  R  ( v  P P  _ D  R  sh P  1  1 }  -  P P  +  +  X  !  (3.14) sh P  R  29  By  comparing  recognizes  the  above  equation  to  Equation  2.1  one  that,  sh - p ^ P  =  1  -  (3.15)  P  where  is  Q  Nelson's  Substituting  E  =  E  "  There  2)  The  Equation  R  +  1  -  (1-Q)  analysis must  be  r a t i o  of  i . e .  changes  reject  model, annular the  in  is  1,  Equation  3.14:  R  (  perfect shive  that  for  mixing  in  and  Equation the  pulp  permeability  model  based  on  that since the  (1-Q)  2.1  screening  is  '  to  1  )  hold,  zone;  p e r m e a b i l i t i e s r a t i o  2  must  u n a f f e c t e d  and be by  rate.  screening  reasonable  -  shows  the  other  extent  Figure  into  Q + QR  constant,  The  3.15  constant.  R  This 1)  screening  of  the  zone  radial  screening,  assumption is  r a d i a l for  pressure  a  ordered,  that i.e.  the  mixing  homogeneity  is  pulp  such  screen  "thickness"  of  the  the flow  down  occurs  ensured. as  plug  that  screening  only  flow the to  This  is  shown  in  zone  is  30  small  compared w i t h The  analysis  annular screen from  element plate.  of  this  dQ  where Q at  =  z  TT  -  D V  a  i s the a x i a l  z  plate  the r o t o r  screening  Balancing  distance Z  zone  the flows  to the  and into  h a s an and o u t  annular  dZ  flow, V  a  i s the average  s u r f a c e , and D  radial  i s the outer  velocity  diameter  of  zone.  Considering  the flow  of pulp  fibres  into  and o u t o f t h e  element:  = Q C z z.p  z #  p  from  (Q+dQ ) (C +dC ) z z z.p z.p  i s the average  the entry  TT DV P C dZ apz.p  c o n c e n t r a t i o n of pulp  to the annular  screening  p u l p p e r m e a b i l i t y , as d e f i n e d i n E q u a t i o n Simplifying  dC C  by c o n s i d e r i n g an  i s l o c a t e d a t an a x i a l  to the annular "dZ".  from  of the zone.  element g i v e s ,  the annular  "Z"  model p r o c e e d s radially  The e l e m e n t  thickness  the screen  where C  using t h i s extending  the entry  elemental  t h e h e i g h t and c i r c u m f e r e n c e  z.p  z.p  Equation  • V* 1  (3.17)  at a distance  zone,  and Pp i s  3.8.  3.17:  (3.18)  31  Assuming the  above  that  equation  dC  r.p "f . p  Note:  In  is  independent  to  obtain:  of  Z,  one  may  integrate  z. p Q,  z.p  When  identities  Pp  Z=0, hold  Q  for  Qf;  the  when  Z=H,  concentration  (P-l)  r.p "f.p  =  z  l_  (  z  =  Q  r  S i m i l a r  variables.  In  J  n V  Q  « f  1 }  (3.19)  f.p  An  analogous  concentration  of  equation  can  :  f .sh  derived  for  the  relative  shives:  ^ s h " r. s h  be  1  * (3.20)  32  Combining  Equation  (Equation  3.13)  rate  with  3.19  the  d e f i n i t i o n  of  reject  gives:  (3.21) L-  Q  f  -J  L i k e w i s e definition  of  E q u a t i o n  can  3.20  efficiency  (Equation  be  combined to  3.12)  w i t h  the  give:  (3.22)  Combining  Equations  and  3.21  gives:  3.22  sh E  (3.23)  =  Although of  Z,  in  V  R.  s  one .  To  Pp  and  would  The  P  As  approximation,  increase  with  V  P  one s  ^  assumed  independent  affected  by  turn,  is  directly  related  between  over  be  be  some  may  to  to  s  in  3.23,  relationships  linearly  been  and is  Equation  the  f i r s t  p  velocity  concerning a  have  s  expect  slot  simplify  P jj  assumptions P  p  and  assume  the  range  R,  that of  changes  must  and  P  Pp and  be s  interest.  made  and  n  P  to  s  n  R.  both This  33  assumption thesis,  is  supported  described  in  by  the  Chapter  experimental  5.  findings  of  this  Thus,  (3.19)  (3.20)  where  k^  and  Combining  E  where  C  k2  are  constants  Equations  =  R  is  a  3.18  -  of  proportionality.  3.20:  (2.2)  C  constant,  as  defined  below,  P C  =  sh P  P The  p h y s i c a l  considering  three  s i g n i f i c a n c e extreme  screening  1)  Shive  permeability  (i.e.  C=l).  In  and  efficiency  be  considered  2)  Shive  ( i . e .  C  this is  to  be  is  to  acting  permeability  approaching  0).  is  C  the like much This  there reject a  tee less  can  be  appreciated  by  situations:  equal  situation  equal  of  to  f i b r e  is  no  screening  rate. in  a  than  p e r m e a b i l i t y  The  pipe  screen  may  network.  fibre  corresponds  effect  to  permeability n e a r - i d e a l  34  screening,  since  even  very  for  3)  a  S h i v e  ( i . e .  efficiency  accept might  pulp c a l l  The  simple  >  is  are  e q u a t i o n s  less  and  more  made  screen  at  a a  ( i . e .  100%)  an  the  shives  than  unusual  reject  than  the  f i b r e situation  rate feed  and  the  pulp.  One  screening".  the  c l e a r l y  one  g r e a t e r  is  than  presented  p r o v i d e  measurements  much This  above  plug  straightforward.  models  approach  rate.  1).  be  "reverse  d e r i v a t i o n s  and  industrial  C  contain  equation  w i l l  reject  would  would this  screening  two  small  p e r m e a b i l i t y  p e r m e a b i l i t y since  e f f i c i e n c y  flow  The  s t a t e d . means single  performance.  the  screening  assumptions Most  of  for  in  a  flow  equation  are  underlying  the  importantly,  r e l a t i n g  aperture  mixed  these  p e r m e a b i l i t y laboratory,  to  35  4.  The s i n g l e  preceding s l o t  to  experimental in  a  objectives 1.  analysis o v e r a l l  part  dilute  EXPERIMENTAL  of  this  suspension of  The  the  relates pulp  work  near  of  fibre  s c r e e n  the  entry work  fibre,  the  of  motion  a  were  flow  permeability  at  p e r f o r m a n c e .  examines  experimental  influence  WORK  single  to  and  a The  of  fibres  slot.  The  determine:  slot  variables  on  permeability. 2. A  How flow  simulate screen. flow  fibres loop  the  move  with  flow  a  the  a  was  slot  a  channel-slot  plexiglas  past  Permeability  through  at  and  channel  was  p l a t e  slot  screen measured  the  flow  by  sampling  (reject)  flow  bifurcation. constructed in  a  to  pressure  the  (accept)  downstream  of  the  slot. F i b r e observed  using  apparatus, given  4.1  t r a j e c t o r i e s high  speed  experimental  in  the  p l e x i g l a s  cine-films.  procedures  A  and  channel  description  analytic  were  of  the  procedures  is  below.  Fibre  Suspension  Eight  types  p r o p e r t i e s d i s t r i b u t i o n s Appendix  IV.  of  are of  fibres  l i s t e d the  were in  used  T a b l e  i n d i v i d u a l  in II.  f i b r e  this  study, D e t a i l e d  types  are  and  their l e n g t h  given  in  36  Table  II  :  Physical  material  Properties  of  Experimental  Fibres  average length (mm)  nominal diameter (mm)  estimated stiffness ( x l O Nm )  nylon  1.0  .043  350  nylon  1.5  .043  350  nylon  3.1  .043  350  nylon  3.1  .230  rayon  1.0  .012  0.5  rayon  1.2  .020  4  -  290  1  2  2  000  7  pl0.rl4 kraft pulp  3.3  .030  4  8  pl4.r28 kraft pulp  2.6  .030  4  9  whole kraft pulp  2.6  .030  4  whole CTMP p u l p  1.8  .030  100  10  37  In  preparing  ensure  that  undamaged, Because  wood a  A l l  change  p h y s i c a l  before To  and  short more  in a  this 500  In  This  suspension  can  be  used  per  l i t r e .  of  were a  sample  The  but  use.  in  water  to  that  and  they  were f i b r e s  the  that  start  no  of  a  were  inspected  were  undamaged.  they t r i a l  fibres  concen-  ensure  at  F i b r e s  damage,  minutes)  c o n c e n t r a t i o n .  significant  occurred  to  stable,  Synthetic  in  verify  f i b r e  dimensionally  not  stored  taken  entanglement,  before  to  was  duration  were  used  for  was no  t r i a l s .  study.  fibres).  to  absorption.  fifteen  techniques  ml  prone  t r i a l  care  appropriate  properties  risk  than  microscope. the  a  three  Two  the  were  water  the  (less than  of  after  minimize  are  fibres  because  at  together,  trations.  t r i a l  discrete,  disintegrator  bonded  in  suspension,  were  present fibres  in  found  fibre  fibres  and  dispersed were  the  the  direct  and  are  of  using  useful (eg.  was  for  higher  concentration  were 12.5  a l l  of  filtered power the  over be  which 500  gave  to  from  stereo  fibres  precisely-cut  to  c o n c e n t r a t i o n s  while  a  when  found  fibre  fibres  concentration  effectively  measurements,  measure  method,  is  a l i k e  range  to  counted  method  Lower  used  in  synthetic  this  method  2000  fibres  h i g h 1 y - v a r i a b 1 e  concentrations  made  counting  d i f f i c u l t . The involved  second a  method  Kajaani  of  FS-100  determining Fibre  Length  fibre Analyzer  concentration (P4).  This  38  instrument One  may  counts  thus  fibres  use  fibres  simultaneously  measure  range  of  fibre  lengths.  to  ml  sample  80  the in  to  fibre this  about  The  000  such  a  high  the  s l o t  f i b r e s  4.2  fibres  e n t r y  The study in  was  the  the  and  past  a  row  of  is  then  of  the  that  Kajaani  40  disadvantage  r a t e  then  a  drawing  fibres  As  a  a  of  a  and  for  number  cause  with  test,  and  FS-100  concentration  of  discussed  in  Chapter  5,  fibres  accumulate  at  to  a f f e c t s  it  may  fibre  p e r m e a b i l i t y  be  p r e f e r a b l e  concentration  concentrate  of  to 1000  the  samples  loop  used  for  FS-100.  Loop principal  Figure  shown  in  7  its  and  components  of  Figures  8  f i b r e  prior  reservoir  to was  7,  function  Reservoir.  where  adjusted  loop  by  and  requires  work,  a  photodiodes  the  may  future  l i t r e ,  with  are  A.  In  it  lengths.  concentration  tube  the  A  in  operates  of  l i t r e .  a  fibre  from  their  lengths  capillary  that  per  at  flow  per  Flow  is  measuring  FS-100  measure  concentration  the  analysis  a  in  distribution.  measurements. operate  a  as  various  s i g n a l  application 50  of  The  provide  length  well  changes  through  p h o t o d i o d e s . interpreted  as  The  the and  are  reservoir  the  start pump's  of  9.  Each  described  concentration the  flow  served  and a  supply  tank.  this  component  shown  below. two  water  t r i a l .  in  functions:  temperature  And  during  Water  a  It was  t r i a l ,  temperature  39  Reservoi r Pump Return Line Feed Line P l e x i g l a s Test  F. G. H. I. J.  Section  Figure  7  Flow  Accept Accept Reject Reject Reject  Loop  Line Sampling  Receptacle  Sampling Sampling  Line Receptacle  Schematic  40  Figure  8  Flow  Loop  and  Plexiglas  Channel  41  Figure  9  Plexiglas  Channel  and  High  Speed  Cine-Camera  42  in  the reservoir  temperature. only  i n order  t o conduct  B.C.D. centrifugal a  pipe  line  i . e . room  (C) was  and F e e d  (B) was used  shut  t h e number  of  fibres  an e x p e r i m e n t .  Pump pump  to minimize  (D) t o t h e p l e x i g l a s  channel  Centigrade,  The o p e r a t i n g w a t e r volume i n t h e r e s e r v o i r was  80 litres,  required  was s e t t o 2 0 d e g r e e s  Piping.  o p e n - i mpe 11 e r  t o pump t h e s u s p e n s i o n test  o f f except  was r e q u i r e d .  An  channel  (E).  when a v e r y  A l l pipes  through  The  bypass  low f l o w  to the  i n the loop  were  1.5  inch  PVC. E. is  Plexiglas  Test  t h e key e l e m e n t  Figure with  9.  distance  (19 mm)  between  industrial single  i n the flow  I t contains  a height  screen.  slot,  simulates  that  slot  widths  are  t h e nominal  test  widths  with  commercial  to the channel  sections  o f 0 . 2 5 mm,  on t h e d i s c h a r g e  turbulence  equal  square  were  plate  0 . 5 mm  at the s l o t  entry.  s i d e was s l i g h t l y  screen  plates).  at the s l o t  slot  study (Note:  The w i d t h  that these  of the  g r e a t e r , as i s n o r m a l  Turbulence  c o n t r a c t i o n at the channel  This  Different,  in this  and 1 mm.  i n an  contains a  axis.  screen.  used  channel  to the r a d i a l  and s c r e e n  i n a pressure  section  a n d i t i s shown i n  3 0 cm l o n g  drum  test  The b o t t o m w a l l o f t h e c h a n n e l  slot  abrupt  loop  i s roughly  the rotor  an a p e r t u r e  had  The p l e x i g l a s  a straight  perpendicular  interchangeable  an  Section.  was g e n e r a t e d  entry.  was v a r i e d by u s i n g  The l e v e l  channels  by of  t h a t had  43  the  slot  t r i a l s from  at  different  were the  run  of  2  equivalent An be  and  to  F.  the  in  the  then  flows  close  to  the  wide  slot  used of  to  any  run  and  Most  diameters  with  an  another  entry  with  to  the be  the be  through purge  fibre  for  14  air  the  varied slot 1  the  of  m/s. slot.  from  the  accumulation.  can '  Lissenburg v e l o c i t y  ten  centre  The  diameters  of  the  pipe  a  easily rate  from  and  and  the  small  chamber  and  to a  a  tubing the  9  reservoir  the  velocity m/s.  t r i a l ,  section,  or  in  in  a  rate  0.5  mm  described screen  causes  clear  the  is  back-  backflushing to  to  the  flow  As  tubing  F ) .  concentration  commercial the  (Line  i n s t a l l e d  control  The  in  Before  through  fibre  i n s e r t s ,  0  flow  flexible  Squeezing  test  pipe  the  into  fibres.  v e l o c i t y  a  Flow).  line  from  slot  (L3).  p l a s t i c  flow  at  through  flow  the  turbulence  in  passes  moved  at  literature.  the  0.09  (Accept  be  K  the  wall"  channel  may  intensity  velocity  the  restrict  may  p r e v i o u s l y ,  flushing  to  Tapered  impeding  estimated  entry.  equivalent  was  of  about  Piping  Receptacle  outlet,  without  mean  reservoir  outlet  measurements.  in  ratio  is  plexiglas  tubing  Sampling  t r i a l  turbulence  the  local  Discharge  tubing  the  that  "very  slot  The  of  constriction  0.35  channel  8  diameters,  measurements  found  a  the  located  One  e q u i v a l e n t  from  component beyond  slot  entry.  estimate  a l .  the  from  diameters.  made  et  with  channel  l e n g t h  distances  was slot  44  H.  Discharge  Piping  from  the  plexiglas  test  Line  H.  A  velocity 8  in  m/s.  a  the  This  screen  Section  creates  uniform  and  Sampling  flow  is  time.  rate)  m/s.  and  this  the  and in  To  to  redirect  sample  subsamples  is are  J  the  for  then  the  a  feed  varied  from  0  taken  to  estimated  in  Line  Reservoir to  fibre  the  flow  A.  along  is  This  flow,  c a r e f u l l y  for  F  maintain  reject  (to  to  parallel  in  flow  weighed  via  the  reservoir  sample  Receptacle  to  flow  permits  valve  back  the  reservoir  screen;  the  of  velocity  three-way  flow  the  be  average  The  turned  to  to  i n d u s t r i a l  the  Most  l i n e  channel  turbulence  The  Flow):  returns  in  suspension.  valve  of  5  enough  three-way  length  an  direct  f i b r e  into  in be  to  valve  includes  plate  set  section  plexiglas  range  3 . 2 to  normally flow  diaphragm  (Reject  a the  Line  I  measured  determine  the  concentration  measurement. Additional in  Appendix  4.3  details  of  loop  are  given  III.  Cine-Photography High  the  technical  speed  slot  lighting were  entry and  in  to  either  side  the  3 mm b l a c k  obtained.  mately)  cine-films  the  The  plexiglas nylon  taken test  fibres,  f i e l d  of  focus  half  of  the  central  wall  were  were  not  in  of  fibre  section. clear was  and  Using  silhouette limited  channel.  focus,  motion  Thus  could  be  near backimages  (approxifibres  near  identified  45  and  disregarded.  immediately wire  was A  was  inserted  used  over  The  the 100  fibre  f i b r e s  per  Further  t e c h n i c a l  frame The  f i l m  of  mirror the  and  of  positions  and  correction between  the  of  in  used  used  the  pipe  removed  and  a  pictures  per  second  in  this  the  next  study  Appendix  III.  manually to  thin  chapter.  contain  just  and  programmes  fibre camera  from  shown  in  a  Figure  onto  the  process. 10,  a  location  cursor,  the  film  images.  mirror  entered  repeated  each  fibre  a  with  l i g h t i n g  in  the  f i b r e s d i f f i c u l t .  and  fibre  about  along  then The with  storage. were  w r i t t e n  to  p r o c e d u r e :  frame  positions and  each  operator  and  are  d i g i t i z i n g associated  f i l m i n g  mid-point  frame  were  becomes  digitizing  The  data  of  films  c o n c e n t r a t i o n  r e f l e c t  pad.  pad  these  fibres  the  one  for  for  this  orientation  by  film  the  focus,  forth. 3000  of  end-point  Computer needs  and  digitizing  computer  used  i n d i v i d u a l  in  digitizing  the  and  above  projected  fibre  advanced  films  of  was  discussed  d e t a i l s  given  was  each  films  l i t r e ;  recorded  horizontal  back  approximately  tracking  position  was  channel  concentrations  are  field  each.  and  The  of  the  the  moved  foot  overlap  equipment  of  three  frames  The 2000  and  rate  for  4000  establish  downstream  framing  Note:  To  numbers to  channel  on  account due  to  meet  the  s t o r a g e computer for  various of  diskettes;  relative  camera  f i b r e  motion  vibration;  46  Figure  10  Film  Analyzing  Equipment  47  instant  display  c o l l e c t i o n tories;  of  and  trajectory  images fibre  printing  fibre  are  of  angles,  indices  programmes the  fibre  i s o l a t e d  the  coordinates,  for  of  and  retrieval  in  and  the  images  a  l i s t  linear  film  listed  on  frame  form  a l l '  fibre  trajecend-point  rotational  II  monitor;  fibre  indices.  Appendix  analysis  to  of and  computer  velocities,  These  along  computer  with  of  d i g i t i z e d  as  the  programmes  fibre  t r a j e c -  tories . Fibre segment  location  connecting  from  the  1.75  mm  fibre  typical  of  fibre  the  because  according  to  the  half  of  wall  fibre.  plate  was  assessed  edge  of  distance  "snapshots"  the of  trajectories  that  here  the to to  discussed  as  the  the  line  distance  at  a  s l o t .  between  plane This  slots  give that  in  assessed in the  in  a  to  in  zone  will  in  consider  centre  Chapter  in  each from  of  of  the  manually  Chapter  Fibre  2. film  zone the  the  c l a s s i f i e d 5.  vary  isolated  assessment the  by  particular  Measurements an  simply  any  discussed  concentration  flow.  were  appear  was  relative  be  through  proximity,  accumulated relative  cannot  velocity  followed  assess  as  The  the  the  fibres  the  these  categories,  to  of  of  upstream  average  and  Fibre  screen  the  concentration  points  concentrations  frames  were  end  mid-point  screen.  number  procedure  frames  defined  the  industrial  counting  The  to  corresponds  Local  zone  the  upstream  distance  was  of film  fibre  channel. into  velocity  six and  48  rotation fibre of  the  r a t e .  rate  were  position  (or  obtained fibre  aforementioned Framing  determined  are  given  angle)  plane  rates in  by  and  between  of a  m u l t i p l y i n g  interest  images by  d e s c r i p t i o n  Appendix  III.  the  the of  on  change either  film how  in side  framing  they  are  49  5.  The  influence  p e r m e a b i l i t y , examined  in  describe  what  screen  5.1  mm  of  f i b r e s  Finally,  limit  the  is  also  shown  long),  a  s l o t  v a r i a b l e s  near  model  passage  but  permeability  of  is  a  on  s l o t  are  proposed  fibres  to  through  of  on  also  findings  data  show  the  of  fibre  shown are  obtained  decreases with  three  CTMP,  and  short  increases mm  long  s t i f f e r  a  Figure  and  shives  increased  fibre  on f i b r e  nylon), length.  (i.e.  fibre  F l e x i b i l i t y fibres  with  fibre  pulp  has  (less  than  increased  kraft nylon  length,  Frith  of  a l l  f l e x i b i l i t y  consistent  by  likelihood  in  For  length.  for  3  the  f l e x i b i l i t y  increased  fibre  fibre  of  and  (kraft,  with  influence  between  are  screening  apertures  sharply  that  11.  study  permeability  r e l a t i o n s h i p s  that  this  permeability  its  times  l e n g t h  Figure  influence  on  The  These  in  in  dependent  effect  five  f i b r e  decreases  a s s o c i a t e d  length. about  and  motion  of  considered  l i t t l e  flow  Measurements  are  permeability  1  factors  e f f e c t s  permeability  type)  the  DISCUSSION  slot.  The  The  AND  f i b r e ,  chapter.  Permeability  types  of  and  this  RESULTS  fibre  fibres  f i b r e s .  is  These  f l e x i b i l i t y  and  12. with Fisher  passing shive  i n d u s t r i a l  pulp  (Fl).  data  Their  through  the  screen  length  and  width.  Fibre length  Figure  11  E f f e c t s of F i b r e on Permeability  Length  (mm)  and  Fibre  Type  1.0 O I mm • I mm • 3 mm • 3 mm  rayon nylon kraft pulp nylon  Fibre stiffness (l\Lm ) 2  Figure  12  Effect  of  Fibre  Stiffness  on  Permeability  52  There  is  measurements with  the  Figure  Kajaani  FS-100,  "staple"  at  pulp  of  slot  concentrations  K a j a a n i  fibres  Since fibres  t h e s i s  through  used  the is  and  unobstructed in  may  have  drop  slots,  kraft  thesis  be  the  not  be  f i b r e were  f i b r e s , the  the the  passage  permeability. the  fibre  w i l l  to  involving  in  with  the  however,  impeded  caused a  the  tests,  H i g h e r  tests  no  stapling  would  p u l p  concerned  this  most  fibres  k r a f t  to  f i b r e s  fibre  entry  In  gave  involving  of  In  in  was  due  f l e x i b l e  s l o t  stapling.  mainly  subsequently  for  flexible  fibres  slot  tests  r e s u l t s .  f l e x i b l e  stapled  in  shown  there  likely  phenomenon  the  of  through  this  at  use  is  made  counts  fibres  chapter.  the  and  of  this  increased  FS-100  accumulation  in  The  t e s t  cause  effect  as  manual  nylon  tendency  entry.  measurements  the  used  a f f e c t  and  for  and  p e r m e a b i l i t y  Analyzer,  fibres,  but  stapled  to  to  Length  This  the  l a t e r  f i b r e s  s u f f i c i e n t  observed  values;  and  the  considered  data  k r a f t  between  counts,  concentrations  Kajaani  of  Fibre  d i f f e r e n c e .  f i b r e  amount  manual  FS-100  For  s i g n i f i c a n t  is  on  permeability  higher  d i s c r e p a n c y  based  11.  higher  some  passage  of  permeability  based  on  manual  counts. The claim  that  section what  data  presented  what  used  happens  in at  happens this an  in in  study  aperture  Figures  the  slot  11 of  corresponds in  an  and  the in  industrial  12  support  experimental a  general pressure  way,  the test to  screen.  53  There  is  (2.6  mm  nylon  a  forty-two  long)  kraft  f i b r e s .  Equation  2.2.  t y p i c a l  of  s i m u l a t e  r e s u l t s  caused 14. beyond  of  were  for  b i l i t i e s Figure not,  5.2  the  slot  slots  for 15.  both  =  rate  our  may  in  curve  is  attempt  be  to  considered  is  very  0.02  that,  d i l u t e  i n t e r a c t i o n  since f i b r e  is  not  a  and  decreased  of  slot  to  shown  velocities  1 m/s  order  as  slot  upstream  studied  velocity  exaggerate  in  and  of  velocity  Figures was  an  clarify  13  extended industrial  the  effect  velocity. are  associated mm  Changes  in  affect  and  3  mm  channel  fibre  with  increased  nylon entry  f i b r e s , length  permeability  to  much,  fibre as the as  permeashown  in  slot  do  shown  in  16.  Fibre  be  shive-like  C  reject and  u s i n g  permeability,  1  Trajectories  Considerable may  -  of  between  screening.  estimated in  long)  conclusion  f i b r e  velocity  range  however,  Figure  slot  screen  Wider  important  mm  value  s c r e e n i n g  o b t a i n e d  pulp  a  industry,  pulp  increased  increased  in  permeability  (3  efficiency  found  and  in  and  gives  s i g n i f i c a n t  The  pressure  ratio  A second  Increased  far  fibres  i n d u s t r i a l  prerequisite  and  pulp  resulting  curves  s u s p e n s i o n s ,  both  difference  This The  successful. these  fold  gained  Near  insight  from  the  a  into use  of  Slotted pulp high  Plate  screening speed  fundamentals  cine-photography.  Slot velocity  Figure  13  (m/s)  E f f e c t s of S l o t V e l o c i t y on Permeability  and F i b r e  Type  Slot velocity  Figure  14  E f f e c t s of S l o t V e l o c i t y on Permeability  (m/s)  and Upstream  Velocity  56  Figure  15  E f f e c t s of S l o t V e l o c i t y on Permeability  and  Slot  Width  57  Figure  16  Effect  of  Entry  Length  on  Permeability  58  Visual  observation  can  across  the  how  how  they  channel,  move  Three involved  when  Film  2  (0.043  mm f i b r e s ,  film  discussed analysis, shown  in A  were  and  Figure  3,  was  based as  flow  films  revealed  lower  than  uncertain. fibres  and may  of  4,  are  the  of  t h i s  3  of  7.2  but  7.1  and  are  film  shown  3.2  m/s  fibres. flexible  Details  Table  V.  Figure  of  Some 17.  As  digitized  for  trajectories  are  were  computer-generated  1  involved  in  images  slot.  nylon  m/s.  in  and  F i l m  more  also  given  the  study:  of  Film  1  with  shive-like  velocity  Film  channel,  18.  the  exit in  layer,  a l l  motion  that the  mainstream.  It  may  be  wall;  cause  The  the to  effect" gradient  in  in  cause  velocity  migrate  shown  the  of  exit  this  gradient  away  for  from may  flow  l o c a t i o n the  be  fibres  in  observations  collisions  screening  decreases  in  f i b r e  consequence of  or  f i b r e s  "wall  concentration  a  of  that  These  debris  concentration  in  as  films.  small  Analysis  fibre  such  three  of  tracers.  the  this  in  d i s t r i b u t e d  the  interact  conditions,  fibres.  from  evident  on  flow  conditions  examples  and  are  in  v e l o c i t i e s  slot  Chapter  acted  the  a  well-defined  Figure  role  but  oriented  mm d i a m e t e r  same  frames  in  s l o t  nylon  experimental  typical  wall  the  are  f i b r e s  a n a l y z e d  0.230  mm d i a m e t e r )  0.043 the  and  and  how  approach  were  upstream  involved  they  they  f i l m s  respectively,  reveal  which in  layer  is  between  the  wall.  significant of  is  effect  adjacent the  the  the The if  increasing  59  stiffness shives  or  in  the  screening A  s i z e . flow  would  of  into  layers,  of  as  is  set  the  of  feed  than the  the  the  combined  is  near  in  the IV.  of  in  The  Table  fewer  and  thus  I  For  is  nominal  This  Layers  V.  plate  height  flows.  thicknesses  aperture,  screen  channel  accept  r e l a t i v e l y  bifurcation.  given  Table the  be  screen  flow  data  to  and  then  the by  zone  equal  the  divided  exit  layer  m u l t i p l i e d  thickness and  II  by  is  for  less  each  of  films. The  observed  into  the  five  tive  incidence  The  film  defined  thickness ratio  simply  the  analysis,  would  entering  occur  summary  sake  There  total  "motion of  increased  consistent  Figure  13.  The  and  fibres  and  E)  motion Motion  the  between  the  the  plane  Stapling  occurred  in  Film  angles.  Passage  is  and 2,  without  Types  D  Films  an  the  with  layers  contact  only slot  for  and 2  and  of  slot  mm  to  contact  that  shown  20  in  and  its  and  21.  Types the  Types  to  motion  upstream  (Motion fibres  equal  fibre  (Motion  V.  shows  19,  adjacent  r e l a -  these  a  the  Table  is 3  in  Figures  (1.75  The  in E  into  measurements  motion in  III.  given  increase  the  interest  s l o t but  is  shown  three  of  Table  permeability  interacted  within  in  c l a s s i f i e d  types  of  causes  orientation  that  were  slot).  with  were  listed  comparison  c o r r e l a t i o n  A l l  at  of  velocity  types,  p l a t e  various  A  slot  trajectories types"  incidence  p e r m e a b i l i t y .  location  fibre  C  with  negative  (Motion  Type  B,C,D slotted of  the  and  D)  fibre E)  was  60  Figure  17  Motion  of  Fibres  Near  a  Slot  (Cine-Film)  61  iLIST  Figure  2 RUN*-  18  Motion  of  aLOAD  Fibres  11  Near  4SAUE" 5C0NT**  a Slot  (Computerized  Images)  62  Table  III  :  Fibre  Type  Motion  Types  Motion  The f i b r e moves p a s t the slot w i t h o u t e i t h e r end e n t e r i n g the s l o t or t o u c h i n g a s l o t wall.  One e n d o f s l o t and w a l l s , but the s l o t mainstream.  the f i b r e enters the touches one of the i s then swept out of and back i n t o the  One e n d o f t h e f i b r e e n t e r s the s l o t a n d t h e f i b r e i s immobilized b a l a n c e d on the downstream edge of the s l o t . T h i s i s c o m m o n l y c a l l e d "stapling".  The f i b r e passes through s l o t after contacting one both) of the s l o t walls.  E  the (or  The f i b r e passes through the s l o t without contacting either slot wall.  Channel  Layer  Definitions  Boundar ies  From the s u r f a c e of the slotted p l a t e to a p l a n e 1/8 a f i b r e length above the s u r f a c e .  From a plane 1/8 a f i b r e length above the p l a t e s u r f a c e to a plane 1/4 a f i b r e l e n g t h above the surface.  From a plane 1/4 a f i b r e length above the p l a t e s u r f a c e to a plane 1/2 a f i b r e l e n g t h above the surface.  From a p l a n e 1/2 a f i b r e length above the p l a t e s u r f a c e to a plane 1 f i b r e length above the s u r f a c e .  From a p l a n e 1 f i b r e length the surface to the channel line (or to a p l a n e 1 f i b r e below the top of the f i l m if the c e n t r e l i n e and top f i l m frame are less than 1 length apart).  above centre length frame, of the fibre  From the channel centre line (or plane 1 f i b r e length below the top of the f i l m frame) to the edge of the f i l m frame.  64  Table  V  :  Film  Data  Summary  Film 1 Experimental  upstream v e l o c i t y (m/s) slot velocity (m/s) nylon fibre length fibre diameter (mm) slot width (mm) number of f i b r e s observed measured permeability exit layer thickness (mm)  Relative layer layer layer layer layer layer  I II III IV V VI  B C D E  3  7.2 3.2 3.1 0.230 0.5 298 0.01 0.23  7.9 3.1 3.1 0.043 0.5 695 0.09 0 . 20  7.1 7.1 3.1 0.043 0.5 827 0.86 0.53  Concentrations: ( 0 - 0 . 3 8 mm) (0.38 - 0.75 (0.75 - 1.50 (1.50 - 3.00 (3.00 - 8.75 * disregarded  Distribution A  2  Conditions:  of  Motion  mm) mm) mm) mm) *  0.32 0.32 0.90 0.99 1.00  0.33 0.58 1.01 1.06 1.00  0.12 0.46 1.17 1.09 1.00  97.3%  97.2%  94.8%  2.7  1.8  1.2  nil  0.9  2.5  nil  0.1  0.6  nil  nil  0.8  100.0  100.0  100.0  Types:  s i m p l e movement downstream slot contact then movement downstream immobilization at the slot slot passage with slot wall contact slot passage without slot wall contact total  65  £ 1.50  O  E  £  o  1.25  o  -o o o o o ® o o o o  <8>  1.00  a  <8>  . J  o  o ® o o  <o 0.75 E o  1=1 <D  0.50  O -J  £ 0.25 h C/>  Q  01 2  Figure  19  Motion types 0®90f ABCDE  •1.0 -0.5  ®  <8>  r-H k_ <D >* O  0  0  0.5  1.0  n  "2  Angle (radians)  C o r r e l a t i o n of F i b r e Motion, F i b r e and F i b r e O r i e n t a t i o n for Film 1  Position,  E E  1.50  CD  1.25  ®  O  o  o o  ®  c?°§ 8 3D° O °oo o o ° O  0  3 OO  0.75  E o  o co ^ Q  ®f • •  * o  Motion types  o®oot A B C DE  0 -f  o  ° 0  ® ®  0.25  °  o  Z. 0.50  CD O  O  (  1.00  CD CD  O CO  •oo o ^ o o ocP°° o „ o ° o o  -1.0 -0.5  o® 9  ®  ®  O  © ®  0  0.5  1.0  u  2  Angle (radians)  Figure  20  C o r r e l a t i o n of F i b r e M o t i o n , F i b r e and F i b r e O r i e n t a t i o n for Film 2  Position,  67  e  1.50  £  •O-  ®  1.25  O Q .  o  1.00  CD CD  u0  °  0.50  <D 9-  0  O  Q  co 0.75  E o  •o- o o (9(2) o oo° ° 3 o o o o 3 § o o o<3 ® o 3 O n ® <* (3)0  Motion types  0.25  to  5  A  *  CD  >.  O  V *  - I  3  CD  A B C DE  0  TT 2  -1.0 -0.5  0  0.5  1.0  TT 2  Angle (radians)  Figure  21  C o r r e l a t i o n of F i b r e Motion, F i b r e and F i b r e O r i e n t a t i o n for Film 3  Position,  68  observed  in  negative  angles-  some  Film  general  fibres show  3  Analysis  of  There  is  a  axial  25%  less  than  the  2)  The  fibre  velocity  agreement three  flow  on  restricted  Films the  slot.  1,  2  data  to  and  velocity  The  of  A Model model  experimental  factors: the  wall  3  fibres  also  and  with  provides  orientation  presented  across  (i.e.  velocity in  in  in  of  Table  VI  container  and  listed  are  channel, I)  is  and  about  V).  IV  measurements  the  Layer  (Layer  Layers  velocities  velocity  fibre a exit  transverse  3-5%  near  axial  geometric  model,  bulk  is  Fibres  A  the  velocities  observed  turbulence)  degree  gradient  midstream  Bulk a  velocity near  the  into  The  4)  in  of  be  and in  V  are  Table  were  V,  made  independent  in for  by  of  fair a l l  timing  the  fibre  measurements.  3)  5.3  with  films.  velocity  of  the  to  that:  the  from  found  information  upstream  1)  the  and  the  the  axial  centre  orientation.  necessity,  for  Fibre for  be  of  effect"  layer  are  component  mainstream the  Fibres  velocity.  channel  close  to  parallel  (arising  to  have the  a  slight  wall  the  must,  wall.  Passage p a s s a g e this  permeability  "wall  of  aligned  f i b r e  findings  velocity  and  at an  is  s u g g e s t e d  t h e s i s . a  s l o t  "entry  candidates  to  by  According is  pass  to  determined  effect".  Only  through  the  the  this  by  two  fibres slot.  Table  VI  Fibre  Velocity  F i lm  and  Orientation  Layer I  II  III  IV  V  V  x  (m/s)  1 2 3  6.1 5.2 4.8  6.6 6.0 6.1  6.5 6.6 6.3  6.9 7.1 6.6  7.4 7.3 7.0  V  y  (m/s)  1 2 3  -0.2 -0.3 -0.7  -0.4 -0.2 -0.3  -0.2 -0.2 -0.4  -0.1 -0.1 -0.3  -0.1 -0.1 -0.2  (rad/s)  1 2 3  -97 -462 -439  -18 -272 -321  283 -215 -347  332 -200 -45  -140 63 -93  0.05 0.03  0.04 0.06 0.10 0.08 0.05 0.08 0.09 0.13 0.12 0.19 0.21 0 . 20 0.23 0.25 0.28 0.20 0.13 0.16 0.11 0.11 0.06 0.06 0.06 1.00 1.00 1.00  0.08 0.07 0.09 0.10 0.11 0.12 0.13 0.16 0.15 0.19 0.14 0.18 0.14 0.15 0.13 0.15 0.15 0.14 0.12 0.14 0.11 0.10 0.08 0.07 1.00 1.00 1.00  u  angle -  TT  distribution: -  3  2 -3  -  TT  TT  8 —  4  TT  —  Tf  4 -  TT  8  8  TT  -  0  -  TT  8 0  8 Tf  -  TT  8 TT  4 —  3  4 3  TT  Tf  8 -  8  Tf  2 total  1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3  —  -  0.33 0.43 0.83 0.33 0.57 0.17 0.33 -  0.05  -  0.11 0.11 0.67 0.26 0.33  -  0.47 0.50 0.33 0.05 0.06  0.05  -  -  1.00 1.00 1.00  1.00 1.00 1.00  -  0.05 0.05 0.22 0.08 0.08 0.26 0.25 0.23 0.30 0.32 0.31 0.22 0.16 0.23  0.06 0.03  0.03 0.05 1.00 1.00 1.00  70  Thus of  the  two  permeability  permeability  P  P  e  at  a  slot  can  with  component  in  stream);  C  C  average  u  =  the For  =  e  the  C  the  Film  feed  2,  the  the  fibres  in  the  =  0.27).  e  The previous entry that  a  of  fibre and  fibre  e f f e c t ; the  product  in  P  w  one  wall w i l l  exit had  a  must  be  in  length,  (i.e.  the  =  s  the  fibre  the  exit  in  t h i s  layer  was  value  of  has  be  exit  any  the  in  was  accept  layer;  t h e s i s , about about  0.09.  that  passed  thickness then  in  calculate  not  explained  the  slot  P,  effect  be  permeability  and  concentration.  layer  the and  can  the C  a n a l y z e d the  =  w  component  effect;  the  permeability,  5.1,  P  wall  fibre  can  that  permeability  concentration  i s ,  exit  section  passage, than  nature  effect a  that  overall  Equation  P  the  u  through  films  fibres  applying  (i.e.  flow  upstream  flow;  the  with  fibre  of  =  e  entry  the  three  concentration in  the  P  associated  concentration  as  (5.1)  w  P = permeability;  associated  shown  components:  e  Here,  be  only  layer of f i b r e  this  be  a  layer  that  In  Hence,  by  the  in  is  way.  much  e l i g i b l e  the The  Given  candidate is  the s l o t  further.  following to  that  0.33.  described  discussed the  33%  27% o f  through  been  the  for less for  71  passage  must  T h e r e f o r e ,  be to  substantially during  to  an  and  must  travel  enter  less  it  main  the  fibre slot;  f i b r e  through to  be  carried  slot  most  must  turn  fibres  can  bend  slot.  However,  through forward  the by  downstream  close  likely  to  slot.  the  edge  to  the  the  to  main  of  w a l l ,  pass This  wall,  more  rotate  the  to  section).  is and  needs  plate.  fibres  the  pass  the  screen  the  flow.  the  are  the  Flexible  order  previous  the the  most  contacts  the  the  slot,  flow  may  approach  in  closer  to  in  angles,  noted  the  to  to  entry.  fibre  that  that  fibre  (as  since  the  parallel  the  the  rotate  returns  negative  slot  follow  extent  Fibres  slot  and  almost  through  the  rotation,  slot,  the  at  fibres  During flow  pass  turning  rigid  aligned  through is  the  be  the  reasonable  less  favourable  to  with  it  the  aligned  must angle,  with  the  slot. This to  model  explain  why  p e r m e a b i l i t y b i l i t i e s  than r i g i d  exposed  to  have  higher  conform having  to to  they  do.  fibres  f i b r e  tips  forces  the  slot.  in  streamlines  rotate  and  at  flow,  Short (see into the  slot  and  entry  slot  can  be  variables  have  higher  11),  because  slot,  less  of  mainstream fibres Figure  passing the  into  which would  12), the  the could  be  mainstream  and  affect  when  fibre pull  expected  because slot,  used  permea-  Figure a  (see  straddle  a  fibres  Flexible  permeabilities the  motion  fibre,  long  drag  from  fibre  certain as  s h o r t ,  f i b r e  of  they  rather slot  a is the to can  than flows.  72  Increased for  two  move  slot  reasons:  into  the  increases, exit  velocity  slot  and  layer.  1)  drag  wider  into  the  discussed enter  by  the  in  be  slots  plate  cannot  pass  c l e a r .  that  2)  The  exit  concentration  for  the  fibre  more  of  for  in  the  increased  reasons: and  The  the  s l o t  (see  a  to  thickness  cause  decrease,  I n c r e a s e d  15)  fibre  fibres  s i m i l a r  time  the  layer  velocities  14)  (Figure  cause  p e r m e a b i l i t i e s  allow  (Motion of  the  rotate,  flow  is  and of  C  above  in  exit  width  is  F i g u r e  fibre  the  The  balanced  by  so  there  fibres  the  w i l l  and  Nonetheless,  is  to  1 5 ) ,  rotate  the  the  to  exerted drag  and  the  the A l l  screen  plate remains  edge on  flow  pulp  of  the fibre  by  through  that  a  f i b r e s  screens  a  the  motion.  apertures as  be w i l l  the  fibre  point  also  fibres  exerted  further  plate.  stapling  can  downstream  drag  no  III)  Certain  r e s t r i c t  grow  screen  Table  model.  strike  backflushing  concern.  Type  there.  aperture, through  of  passage  slot.  flow  screen  industrial  on  immobilized  Accumulations  them  and  i n c r e a s e s .  terms  s l o t  means  forces  the  higher  s l o t ,  mainstream  some  forces  stapling  the and  it  ( F i g u r e  with  Fibre  slot  increase;  t h i c k n e s s  associated  move  drag  fibre  Decreased mainstream  mainstream  because  The  with  p e r m e a b i l i t i e s  l a y e r  promotes  to  subject  have keep of  73  SUMMARY  6.  This slots, pulp  thesis  and  the  is  findings  are  1. an  as  side  through  a  a  screen  screen  used  the  as  of  this  of  the  flow  f i b r e  passage  knowledge  to  through  pressurized  work,  and  the  velocities  near  an  screen  Typically,  of  with  p r i n c i p a l  follows.  pressure  assumptions.  were  summary  We e s t i m a t e d  i n d u s t r i a l  feed  A  CONCLUSIONS  concerned  application  screening.  AND  the  plate  plate  guidelines  bulk is  6  aperture in  using  simple  velocity m/s,  is  1  aperture  e n g i n e e r i n g  parallel  and  the  m/s.  bulk  These  our  experimental  two  e f f i c i e n c y  in  to  the  velocity velocities  study  of  pulp  screening. 2.  We  equations  d e r i v e d  given  e l s e w h e r e  in  widespread  use.  based  on  mixing  two  be and  used  the to  s h i v e s  performance.  below. the Our  to  analysis  the  constants  relate at  a  These  equations  l i t e r a t u r e ,  different  adjacent  Moreover,  the  the  and  revealed  assumptions screen in  relative  s i n g l e  have  r e j e c t been  E q u a t i o n that  the  concerning  plate  these  -  in  a  to  2.1  is  in  equations  are  the  ( ' C  permeability  aperture,  reported  amount  pressure  equations  of  rate  and pulp  i n d u s t r i a l  of  screen. 'Q')  can  fibres screen  74  The  plug  E  "mixed  E  =  3.  R  We  plexiglas  C  a  measurements  single to  and  (see  a  single  performance because  significant  loop  slot,  and  in  in  through  be  Equation  the  s u s p e n s i o n was  fibre  interaction  This an  related (or  dilute, is  not  at  in  a  which  gave  a  value  of  ' C pulp  p e r m e a b i l i t y to  i n d u s t r i a l  Equation one  a  a  p r e s s u r e  i n d u s t r i a l  how  2.1  tests  fibres  obtained  i l l u s t r a t e s may  nylon  2.1).  performance  slot  contained  commercial  were  Equation  that  conducted  shive-like  permeabilities  e x a m p l e  at  flow  those  fibres  excellent  T h i s  Moreover,  i s :  experimental  with  0.02  to  s c r e e n .  that  an  pulp  =  corresponds  screen  equation  comparable For  of  (2.1)  (2.2)  suspension,  value  is:  c  channel  screens. dilute  flow"  built  v e l o c i t i e s  equation  R - Q + QR  1  The  flow"  may  2.2).  conclude  prerequisite  for  screening. 4.  We  v a r i a b l e s length slot  measured  on  caused  width  and  the  effect  p e r m e a b i l i t y . an  increase  increased  in  of  Reduced  f i b r e , f i b r e  permeability,  flow  flow,  v e l o c i t y  as  and  slot  s t i f f n e s s  and  did  through  increased the  s l o t .  75  These  findings  are  e x p e r i e n c e , previously 5. using  and  p r o v i d e  consistent  with  q u a n t i t a t i v e  i n d u s t r i a l  i n f o r m a t i o n  not  available.  We  high  t o r i e s  qualitatively  observed speed  using  suggested  the  cine-films,  custom  that  motion  the  and  computer  screening  of  fibres  analysed  at the  programmes.  of  fibres  a  fibre  The  occurs  slot  entry trajec-  observations  by  two  distinct  mechanisms: i)  Wall  s l o t  Effect  come  plate. due If  from  This  to  a  layer  ii)  by  flow  layer  slot.  than  oriented width  a  order the  fibre  nearly  is to  turn  case  of  s t i f f  fibre f i b r e  fibres  fibres  than  the at  would  to  to  be  into  the  screen  fibre  the  screen  mainstream the  according  fibres  passing  adjacent  present  vary  pulp  As to  noted be  exit  a  90  layer  fibres,  forward  to  the  to  the  enters to  a  flow, plate.  stiffness  screened  fibre  for  than  in  screen fibre  pass  through  entire  fibre  the  the  slot, extent  the  must  passage  thickness  f i b r e s  smaller  degrees  and  above,  candidate  length,  much  turns  layer"  gradient  parallel  also  have  the  from  one  bifurcation.  Because  less  fewer  and  of  "exit  has  Effect in  a l l  gradients  shives  Entry  exit  thin  concentration  length,  another  the  a  concentration  and  the  Virtually  is  be  in  the  through  the  t y p i c a l l y  this  layer  must  p l a t e .  Since  length,  some  the must  that  s l o t .  it  flow  be s l o t  fibres In  rotate.  main  much  the  Before  may  contacts  carry the  76  downstream  edge  of  the  More  flexible  fibres  into  the  with  flow.  Thus  screen and  slot  plate  slot  can  much  bend less  pulp  fibres  than  shives,  and  are  returns  during chance more  since  to  the  while of  flow.  turning  and  pass  re-entering  the  main  likely  shives  main  are  to  pass  through  generally  a  stiffer  longer. Permeability  these  two  effects,  permeability.  components and  their  may  be  product  associated is  the  with  o v e r a l l  each  of  f i b r e  77  7.  Pulp  screening  immediate has a  RECOMMENDATIONS  and  for  an  area  substantial  elucidated  b a s i s  is  various future  FOR F U T U R E  of  research  benefits  aspects  work,  of  WORK  to  can  industry.  pulp  which  that  This  screening  could  take  provide  and  one  thesis provided  of  several  di rect ions:  1.  Higher  involves this  need  on to  require  2.  a  higher and  pulp  a  Fibre  to  of keep  within  the  at  it  clear  In  normal  screen  pulse.  A  screen  a v o i d e d  might  be  here.  Novel  slot  screen  have  Thus this  of  the  an  there thesis  slot  of  important  is, a with  c l e a r  a  study  This our  in  would  laboratory  fibres.  screen until  knowledge  to  to  screening  considered  c o n s i s t e n c i e s .  performance,  used  pulp  were  known  of  backflushing  affect  examined  findings higher  they  performance.  is  than  performance.  the  Stapling.  rotor-induced  how  consistency  screen  means  Industrial  consistencies  screening  channel  mulate  C o n s i s t e n c i e s .  supplement  pulp  flow  much  t h e s i s ;  effect  of  Pulp  operation,  they of and  increase plate  are  how  flushed  the  how  accu-  away  staples  stapling  screen  p r o f i l e s  fibres  form, can  capacity would  by  also  be and be  78  3.  Pulp  flows  Screen  within  designs.  In  pressure c e r t a i n  key  gather  in  order  interest.  this  was  the  as  to  of  could  simple  pulp extent  rotor  develop  a  better  proposed.  the  information  A  screen  thesis,  aspects  such  between  to  pressure  screen  measured, zone"  a  Modelling.  and  on a  a  variety  to  improve  plate. of  which  on  in It  this  w i l l  a  model, be  "screening  would  be  of  s h o u l d  the  industrial  the  screen  model  operation  mixing  of  improved  engineering  screen  screen  model  lead  To  of  understanding  be  pulp of  useful screens  g e n e r a l  79  NOMENCLATURE  screen  plate  open  area  c r o s s - s e c t i o n a 1 s c r e e n i n g zone overall  fibre  screening  area  of  the  annular  width  index  fibre concentration in the exit layer adjacent to the s l o t t e d p l a t e (e), in the (accept) flow through the slot (s), and i n the flow upstream of the s l o t (u) c o n c e n t r a t i o n of p u l p f i b r e s in the ( f . p ) , accept (a.p), and reject streams of a p u l p s c r e e n c o n c e n t r a t i o n of s h i v e s (f.sh), accept ( a . s h ) , and streams of a p u l p s c r e e n  feed (r.p)  in the feed reject (r.sh)  average c o n c e n t r a t i o n of pulp at a p l a n e located a d i s t a n c e " Z " from the entry to the annular screening zone outer zone  diameter  of  the  annular  debris reject efficiency modulus of e l a s t i c i t y h e i g h t of the a n n u l a r pressure screen moment  of  or  screening  zone  in  a  inertia  moment of inertia "n" fibres constants  of  number  fibres  of  screening  of  a  shive  proportionality in  a  shive  comprising  80  p e r m e a b i l i t y , c o n c e n t r a t i o n upstream flow. "entry  effect"  the r a t i o in the s l o t  permeability  permeability  of  pulp  permeability  of  shives  "wall  effect"  "screening quotient", performance  axial zone  flow  rate  reject rate in on mass f l o w ) slip  in  a  component  an  index  (f),  the  of  accept  annular  pressure  screen  (a),  and  screening  screen  (based  factor  fibre wall t h i c k n e s s , slotted plate average r a d i a l plate surface tip  component  fibres  permeability  pressure screen feed reject flow rate (r)  of f i b r e flow and  speed of  v e l o c i t y  a pulp  bulk v e l o c i t y aperture  or  at  screen  through  thickness  a  the  of  screen  rotor screen  p l a t e  c i r c u m f e r e n t i a l v e l o c i t y component within the annular screening zone of a pulp screen (t), a x i a l v e l o c i t y component (z), and the resultant of the preceding two v e l o c i t y components (u) l o c a l f i b r e slotted plate channel (x), slotted plate slot  width  v e l o c i t y p a r a l l e l to in the experimental and p e r p e n d i c u l a r to (y)  the test the  81  exit  layer  thickness  a x i a l distance from the annular s c r e e n i n g zone to interest  entry to some p o i n t  the of  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 perpendicular to the s l o t t e d plate and parallel to the flow in the experimental channel  82 BIBLIOGRAPHY  Al  A n d e r s s o n , 0 . , a n d W. B a r t o k . to F i b r e C l a s s i f i e r s . " Svensk 367-373.  "Application of Feed-back Papperstidning, 58 (1955),  Bl  B a d g e r , W . L . , and J . T . Banchero. Introduction to Chemical Engineering. New Y o r k : McGraw-Hill, 1955, pp. 618-636.  B2  Brereton, T. "Probability Screening and the E f f e c t s of Major Operating Variables." F i l t r a t i o n and S e p a r a t i o n , 12 ( 1 9 7 5 ) , 692-696.  B3  B r o w n i n g , B . H . , and J . R . P a r k e r . The C h a r a c t e r i z a t i o n of Offset Lint and the T e s t i n g of Offset Papers. Proc. of the Symposium on Mechanical Pulp, EOCEPA, 1970, pp. 67-81.  CI  Chollet, J . , M. D u f f y , and 0 . in Sulphite Pulp." Pulp and 60, No.4 (1959), T123-T128.  C2  Clarke-Pounder, I.J. 56th Annual Meeting,  Fl  F r i t h , M . D . , and D . J . F i s h e r . The E f f e c t of C o n s i s t e n c y on S c r e e n i n g of TMP a t Powell 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 . October, 1978.  HI  Hoglund, H . , E.Johnsson, and G. T i s t a d . "Shives in M e c h a n i c a l P u l p . P a r t 2 . An O p t i c a l Method of D e t e r m i n i n g Their Length D i s t r i b u t i o n . " Svensk Papperstidning, 79 ( 1 9 7 6 ) , 411-417.  H2  Hopkins, R . M . , R. M a c P h e r s o n , and L . J . M o r i n . "Analysis of the E f f e c t s of C e n t r i f u g a l Pulp Cleaners and P r e s s u r e Screens on Newsprint Runnabi1ity." Pulp and Paper Magazine of Canada, 6 3 , No.12 (1962), T563-T570.  H3  Humber, D . F . " P r a c t i c a l Screens." Unpublished Notes.  Kl  K e l l o g g , R . M . , and F . F . Wangaard. C e l l - W a l l Density of Wood." Wood (1969), 180-204.  Sepall. "Studies Paper Magazine of  Pipeline Screening. Proc. CPPA, 1970, pp. D116-D123.  Experiences with January 1981. "Variation and F i b r e ,  of Dirt Canada,  of  the  Several  in the 1, No.2  83  K2  K u b a t , J . , and B. Concentrations." 319-324.  S t e e n b e r g . " S c r e e n i n g a t Low Svensk P a p p e r s t i d n i n g , 58  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. Flocculation of P u l p Fibres. Proc. of the F u n d a m e n t a l R e s e a r c h Symposium, 1985, pp. 265-310.  LI  L a u r i l a , P., G. Smook, K. C u t s h a l l , and J . M a r d o n . " S h i v e s - how they a f f e c t paper machine r u n n a b i l i t y . " P u l p and P a p e r C a n a d a , 79, No.9 ( 1 9 7 8 ) , pp. 343-362.  L2  Lehman, D.F. " P u l p S c r e e n i n g . " i n Handbook of P u l p P a p e r T e c h n o l o g y " e d . K.W. B r i t t , 2nd e d . New Y o r k : Nostrand Reinhold, 1970.  L3  L i s s e n b u r g , R.C.D., J.O. H i n z e , and H. L e i j d e n s . "An Experimental I n v e s t i g a t i o n of a C o n s t r i c t i o n on Turbulent Pipe Flow." A p p l . S c i . Res. 31, (1975), pp. 343-362.  Ml  M a t h e w s , C.W. Deskbook I s s u e  M2  M a t h e w s , C.W. "Screening." No.79 ( 1 9 7 1 ) , pp. 76-83.  M3  M a c d o n a l d , R.G., e d . P u l p and P a p e r M a n u f a c t u r e . V o l . 1 , 2nd e d . , New Y o r k : M c G r a w - H i l l , 1969, pp.726-739.  M4  M a c M i l l a n , F.A., W.R. F a r r e l l , and F.G. B o o t h . " S h i v e s i n N e w s p r i n t : T h e i r D e t e c t i o n , Measurement and Effects on Paper Q u a l i t y . " P u l p and P a p e r M a g a z i n e of Canada, 66, No.7 ( 1 9 6 5 ) , T361-T369.  M5  Mason, S.G. "The M o t i o n o f F i b r e s i n F l o w i n g L i q u i d s . " 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 , 51, No.10 (1950), 93-100.  M6  M u l l i n s , E . J . , and T.S. M c K n i g h t , e d s . , C a n a d i a n Woods, T h e i r P r o p e r t i e s a n d U s e s . 3 r d e d . , U n i v . of T o r o n t o P r e s s , 1981, pp. 73-76.  Nl  N e l s o n , G.L. "The S c r e e n i n g Screening Performance." 133-134.  PI  P e r r y ' s Chemical "Screening."  "Screening." Chemical ( 1 9 7 1 ) , pp. 99-104. Chemical  Handbook,  The 8th  and Van  Engineering, Engineering,  Quotient: A Better Tappi, 64, No.5  Engineers'  Particle (1955),  6th  Index f o r (1981),  ed.  (1984).  84  P2  P a n s h i n , A . J . , C. De Zeenw C. , and H.P. Brown. Textbook o f Wood T e c h n o l o g y . V o l . 1 , 2nd e d . , New York: McGrawH i l l , 1964, pp. 175-176.  P3  Popov, E.P. I n t r o d u c t i o n to Mechanics Englewood H i l l s , N.J.: P r e n t i c e - H a l l , 1968.  P4  Piirainen, R., " O p t i c a l Method P r o v i d e s Quick and A c c u r a t e A n a l y s i s of F i b r e Length." P u l p and P a p e r , 59, No.11 ( 1 9 8 5 ) , pp.69-71.  Rl  R o b e r t s , E . J . , P. S t a v e n g e r , J . P . Bowersox, A.K. Walton, M. Mehta. "Solid/Solid Separations." Chemi c a l E n g i n e e r i n g , Deskbook I s s u e (1971) , pp. 89-98.  R2  R i e s e , J.W., H.L. S p i e g e l b e r g , and S.R. K e l l e n b e r g e r . "Mechanism o f S c r e e n i n g : D i l u t e S u s p e n s i o n s o f S t i f f F i b e r s a t Normal I n c i d e n c e . " T a p p i , 52, No.5 (1969), pp. 895-903.  51  S j o s t r o m , E. Wood C h e m i s t r y . 1981, pp. 9-12.  52  Seifert, P. S c r e e n i n g of P u l p . 1982 P r e p a r a t i o n C o u r s e N o t e s , 1982, pp. 19-27.  53  S c h l i c t i n g , H. B o u n d a r y L a y e r T h e o r y , t r a n s . J . K e s t i n , 4 t h e d . , New Y o r k : M c G r a w - H i l l , 1960, pp.600-604.  Tl  T A P P I . " S h i v e C o n t e n t of M e c h a n i c a l P u l p Fractionator)." T a p p i U s e f u l Method 242.  T2  Tam Doo, Wet Pulp (1982).  T3  TAPPI. " S c r e e n i n g S y m b o l s , T e r m i n o l o g y and E q u a t i o n s . " T a p p i S t a n d a r d I n f o r m a t i o n S h e e t 003-4 (1974).  T4  Thomas, A.S.W., and K.C. C o r n e l i u s . " I n v e s t i g a t i o n of a Laminar Boundary-Layer Suction Slot." AIAA J • , 20, No.6 ( 1 9 8 2 ) , pp. 790-796.  Wl  W a h r e n , D. "Fundamentals of S u s p e n s i o n S c r e e n i n g . " S v e n s k P a p p e r s t i d n i n g , 18 ( 1 9 7 9 ) , pp. 539-546.  P.A., and Fibres."  New  York:  of  Solids.  Academic P r e s s , TAPPI  Stock  (Sommerville  R.J. Kerekes. "The F l e x i b i l i t y of P u l p a n d P a p e r C a n a d a , 83, No.2  APPENDIX  EXPERIMENTAL  I  DAT  Table VII film # 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  fibre  type  dyed s h i v e s  High Speed C i n e - F i l m s suspending medium 1% k r a f t  •t  shives  water  pulp  feed  velocity (m/s) 0.3 1.1 0.9 6.5  accept v e l o c i t y (m/s) 1.0 2.1 0.6 2.6  6.9 II  1.5  7.6  It  II  0.5  lx.043 mm  nylon  7.4  5.1 5.5  II II  0.5  7.2 lx.043 3x.200 3x.043 lx.043  mm mm mm mm  nylon nylon nylon nylon  3x.043 mm n y l o n p!4.r28 k r a f t  water  7.2 7.9 6.9 7 .1  5.5 3.2 3.1 3.1 7.1 3.0  00 <Ti  Table VIII sst #  s l o t width (mm)  1 2 3 4  3.2  5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28  fibre  " II  0.25 " 0.5 II  1.00 II  " 0.5  accept v e l o c i t y (m/s)  permeability  noti  0.75 0.32 0.34 1.27  .052 60 80 150  6. 9 6. 8 6. 5 7 .6  0. 6 1. 9 2. 0 5. 1  0.37 0.52 0.63 0. 58  2  k r a f t pulp lx.043 mm n y l o n  280 140 350 80  7.6 7. 6 7. 6 7. 4  5. 1 4. 4 4. 4 5. 5  0.03 0.07 0.28 1.05  3 3 3  k r a f t shives k r a f t pulp 3x.400 mm n y l o n 3x.043 mm n y l o n  130 170 180 820  7. 4 7. 4 7. 2 7 .9  5 .5 5. 5 3. 2 3. 1  0.09 0.55 0.01 0.09  lx.043 mm n y l o n pl4.r28 k r a f t lx.043 mm n y l o n  900 1650 1430 1340  6. 9 7 .3 6. 8 6. 5  3. 1 3. 1 13. 2 3. 7  0. 50 0.40 0.91 0.57  lx.043  1260 2320 1910 1930  6. 5 6. 4 6. 2 6. 3  6. 6 3. 3 1. 9 5. 8  0.67 0.78 0.47 1.03  1750 1580 1350 1390  6.5 6. 5 6.5 6. 3  2.8 5. 9 1. 6 3. 2  0.78 1.09 0. 62 0.76  "  ii  velocity (m/s)  2. 6 2.0 1. 0 4. 3  II  "  _  feed  6. 9 6. 9 3. 5 1. 9  shives •I  " " 0.5  feed cone. (fibres/1) .064 .042 .082  kraft  M  " " 1. 5  type  P e r m e a b i l i t y Measurements  lx.043  mm  nylon  " kraft  shives II  mm " " " n  " II  "  nylon  notes; 1. Unless o t h e r w i s e i n d i c a t e d , f i b r e counts were made manually. 2. C o n c e n t r a t i o n measurement based on mass i n s t e a d o f a f i b r e count. Feed cone, u n i t s a r e g/1, not 3. Three h o l e s , a l i g n e d p e r p e n d i c u l a r t o the flow, were used i n s t e a d o f a s l o t . 4. The d i s t a n c e from the channel e n t r y t o the s l o t was equal t o 2 e q u i v a l e n t c h a n n e l d i a m e t e r s .  2 2 2  3  4  fibres/1.  Table VIII test  #  s l o t width (mm)  f i b r e type lx.043  mm " 3x.043 mm "  nylon  P e r m e a b i l i t y Measurements f e e d cone. (fibres/1)  feed v e l o c i t y (m/s)  1360 1170 1360 1320  6.4 6.3 6.5 6.4  3.2 3.4 3. 3 5.9  0.64 0.75 0.21 0.78  6.3 6.3 6.3 7.1  1.9 8.4 4.9 7. 1  0.03 1.00 0.56 0.86  2320 1110  7.0 6.4 6.4 6.4  3.0 2.0 1.3 . 3.4  0.67 0.47 0.28 0.74  1640  6.4 6.3 6.2 6.3  0.9 3.7 1.8 0.9  0.01 0.11 0.02 0.04  6.4 6.4 3.6 3.7  2.7 1.6 1.2 4.8  0.53 0.18 0.06 0.99  3.6 1.8 1.8 1.8  3.2 1. 1 2.2 4.0  0.53 0.02 0.74 1.04  6.5 6.2 6.3 6.2  3.4 1.9 0.9 0.9  0.84 0.52 0. 30 0.27  29 30 31 32  0.5 " " "  33 34 35 36  " "  " "  1320 1220  "  "  2000  37 38 39 40  " "  nylon  pl4.r28 k r a f t "  41 42 43  0.25  3x.043 mm  44  1.00  "  1.00 0.5  3x.043 mm "  nylon  1540  45  46 47 4  nylon  1350  8  49  50 51 52  "  53  "  lx.012  mm  rayon  1360  55 56  "  lx.020 mm  rayon  800  54  "  notes: 5. The d i s t a n c e from the channel  (continued)  1330  e n t r y t o the s l o t was  accept v e l o c i t y (m/s)  e q u a l t o 14 e q u i v a l e n t c h a n n e l  permeability  notes  diameters.  oo oo  Table VIII test #  fibre  s l o t width (mm)  57 58 59 60  0.5  lx.020 mm  II  pl0.rl4  61 62 63 64  II  II  II  pl4.r28  65 66 67 68  II  69 70 71 72  II  73 74 75 76  11  77 78 79 80  II  II  "  II  II  II  type rayon kraft  kraft  II  f e e d cone. (fibres/1) 800 II  1010 II  II  kraft  II  "  P e r m e a b i l i t y Measurements  830 II II  pulp  63900 II  II  II  II  II  II  II  II  "  132400  CTMP  II  II  .043  II  mm d i a . n y l o n II  It II II  II  40600  kraft  pulp  " .074 II  II  CTMP " "  .055 n  M  feed  velocity (m/s)  (continued) accept v e l o c i t y (m/s)  permeability  notes  6.3 6.4 6.4 6.3  2.2 3.4 3.4 1.9  0. 0. 0. 0.  57 81 66 32  6.3 6.4 6.3 6.3  0.9 3.4 1.9 0.9  0. 0. 0. 0.  11 67 38 18  6.4 6.4 6.4 6.4  3 .1 3 .1 2.0 0.9  0. 0. 0. 0.  61 42 45 25  6 6 6,7 6  6.4 6.4 6.4 6.4  3.1 1.9 0.9 3.2  0. 58 0. 55 0. 39 0.47  6,7 6,8 6 6,9  6.4 6.4 6.4 6.4  1.9 0.9 2.6 1.8  0. 0. 0. 0.  38 26 31 14  6 6 2,8 2  6.4 6.3 6.3 6.3  0.9 2.9 1.8 0.9  0. 0. 0. 0.  09 65 48 35  2 2,9 2, 10 2  notes: 2. C o n c e n t r a t i o n measurement based on mass i n s t e a d o f a f i b r e count. Feed cone, u n i t s a r e g / l , n o t f i b r e s / 1 . 6. F i b r e count made u s i n g t h e K a j a a n i FS-100. P e r m e a b i l i t y l i s t e d as a f u n c t i o n o f f i b r e l e n g t h below. 7. A c c e p t l i n e p u l s e d a t t h e r a t e o f 8 p u l s e s p e r minute d u r i n g t h i s t e s t . 8. Accept l i n e p u l s e d a t the r a t e o f 10 p u l s e s p e r minute d u r i n g t h i s t r i a l . 9. A c c e p t l i n e p u l s e d a t t h e r a t e o f 17 p u l s e s p e r minute d u r i n g t h i s t r i a l . 10. A c c e p t l i n e p u l s e d a t the r a t e oF 6 p u l s e s p e r minute d u r i n g t h i s t r i a l .  Table f i b r e length (mm)  IX  f i b r e cone. (fibres/1)  T e s t s 65-68  Fibre Length/Permeability  Data  permeability ( t e s t 65)  permeability ( t e s t 66)  permeability ( t e s t 67)  permeability ( t e s t 68)  0.00-0.20 0.20-0.41 0.41-0.61 0.61-0.82  4100 5900 8000 4300  0. 79 0.84 0.82 0.74  0.73 0.76 0.67 0.58  0.78 0.79 0.69 0.63  0.78 0.59 0.45 0.30  0.82-1.02 1.02-1.23 1.23-1.44 1.44-1.64  3700 3300 3100 3100  0.73 0.68 0.63 0.57  0.48 0.43 0.40 0.38  0.57 0.48 0.46 0.39  0.25 0.21 0.18 0. 16  1.64-1.85 1.85-2.05 2.05-2.26 2.26-2.47  2800 2800 2700 2500  0. 54 0.54 0.51 0.50  0. 34 0.31 0.29 0.25  0.36 0.33 0.29 0.25  0.11 0.09 0.07 0.06  2.47-2.67 2.67-2.88 2.88-3.08 3.08-3.29  2400 2200 2100 1800  0.46 0.46 0.45 0.43  0.21 0.19 0.18 0.17  0.21 0.21 0.20 0.19  0.06 0.06 0.06 0.06  3.29-3.50 3.50-3.70 3.70-3.91 3.91-4. U  1700 1400 1300 1100  0.43 0.40 0. 38 0.33  0.17 0.18 0.18 0.17  0.19 0.17 0.16 0.14  0.05 0.04 0.03 0.03  T a b l e IX f i b r e length (mm)  T e s t s 65-68  f i b r e cone. (fibres/1)  Fibre Length/Permeability  Data  (continued)  permeability ( t e s t 65)  permeability ( t e s t 66)  permeability ( t e s t 67)  permeability ( t e s t 68)  4.11-4. 32 4.32-4. 52 4.52-4. 73 4.73-4. 94  1000 800 700 500  0. 30 0.25 0.24 0.25  0.16 0.13 0.11 0.08  0.13 0.12 0.12 0.13  0.03 0.03 0.03 0.02  4.94-5 .14 5.14-5. 35 5.35-5. 55 5.55-5. 76  400 200 200 100  0.29 0. 36 0.35 0. 32  0.09 0.10 0.09 0.08  0.12 0.11 0.10 0.08  0.01 0.01 0.02 0.02  5.76-5. 97 5.97-6. 17 6.17-6. 38 6.38-6. 58  100 100 50 30  0.29 0.23 0.21 0.16  0.08 0.08 0.11 0.22  0.08 0.09 0.06 0.06  0.01 0.00 0.00 0.00  6.58-6. 79 6.79-7. 00 7.00 +  20 10 300  0.20 0.00 0.21  0.14 0.00 0.00  0.08 0.00 0.00  0.00 0.00 0.00  k r a f t pulp 0.5 6.4 1.8 0  k r a f t pulp 0.5 6.4 2.0 8  k r a f t pulp 0.5 6.4 0.9 0  T r i a l conditions: f i b r e type k r a f t pulp s l o t w i d t h (mm) 0.5 f e e d v e l o c i t y (m/s) 6.4 a c c e p t v e l o c i t y (m/s) 3.1 p u l s a t i o n r a t e ( p u l s e s p e r min.. ) 0  Table X f i b r e length (mm)  T e s t s 69-71  f i b r e cone. (fibres/1)  Fibre Length/Permeability  Data  permeability ( t e s t 69)  permeability ( t e s t 70)  permeability ( t e s t 71)  0.00-0.20 0.20-0.41 0.41-0.61 0.61-0.82  14400 22400 26900 16100  0.65 0.70 0.67 0. 57  0.75 0.78 0.71 0.51  0.79 0.63 0.44 0.32  0.82-1.02 1.02-1.23 1.23-1.44 1.44-1.64  12500 9500 7300 5500  0.53 0.50 0.50 0.48  0.45 0.40 0.38 0.33  0.28 0.23 0.18 0.14  1.64-1.85 1.85-2.05 2.05-2.26 2.26-2.47  4100 3300 2400 1900  0.46 0.40 0.35 0.31  0.29 0.23 0.20 0.17  0.12 0.09 0.08 0.06  2.47-2.67 2.67-2.88 2.88-3.08 3.08-3.29  1500 1100 900 700  0. 30 0.32 0.32 0.32  0.17 0.17 0.15 0.11  0.06 0.05 0.05 0.03  3.29-3.50 3.50-3.70 3.70-3.91 3.91-4.11  600 400 300 200  0.31 0.30 0.31 0.36  0.11 0.12 0.11 0.11  0.02 0.01 0.01 0.03  Table  X  f i b r e length (mm)  Tests  69-71  Fibre Length/Permeability  Data  (continued)  f i b r e cone. (fibres/1)  permeability ( t e s t 69)  permeabilitry ( t e s t 70)  permeability ( t e s t 71)  4.11-4.32 4.32-4.52 4.52-4.73 4.73-4.94  100 80 80 60  0.43 0.48 0.42 0.26  0.15 0.19 0.15 0.12  0.06 0.07 0.04 0.00  4.94-5.14 5.14-5.35 5.35-5.55 5.55-5.76  50 30 30 10  0.17 0.00 0.00 0.28  0.07 0.00 0.00 0.00  0.00 0.00 0.00 0.00  5.76-5.97 5.97-6.17 6.17-6.38 6.38-6.58  10 10 0 0  0.83 1.79  0.00 0.00  0.00 0.00  6.58-6.79 6.79-7.00 7.00 +  0 0 10  T r i a l conditions: f i b r e type s l o t w i d t h (mm) feed v e l o c i t y (m/s) accept v e l o c i t y (m/s) p u l s a t i o n r a t e ( p u l s e s p e r min.)  -  -  -  -  -  2.61  0.00  -  0.00  CTMP 0.5 6.4 3.1 8  CTMP 0.5 6.4 1.9 10  CTMP 0.5 6.4 0.9 0  -  -  T a b l e XI f i b r e length (mm)  T e s t s 72-74  f i b r e cone. (fibres/1)  Fibre Length/Permeability  Data  permeability ( t e s t 72)  permeability ( t e s t 73)  permeability ( t e s t 74)  0.00-0.20 0.20-0.41 0.41-0.61 0.61-0.82  5700 3800 3900 2000  0.36 0.64 0.79 0.65  0.37 0.70 0.77 0.78  0. 35 0.58 0.53 0.49  0.82-1.02 1.02-1.23 1.23-1.44 1.44-1.64  2800 3000 2700 2900  0.62 0. 59 0.56 0.47  0.55 0.45 0.39 0.24  0.32 0.25 0.20 0.13  1.64-1.85 1.85-2.05 2.05-2.26 2.26-2.47  2800 2400 900 300  0.42 0.41 0. 38 0.42  0.17 0.15 0.17 0.28  0.09 0.09 0.06 0.10  2.47-2.67 2.67-2.88 2.88-3.08 3.08-3.29  200 300 500 1300  0.39 0.21 0.17 0.15  0.28 0.07 0.04 0.03  0.14 0.08 0.04 0.01  3.29-3.50 3.50-3.70 3.70-3.91 3.91-4.11  1900 1700 1000 200  0.15 0.16 0.17 0.25  0.02 0.02 0.02 0.03  0.01 0.01 0.02 0.06  T a b l e XI f i b r e length (mm)  T e s t s 72-74  Fibre Length/Permeability  Data  (continued)  f i b r e cone. (fibres/1)  permeability ( t e s t 72)  permeability ( t e s t 73)  permeability ( t e s t 74)  4.11-4.32 4.32-4.52 4.52-4.73 4.73-4.94  100 50 30 0  0.24 0.25 0.24  0.04 0.06 0.06  0.06 0.06 0.06  4.94-5.14 5.14-5.35 5.35-5.55 5.55-5.76  0 0 0 < 10  0.74  0.00  0.00  5.76-5.97 5.97-6.17 6.17-6.38 6.38-6.58  < < < <  10 10 10 10  0.25 0.00 0.00 0.00  0.00 0.00 0.00 0.72  0.00 0.00 0.00 0.00  6.58-6.79 6.79-7.00 7.00 +  < 10 < 10 60  0.00 0.00 0.00  0.90 0.84 0.00  0.00 0.00 0.00  nylon 0.5 6.4 3.2 17  nylon 0.5 6.4 1.9 0  nylon 0.5 6.4 0.9 0  T r i a l conditions! f i b r e type s l o t w i d t h (mm) feed v e l o c i t y (m/s) a c c e p t v e l o c i t y (m/s) p u l s a t i o n r a t e ( p u l s e s p e r min.)  -  -  -  -  -  -  -  APPENDIX  COMPUTER  II  PROGRAMMES  97  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 ' T h i s program r e c o r d s and d i s p l a y s the p o s i t i o n , o r i e n t a t i o n and 65 ' c u r v a t u r e o f f i b r e s i n a s e r i e s of f i l m frames. The data i s i n s t a l l e d 70 ' i n a f i l e t h a t bears the f i l m number (e.g. F I L r t . l ) . Other programmes 80 ' i n t e r p r e t t h e 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 g i v e n p o s i t i o n or o r i e n t a t i o n . 100 ' 110 ' Variables: 120 ' FRN frame number 130 * FRA frame counter 140 * NFRA FRA p l u s one 150 ' FRAM FRN f o r 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 i n use; =0 otherwise 190 * CX1,CY1,CX2,CY2 c a l i b r a t i o n coordinates (slot corners) 200 ' TRX,TRY,LRX,LRY frame image c o o r d i n a t e s 210 ' TLX, TLY ,LLX, LLY 220 ' TOP,BOT,RIT,LEFT l e n g t h of frame s i d e s 230 ' PX1,PY1,PX2,PY2 p l a t e end c o o r d i n a t e s 240 ' MSX1,MSY1,MSX2,MSY2 m i d - s l o t corner c o o r d i n a t e s 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 a r r a y s o f f i b r e end, middle and end c o o r d i n a t e s 300 * DF$ data s t o r a g e f i l e 310 ' DAT$ date of a n a l y s i s 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 l e n g t h ( i . e . s l o t width) 350 ' Q,R multipurpose counters 360 • 370 CLS 380 OPEN " c o m l : 9 6 0 0 , n , 8 , l , r s , c s , d s , c d " AS #1 390 PRINT f1,CHR$ (32),CHR$(66) 400 ' 410 ' S k e t c h a s c r e e n 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 l o c a t i n g the f o u r c o r n e r s o f the frame image w i t h t h e b l u e b u t t o n - f o l l o w i n g 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  98  630 640 650 660 670 680 690 700 * 710 ' 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 ' 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 1200 1210 1220 1230 1240 1250  CIRCLE (80,172),15 INPUT #l,LLX,LLY,Z IF Z O l THEN 640 CIRCLE (80,172),15,0 CIRCLE (80,27),15 INPUT #1,TLX,TLY,Z IF Z O l THEN 680 Now check t o s e e i f opposing s i d e s have a p p r o x i m a t e l y equal l e n g t h s . TOP=SQR((TRX—TLX)"2 +(TRY-TLY)*2) BOT=SQR((LRX-LLX)"2+(LRY-LLY)*2) RIT=SQR((TRX-LRX)"2+(TRY-LRY)~2) LEFT=SQR((TLX-LLX)"2+(TLY-LLY)*2) PRINT "TOP=",TOP,"BOT=",BOT PRINT "RIT=",RIT,™LEFT=",LEFT PRINT "TRX=",TRX,"TRY=",TRY PRINT "LRX=",LRX,"LRY=",LRY PRINT "LLX=",LLX,"LLY=",LLY PRINT "TLX=",TLX,"TLY=",TLY CK1=ABS(RIT-LEFT)/RIT CK2=ABS(T0P-B0T)/T0P IF CK2>CK1, THEN CK1=CK2 IF CK1>.05, GOTO 540 PRINT "Alignment c o r r e c t to",CK1*100,"%" PRINT " L o c a t e o t h e r key p o i n t s on the s c r e e n p l a t e . " CIRCLE (80,150),15 INPUT #1,PX1,PY1,Z CIRCLE (80,150) ,15,0 CIRCLE (310,150),15 INPUT #1,CX1,CY1,Z IF Z O l THEN 930 CIRCLE (310,150) ,15,0 CIRCLE (330,150),15 INPUT #1,CX2,CY2,Z IF Z O l THEN 970 CIRCLE (330,150),15,0 CIRCLE (559,150),15 INPUT #1,PX2,PY2,Z IF Z O l THEN 1010 CIRCLE (559,150) ,15,0 CIRCLE (300,160),15 INPUT #1,MSX1,MSY1,Z IF Z O l THEN 1050 CIRCLE (300,160),15,0 CIRCLE (310,160),15 INPUT #1,MSX2,MSY2,Z IF Z O l THEN 1090 CIRCLE (310,160),15,0 CIRCLE (330,160),15 INPUT tl,MSX3,MSY3,Z IF Z O l THEN 1130 CIRCLE (330,160),15,0 CIRCLE (340,160),15 INPUT #1,MSX4,MSY4,Z IF Z O l THEN 1170 CIRCLE (340,160),15,0 CIRCLE (300,172),15 INPUT I1,AX1,AY1,Z IF Z O l THEN 1210 CIRCLE (300,1721,15,0 CIRCLE (340,172),15 INPUT #1,AX2,AY2,Z  99  L260 IF Z O l THEN 1250 1270 CIRCLE (340,172),15,0 1280 ' 1290 ' P r e l i m i n a r y i n f o r m a t i o n : 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$(AY2) 1500 PUT #2,5 1505 CAL=SQR((PX2—PX1)"2+(PY2-PY1)~2)/10 1510 • 1520 ' Draw the image 1530 SCREEN 2 1540 LINE (0,0)-(639,199),0,BF 1550 LINE (TLX*.101 + 26.62,225—TLY*•0403) — (TRX*.101 + 26.62,225—TLY*. 0403) 1560 LINE -(LRX*. 101 + 26.62,225—LRY*.0403) 1570 LINE -(LLX*.101+26.62,225—LLY*.0403) 1580 LINE —(TLX*.101+26.62,225—TLY *.0403) 1590 LINE (PX1*.101+26.62,225-PY1*.0403)- (CXI*.101 + 26.62,225-CY1*.0403) 1600 LINE (CX2*. 101 + 26.62,225-CY2*.0 403)-(PX2 *.101 + 26.62,225-PY2*.0403) 1610 LINE (CXI*.101+26.62,225-CY1*.0403)- (MSX2*.101 + 26.62,225-MSY2*.0403) 1620 LINE -(MSX1*.101+26.62,225-MSY1*.0403) 1630 LINE -(AX1*.101+26.62,225-AYl*.0403) 1640 LINE (AX2 *.101 + 26.62,225—AY2 *.0403)- (MSX4 *.101 + 26.62,225-MSY4 * . 0 403 ) 1650 LINE - (MSX3*-101 + 26.62,225-MSY3*.0403) 1660 LINE -(CX2*.101+26.62,225-CY2*.0403) 1670 LPRINT " F i l m No.",DF$,"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 ' D e f i n e each f i b r e by l o c a t i n g the end, middle and end of each w i t h the b l ue b u t t o n . 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 ' R e d e f i n e the p l a t e c o o r d i n a t e s f o r 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  100  1930 CIRCLE (CXI *.101+ 26.62,225-CY1*.0403) ,15,0 1940 CX1=CX1N: CY1=CY1N 2000 ' 2010 ' D e f i n e t h e f i b r e s that appeared i n the p r e v i o u s 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 * I f Z=2 ( b l a c k button) then the f i b r e has d i s a p p e a r e d . 2130 IF Z<>2 GOTO 2170 2140 AX(NFRA,FIB)=0: AY(NFRA,FIB)=0 2150 GOTO 2750 2160 ' I f Z=4 ( r e d button) then t h e s e s s i o n has c o n c l u d e d 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 ' D e f i n e t h e f i b r e s t h a t have appeared f o r 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 ' I f Z=2 ( b l a c k button) then t h e r e a r e 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 ' I f Z=4 ( r e d button) then t h e s e s s i o n has c o n c l u d e d 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  101  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 2740 ' S t o r e t h e l o c a t i o n s of a f i b r e that has d i s a p p e a r e d . 2750 FOR FRA=1 TO FRA 2770 * T r a n s f o r m c o o r d i n a t e s : 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$(FCNT (FIB)) 2950 POT #2 2960 LINE (AX(FRA,FIB)*.101 + 26.62,2 25-AY(FRA,FIB)*.0403)-(BX(FRA,FIB)*. 101 + 26. 62,2 2 5-BY(FRA,FIB)*.0403),0 2970 LINE (BX(FRA,FIB)*.101+26.62,2 25-BY(FRA,FIB)*.0403)-(CX(FRA,FIB)*.101+26. 62,22 5-CY(FRA,FIB)*.0403),0 2980 NEXT FRA 2981 LPRINT " " 2990 CHEK(FIB)=0 3000 FOR Q=l TO FRA 3010 AX(Q,FIB)=0: AY(Q,FIB)=0: BX(Q,FIB)=0: BY(Q,FIB)=0: CX(Q,FIB)=8: CY(Q,FIB )=0 3020 NEXT Q 3030 GOTO 2350 3040 ' 3050 ' T h i s s u b r o u t i n e t r a n s f o r m s pad c o o r d i n a t e s to frame c o o r d i n a t e s . Slot w i d t h i s taken as t h e u n i t o f d i s t a n c e . 3060 TX=(TX-CX1A(FRA,FIB))/CAL 3070 TY=(TY-CY1A(FRA,FIB))/CAL 3080 RAD=SQR(TX"2+TY"2) 3085 IF TX<0 THEN RAD=-RAD 3090 ANG1=ATN(TY/TX) 3100 ANG2=ATN((PY1-CY1)/(PX1-CX1)) 3110 TX=RA0*C0S(ANG1-ANG2) 3120 TY=RAD*SIN(ANG1-ANG2) 3130 RETORN 3140 * 3150 ' We c o n c l u d e t h e s e s s i o n by p r i n t i n g the f i n a l r e c o r d and frame number. 3160 LPRINT "End o f S e s s i o n f o r F i l m Number";DF$ 3170 LPRINT " F i n a l Frame Number =";FRN 3180 LPRINT " F i n a l Record Number =";L0C(2) 3190 END 1  102  10 • 20 * Displaying/Listing Fibre Trajectories 30 ' Robert Gooding 40 * May 1984 50 ' 60 ' G i v e n 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 r e c o r d numbers) t h i s programme draws the f i b r e p o s i t i o n s o f 80 ' those sequences, or p r i n t s the c o o r d i n a t e s of the p o i n t s that d e f i n e 90 ' the f i b r e p o s i t i o n s . 100 ' 110 • 120 ' Variables: 130 ' DFS data s t o r a g e f i l e 140 ' NAM$ analyst 150 DAT$ date of a n a l y s i s 160 ' TRX,TRY,LRX,LRY frame image c o r n e r c o o r d i n a t e s 170 * TLX,TLY,LLX,LLY 180 ' PX1,PY1,PX2,PY2 p l a t e end c o o r d i n a t e s 190 ' MSX1,MSY1,MSX2,MSY2 mid-slot coordinates 200 * MSX3,MSY3,MSX4,MSY4 210 ' SEQ number of sequences f o r d i s p l a y 220 ' RNM a r r a y of s t a r t i n g r e c o r d numbers 230 * RN r e c o r d 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 FCNTM f i b r e sequence counter f o r p r e v i o u s r e c o r d 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 p r e l i m i n a r y 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$) 520 ' 530 ' I n t e r o g a t e o p e r a t o r 540 INPUT "Number o f f i b r e sequences";SEQ 550 IF SEQ=0 GOTO 1570 560 FOR U=l TO SEQ 570 INPUT "Give a sequence r e c o r d number";RNM(U) 580 NEXT U 1  1  103  590 INPUT " d i s p l a y , l i s s t ot c e e l ";IND$ 600 IF IND$="display" GOTO 650 610 IF I N D S = " l i s s t " GOTO 650 611 IF IND$="reel" GOTO 650 620 GOTO 590 630 ' 640 ' C o n s i d e r 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$) 690 IF RN=6 GOTO 780 700 ' 710 ' S e a r c h f o r t h e s t a r t of the f i b r e sequence and load the d a t a . 720 RN=RN-1 730 GET *2,RN 740 FCNTM=CVS(H$) 750 IF FCNT(U)=FCNTM GOTO 720 760 RN=RN+1 770 GET #2,RN 780 FRAM=CVS(G$) 800 ' 810 ' Load d a t a f o r each sequence 820 FCNTM=FCNT(U) 830 FRA=1 840 AX(FRA,0)=CVS(AS):AY(FRA,U)=CVS (B$):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 I N D $ = " l i s s t " GOTO 1500 920 * 930 * Draw t h e s c r e e n 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 ' T r a n s f o r m c o o r d i n a t e s . 1110 CAL=SQR((PX2-PX1)'2+(PY2-PY1)*2)/10 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) 1200 S=BY(Q,0)  104  GOSUB 1370 L210 L220 BX(Q,U)=R BY (Q,U)=S L230 R=CX (Q,0) 1240 S=CY(Q,U) 1250 1260 GOSUB 1370 1270 CX (Q,U)=R 1280 CY(Q,U)=S LINE (AX(Q,U) ,AY(Q,U))-(BX(Q,U),BY <Q,U) ) 1290 LINE (BX(Q,U),BY(Q,U))-(CX(Q,U),CY(Q,U)) 1300 NEXT Q 1310 PRINT"Stact of f i b r e sequence";FCNT(U);" at r e c o r d number";RN;"frame numbe 1311 r";FRAM 1320 NEXT U 1322 IF IND$<>"reel" GOTO 540 RNM(1)=RN+FRA 1323 1324 INPUT ZX$ 1325 GOTO 650 1340 ' 1350 * T h i s s u b r o u t i n e t r a n s f o r m s frame c o o r d i n a t e s to pad c o o r d i n a t e s 1360 ' and then t o s c r e e n c o o r d i n a t e s . 1370 R=R*CAL+CX1 1380 S=S*CAL+CY1 RAD=SQR(R"2+S"2) 1390 1400 IF R<0 THEN RAD=-RAD 1410 ANG1=ATN(S/R) ANG2=ATN((PY1-CY1)/(PX1-CX1)) 1420 R=RAD*C0S(ANG1+ANG2) 1430 S=RAD*SIN(ANG1+ANG2) 1440 R=R*.101+26.62 1450 1460 S=225-S*.0403 1470 RETURN 1480 ' 1490 ' L i s t the c o o r d i n a t e s o f the p o i n t s that d e f i n e t h e 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 PRINT "Frarae";Q;"Fibre";FCNT(U) 1520 PRINT "AX=";AX(Q,U);"AY=";AY(Q,U);"BX="; BX(Q,U);"BY=";BY(Q,U);"CX=" ;cx(Q, 1530 0);"CY =";CY(Q,U) 1540 NEXT Q 1550 NEXT U 1560 GOTO 540 1570 END  105  10 • 20 ' DIGINT.Al 30 * Interpreting D i g i t i z e d Films 40 * *** T h i s programme o n l y c o n s i d e r s f i b r e s that appear i n any 15th frame *** 50 ' Robert Gooding 60 ' June 1984 70 * 80 ' T h i s programme takes d a t a s t o r e d i n f i l e "Film.A" and determines t h e 90 ' d i s t r i b u t i o n o f f i b r e c e n t r e d i s t a n c e s (with r e s p e c t t o the w a l l ) a t 100 ' a p l a n e 1.75 mm b e f o r e the l e a d i n g edge of t h e s l o t . 110 • 120 * V a r i a b l e s : 130 ' AS,B$,C$,D$ r e c o r d l o c a t i o n s of f i b r e p o s i t i o n and c o u n t e r s 140 * ES,F$,G$,HS 150 ' AX,AY,CX,CY a r r a y s of f i b r e end p o i n t s 160 ' N frame c o u n t e r ( w i t h i n 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 l o c a t i o n o f f i b r e m i d - p o i n t ahead o f t h e 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 I F (((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 F i t a s p l i n e t o the f i b r e p o s i t i o n s and determine t h e l o c a t i o n o f t h e 420 ' m i d p o i n t ahead o f 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 I F 1=1 GOTO 540 530 1=1-1 540 Y L = Y ( I ) + Q ( I ) * ( - . 7 5 6 3 - X ( I ) ) + R ( I ) * ( - . 7 5 6 3 - X ( I ) ) " 2 + S ( I ) * ( - . 7 5 6 3 - X ( I ) ) " 3 550 IJ=6 560 I F YL<3.7813 THEN IJ=5 570 I F 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  106  610 615 616 620 630 640 650 660 ' 670 ' 680 690 700 710 720 725 727 730 740 ' 750 ' 760 ' 770 ' 780 " 790 ' 800 810 ' 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 t h e d i s t r i b u t i o n of f i b r e c e n t r e s . 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  T h i s s u b r o u t i n e f i t s a c u b i c 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 t o an a r r a y o f N c o o r d i n a t e p a i r s . Input: coordinate vectors X,Y number o f c o o r d i n a t e p o i n t s N Output: 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 Q,R,S Variables: counters I,IP,IPP m a t r i x elements DD,A4,B4,AS BS,CS,DS,HS  1  Ose d i v i d e d d i f f e r e n c e s t o f i n d A4 and B4 NM=N-1 FOR 1=1 TO 3 IP=I+1 DD(1,I) = ( Y ( I P ) - Y ( I ) ) / ( X ( I P ) - 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 ( I P ) - Y ( I ) ) / ( X ( I P ) - 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  107  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  ' F i n d t h e c o e f f i c i e n t s o f the t r i d i a g o n a l e q u a t i o n s . 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  i  TDMA  ' 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 o f m a t r i x rows N Output: s o l u t i o n vector R Variables P,Q,DEN matrix v a r i a b l e s 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 T h i s s u b r o u t i n e i n s t r u c t s t h e program t o o v e r l o o k c e r t a i n IF (LOC(l)>69) AND ( L O C Q X 7 2 ) 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  sequences.  108  1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100  IF (L0C(1)>1150) AND (LOC(l)<1166) IF (LOC(l)>1171) AND ( L O C U K 1 1 7 4 ) IF LOC(l)=1218 GOTO 340 IF (LOC(l)>1334) AND ( L O C U X 1 3 4 2 ) IF LOC(l)=1361 GOTO 340 IF <L0C(1)>1425) AND (LOC(l)<1428) IF LOC(l)=1468 GOTO 340 IF (LOC(l)>1486) AND (LOC(l)<1492) IF (LOC(l)>1511) AND (LOC(l)<1566) IF LOC(l)=1655 GOTO 340 IF (LOC(l)>1912) AND ( L O C U X 1 9 9 4 ) IF LOC(1)=2059 GOTO 340 IF (LOC(l)>2112) AND (LOC(l)<2119) IF (LOC(1)>2198) AND (LOC(l)<2202) IF LOC(l)=2236 GOTO 340 IF (LOC(l)>2342) AND (LOC(l)<2345) IF LOC(l)=2488 GOTO 340 IF (LOC(1)>2612) AND (LOC(l)<2618) IF (LOC(l)>2652) AND (LOC(l)<2655) IF LOC(l)=2745 GOTO 340 IF (LOC(l)>2800) AND (L0C(1X2823) IF (LOC(l)>2837) AND (LOC(l)<2840) IF (LOC(l)>2927) AND ( L O C Q X 2 9 3 0 ) IF (LOC(1)>3008) AND (LOC(1X3014) IF LOC(l)=3125 GOTO 340 IF (LOC(l)>3345) AND (L0C(1)<3349) IF (LOC(l)>3367) AND (L0C(1X3372) GOTO 370  GOTO 340 GOTO 340 GOTO 340 GOTO 340 GOTO 340 GOTO 340 GOTO 340 GOTO 340 GOTO 340 GOTO 340 GOTO 340 GOTO 340 GOTO GOTO GOTO GOTO  340 340 340 340  GOTO 340 GOTO 340  109  ia • 15 ' DIGINT.A3 20 ' I n t e r p r e t i n g D i g i t i z e d Films 30 ' Robert Gooding 40 ' September 1984 50 ' 60 ' T h i s programme takes sequences o l N f i b r e p o s i t i o n s from f i l e "Film.A" 70 ' and d e t e r m i n e s the d i s t r i b u t i o n o f : 80 ' - f i b r e a n g l e (ranging from - p i / 2 t o p i / 2 ) 90 ' - a x i a l f i b r e v e l o c i t y (m/s) 100 ' - t r a n s v e r s e 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 a r e e v a l u a t e d a t a d i s t a n c e upstream o f t h e s l o t 130 ' c o r r e s p o n d i n g t o the d i s t a n c e between s l o t s i n an i n d u s t r i a l s c r e e n 140 ' (assuming 12% open area) 150 ' 160 ' Variables: 170 ' A$,B$,C$,D$ r e c o r d l o c a t i o n s of f i b r e p o s i t i o n s and c o u n t e r s 180 ' E$,F$,G$,HS 190 * AX,AY,CX,CY v e c t o r s of f i b r e end p o i n t s 200 ' N frame c o u n t e r ( w i t h i n a sequence) 210 ' FRAM frame number 220 ' FCNT sequence number 230 ' X,Y vectors of f i b r e mid-point coordinates 240 ' ANG vector o f f i b r e angles 250 ' VX,VY v e c t o r s of f i b r e a x i a l and t r a n s v e r s e v e l o c i t i e s 260 ' ROT vector o f f i b r e r o t a t i o n a l v e l o c i t y ( i n plane) 270 ' SOLN v e c t o r o f X,Y,ANG,VX,VY,ROT f o r g i v e n FCNT 280 ' M v e c t o r o f zone c o u n t e r s 285 ' RES,RESQ a r r a y s o f zone c o u n t e r s 286 ' MANG a r r a y o f zone/angle c o u n t e r s 290 ' 300 CLEAR 310 CLS 320 OPEN " c : f i l m . a " AS #1 LEN=32 330 FIELD #1,4 AS A$,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 a n g l e and p o s i t i o n f o r each appearance i n t h e 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  550 560 570 580 590 600 610 620 * 630 640 650 660 665 670 ' 680 ' 690 700 710 720 730 740 750 770  FOR 1=2 TO N IM=I-1 VX(IM)=(X(I)-X(IM))/TIME VY(IM)=(Y(I)-Y(IM))/TIME ROT(IM)=(ANG(I)-ANG(IM)J/TIME NEXT I  1  )  780 790 820 825 830 840 850 855 856 860 870 880 890 900 910 920 930 940 950 960 965 970 980 990 1000 1010 1020 1022 1024 1026 1030 1040 1050 1060 1065 1067 1070 1080 1090  ' '  ' '  * '  Locate the i n t e r v a l of i n t e r e s t FOR 1=1 TO N IM=I-1 IF X(I)>-1.75 GOTO 690 NEXT I GOTO 1030 I n t e r p o l a t e and c o l l e c t d a t a f o r each w a l l zone IF 1=1 GOTO 1030 • FRAC=(-1.75-X(IM))/(X(I)-X(IM)) SOLN(1)=Y(IM)+(Y(I)-Y(IM))*FRAC SOLN(2)=ANG(IM)+(ANG(I)-ANG(IM))*FRAC SOLN(3)=VX(IM) SOLN(4)=VY(IM) SOLN(5)=ROT(IM) LPRINT USING "###I######.tFCNT,SOLN(1),SOLN(2),SOLN(3),SOLN(4),SOLN(5 A n a l y z e t h e d a t a i n each o f t h e f i v e "wall d i s t a n c e ' I F SOLN(l)<8.75 THEN J=5 ELSE J=6 IF SOLN(1)<3 THEN J=4 IF S O L N Q X 1 . 5 THEN J = 3 IF S O L N Q X . 7 5 THEN J=2 I F S O L N U X . 3 7 5 THEN J = l L=FIX((SOLN(2)+1.5708)*2.5465)+1 MANG(J,L)=MANG(J,L)+1 M(J)=M(J)+1 FOR K=l TO 5 RES(J,K)=RES (J,K)+SOLN(K) RESQ (J,K)=RESQ (J,K)+SOLN(K)~2 NEXT K IF LOC(l)=3399 GOTO 950 GOTO 360  zones  P r e s e n t the r e s u l t s LPRINT " Z o n e " , " V a r i a b l e " , " A v e r a g e " , " V a r i a n c e " FOR J = l TO 6 LPRINT J,M(J) FOR K=l TO 5 AV=RES(J,K)/M(J) VAR=(RESQ(J,K)—RES(J,K)*2/M(J))/(M(J)-l) LPRINT J,K,AV,VAR NEXT K NEXT J FOR L=l TO 8 LPRINT MANG(1,L),MANG(2,L),MANG(3,L),MANG(4,L),MANG(5,L),MANG(6,L) NEXT L END T h i s s u b r o u t i n e i n s t r u c t s the program t o o v e r l o o k c e r t a i n I F (LOC(l)>69) AND (LOC(l)<72) GOTO 390 I F (LOC(l)>45) AND ( L O C Q X 4 9 ) GOTO 390 I F (LOC(l)>57) AND (LOC(l)<62) GOTO 390 I F LOC(l)=261 GOTO 390 I F LOC(1)=310 GOTO 390 IF (LOC(l)>688) AND ( L O C U X 7 2 6 ) GOTO 390  sequences  Ill  1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200 1205 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320 1330 1340 1350 1360 1370 1380 1390 1400  IF LOC(l)=743 GOTO 390 IF LOC(l)=762 GOTO 390 IF (LOC(l)>841) AND (LOC(l)<848) GOTO 390 IF (LOC(l)>947) AND (L0C(1X954) GOTO 390 IF (LOC(l)>1150) AND ( L O C U K 1 1 6 6 ) GOTO 390 IF (LOC(l)>1171) AND (LOC(l)<1174) GOTO 390 IF LOC(l)=1218 GOTO 390 IF (LOC(l)>1334) AND (LOC (1 K1342) GOTO 390 IF LOC(l)=1361 GOTO 390 IF (LOC(l) >1425) AND ( L O C U K 1 4 2 8 ) GOTO 390 IF LOC(l)=1468 GOTO 390 IF (LOC(l)>1486) AND (LOC(l)<1492) GOTO 390 IF (LOC(l)>1511) AND (LOC(l)<1566) GOTO 390 IF LOC(l)=1655 GOTO 390 IF (LOC(l)>1912) AND (LOC(l)<1994) GOTO 390 IF LOC(1)=2059 GOTO 390 IF (LOC(l)>2112) AND (LOC(l)<2119) GOTO 390 IF (LOC(l)>2198) AND (LOC(1)<2202) GOTO 390 IF LOC(l)=2236 GOTO 390 IF (LOC(l)>2342) AND (LOC(l)<2345) GOTO 390 IF LOC(l)=2488 GOTO 390 IF (LOC(l)>2612) AND (LOC(l)<2618) GOTO 390 IF (LOC(l)>2652) AND (LOC(l)<2655) GOTO 390 IF LOC(l)=2745 GOTO 390 IF (LOC(1)>2800) AND (LOC(l)<2823) GOTO 390 IF (LOC(l)>2837) AND (LOC(1)<2840) GOTO 390 IF (LOC(l)>2927) AND (LOC(1)<2930) GOTO 390 IF (LOC(l)>3008) AND (LOC(1)<3014) GOTO 390 IF LOC(l)=3125 GOTO 390 IF (LOC(l)>3345) AND (LOC(l)<3349) GOTO 390 IF (LOC(l) >3367) AND (L0C(1X3372) GOTO 390 GOTO 420  APPENDIX  DETAILS  OF  III  EXPERIMENTAL  APPARATUS  113  This of  the  appendix  is  experimental  Plumbing Pump:  adjunct  apparatus  to  are  Chapter  listed  3  ,  and  details  herein.  Details: Paramount  c e n t r i f u g a l ; B . C . ;  pressure  18  =  operating  Model  1725  p s i ; =  of  plexiglas  channel  of  channel  30".  Tubing:  0.96  m  rpm,  36  Schedule  =  V-6;  diameter Pumps  hp  and  motor;  running  open  impeller;  Power  measured  pressure  =  13  L t d . ,  shut-off  p s i ;  normal  USgpm.  80 =  6"  by  0.5  normal  capacity  1.5"  1.5  m a n u f a c t u r e d  Vancouver,  Pipe:  an  PVC; length  33";  length  length  of  8  of  of  mm  straightaway  straightaway  i.d.  Tygon  upstream downstream  R-3603  flexible  tubing. Valves :  Four  (modified  to  diaphragm  v a l v e .  different,  custom  Reservoirs: System:  prevent  Two  =  Plexiglas  60  Mater i a l : t h i c k  0.25"  b a l l  water  made, 20.75"  l i t r e s ;  channel  PVC  flow  tips x  valves;  hammer);  Accept  Maximum  capacity  0 . 5 0 "  1.5"  into  normal  =  1.5"  PVC 3-way  the x  80  water  outlet  12"  valve  PVC-steel-neoprene  c o n t r o l l e d  20.75"  capacity  one  by of  (deep)  l i t r e s ;  i n s e r t i n g  the  tubing.  plastic  normal  temperature  =  20  tubs.  operating C.  details: thick  p l e x i g l a s  plexiglas for  f l a n g e s ;  for  channel  j o i n t s  closed  walls, with  114  dichloroethane. I n t e r n a l 0.75"  Dimensions:  deep,  0.75"  F i t t i n g s : neoprene  gaskets;  Camera:  the  3000  =  The  above  marked of  =  frames  per  edge  was  7250  1.5"  0.375"  K20S4E  pipe  long,  flanges  FPT p l e x i g l a s  manufactured  California;  second;  -  -10  4  framing  equation  of  *FN  rate,  actual  with  f i t t i n g .  by  Red  nominal  framing  and  1.594*10~ *FN 2  FN =  was  determined  the  film  marks  were  rate  Lake  framing given  by  was  f i t t e d  100  frame  to  the  a  per  measured  +  3.872*10~ *FN 6  3  number.  using  times  2  timing  light  second.  The  manually,  data,  and  which number  equations  then  the  of  above  chosen.  details:  16  -  -  Clara,  2.809*FN  3.704*10  order  Fi lm:  +  between  lens  12"  equation:  various  Zoom  No.  pictures  equation  the  Further  Model Santa  1363 -  FR  ports  port  Inc.  following  where  accept  Hycam  FR  -  Details:  L a b o r a t o r i e s =  chamber  high.  Feed/reject  Photographic  rate  Feed/reject  with  20  1/50  mm e x t e n s i o n ;  mm E a s t m a n  tungsten,  400  shutter;  f5.6  aperture;  55-60  mm z o o m .  Ektachrome  ASA;  100  foot  video reel.  news  Sun-Dionar  film;  high  16  speed  115  L i g h t i n g : mount;  1200  (white)  Fibre  QEJ-30  watts  total  plastic  length  Kajaani Oy  Four  analyzer  FS-100  Film  500  Fibre  kg/cm  analyzing  P r o j e c t o r :  a r e a ;  by  Length  Analyzer  Finland;  Optical L-W  manufactured  0.2  mm  Model  l i n e s  per  manufactured  Data  1/8"  by  diameter  Analyzer  I n t e r n a t i o n a l ,  Ektanar  Pad:  accuracy;  by  a  custom thick  Kajaani capillary  vacuum.  2  Kodak  500  diffused  in  arrangement:  m a n u f a c t u r e d  Digitizing  light  bulbs  details:  Kajaani,  Photo  California;  power;  Electric  sheet.  Electronics,  tube;  General  lens  ,  2  ",  224A  Woodland  Mk  IV  H i l l s ,  fl6.  MM 1 2 0 1  Digitizer;  inch  r e s o l u t i o n ;  by  Model  Summargraphics  11.7 +/-  x  11.7"  active  0.025"  rated  C o r p . ,  F a i r f i e l d ,  Connect i cut. Computer: monitor,  IBM 640  resolution.  Personal  points  Computer;  (horizontal)  NEC M o d e l x  200  No.  points  JB-1201  M  (vertical)  116  APPENDIX  FIBRE  LENGTH  IV  DISTRIBUTIONS  T a b l e XII fibre length (mm)  Length D i s t r i b u t i o n distribution  o f lx.043 mm  Nylon F i b r e s  (replicated)  f i b r e length (mm)  distribution  0.00 0.07 0.14 0.21  -  0. 07 0. 14 0. 21 0. 28  0.64 0.32 0.16 0.56  0.12 0.27 0.12 0.19  1.41 1.48 1.55 1.62  -  1.48 1.55 1.62 1.69  1.42 0.53 0.46 0.29  1.11 0. 36 0.28 0.16  0.28 0.35 0 . 42 0.49  _  0. 35 0. 42 0. 49 0. 56  0.37 0.21 0.16 0.32  0.12 0.13 0.19 0.41  1.69 1.76 1.83 1.90  -  1.76 1.83 1.90 1.97  0.19 0.08 0.08 0.05  0.12 0.06 0.05 0.04  0. 63 0. 70 0. 77 0. 84  0.58 1.75 3.18 7 . 50  0.69 1.57 3.43 8.33  1.97 2.04 2.11 2.18  -  2.04 2.11 2. 18 2.25  0.03 0.00 0.00 0.00  0.04 0.04 0.04 0.03  0.56 0.63 0.70 0.77 0.84 0.91 0.98 1.05 1.12 1. 20 1.27 1. 34  -  _  -  _  -  -  0. 91 0.98 1. 05 1. 12  10.91 14.64 15.44 13.93  12.61 15.53 15.31 13.27  2.25 2.32 2.40  - 2.32 - 2.40 +  0.00 0.00 0.16  0.03 0.02 0.04  1. 20 1. 27 1. 34 1. 41  11.62 7.22 5.14 2.24  11.45 7.24 4.84 1.78  f i r s t decile f i r s t quartile second q u a r t i l e third quartile ninth decile average w e i g h t e d average  0.72 0.83 0.95 1.08 1.20 0.96 1.00  0.72 0.82 0.94 1.07 1.19 0.95 0.99  Table XIII f i b r e length (mm)  Length D i s t r i b u t i o n o f 1 . 5 X . 0 4 3 mm distribution  Nylon F i b r e s  f i b r e length (mm)  (replicated) distribution  0.00 0.11 0.23 0.35  -  0. 11 0. 23 0. 35 0.47  0.65 0.86 0.83 0.18  2.35 2.47 2.58 2.70  -  2.47 2.58 2.70 2.82  0.23 0.14 0.13 0.10  0.47 0. 58 0.70 0.82  -  0. 58 0. 70 0.82 0.94  0.26 0.29 0.31 0.37  2.82 2.94 3.05 3.17  -  2.94 3.05 3.17 3.29  0.10 0.08 0.08 0.09  0.94 1.05 1.17 1.29  -  1. 05 1. 17 1.29 1.41  0.47 0.65 1.16 5.91  3.29 3.41 3.52 3.64  -  3.41 3.52 3.64 3.76  0.11 0.09 0.05 0.02  1.41 1.52 1.64 1.76  -  1. 52 1. 64 1. 76 1. 88  10.51 19.28 23.78 19. 57  3.76 3.88 4.00  - 3.88 - 4.00 +  0.02 0.02 0.04  1.88 2 .00 2 .11 2.23  -  2. 00 2. 11 2. 23 2. 35  10.85 1.55 0.96 0.31  f i r s t decile f i r s t quartile second q u a r t i l e third quartile ninth decile average w e i g h t e d average  1.25 1.42 1.57 1.70 1.81 1. 55 1.61  mm  Table XIII fibre length (mm) 0.00 0.07 0.14 0.21 0.28 0.35 0.42 0.49  -  -  0.56 0.63 0.70 0.77  _  0.84 0.91 0.98 1.05  _  1.12 1.20 1.27 1.34  -  -  -  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 length (mm)  (continued)  distribution  fibre  distribution  0.07 0.14 0.21 0.28  0.25 0.45 0.29 0.21  1.41 1.48 1.55 1.62  -  1.48 1.55 1.62 1.69  0.35 0.42 0.49 0.56  0.22 0.21 0.11 0.15  1.69 1.76 1.83 1.90  -  1.76 1.83 1.90 1.97  8. 30 2.05 1.23 0.33  0.63 0.70 0.77 0.84  0.14 0.18 0.11 0.14  1.97 2.04 2.11 2.18  -  2.04 2.11 2.18 2.25  0.25 0.14 0.12 0.10  0.91 0.98 1.05 1.12  0.18 0.31 0.39 0.82  2.25 2.32 2.40  - 2.32 - 2.40 +  0.09 0.08 0. 37  1.20 1.27 1.34 1.41  1.16 2.99 4.48 9.92  f i r s t decile f i r s t quartile second q u a r t i l e third quartile ninth decile average w e i g h t e d average  1.22 1.35 1.46 1.56 1.64 1.44 1.47  13.87 18.27 18.72 13.74  mm  T a b l e XIV fibre length (mm) 0,,00 0,,20 0,,41 0.61 0,,82 1.,02 1..23 1,.44 1,.64 1,.85 2,.05 2,.26 2 .47 , 2 ,67 , 2.,88 3,.08 3,.29 3..50 3..70 3,.91  -  Length D i s t r i b u t i o n distribution  of 3x.043 mm  Nylon F i b r e s  f i b r e length (mm)  (replicated) distribution  0.20 0.41 0.61 0.82  8.51 7.80 2.62 0.64  5.18 2.90 1.38 0.98  4.11 4.32 4.52 4.73  -  4.32 4.52 4.73 4.94  0.34 0.11 0.11 0.07  0.43 0.27 0.25 0.20  1.02 1.23 1.44 1.64  0.71 0.59 0.47 0.47  0.91 0.79 0.83 0.60  4.94 5.14 5.35 5.55  -  5.14 5.35 5.55 5.76  0.04 0.01 0.02 0.05  0.18 0.11 0.07 0.13  1.85 2.05 2.26 2.47  0.40 0.31 0.19 0.41  0.45 0.24 0.19 0.46  5.76 5.97 6.17 6.38  - 5.97 - 6.17 - 6.38 - 6.58  0.06 0.05 0.02 0.05  0.25 0.24 0.12 0.00  -  2.67 2.88 3.08 3.29  0.59 6.51 12.28 18.18  0.73 7.07 13.16 19.72  6.58 - 6.79 6.79 - 7.00 7.00 +  0.09 0.14 0.14  0.00 0.00 0.13  --  3.50 3.70 3.91 4.11  18.31 12.57 6.69 ,0.58  20.20 14.02 7.37 0.57  f i r s t decile first quartile second q u a r t i l e third quartile ninth d e c i l e average w e i g h t e d average  0.03 2.51 2.96 3.24 3.47 2.69 3.11  0.52 2.71 3.02 3.28 3.50 2.88 3.14  -  _  -  mm  O  T a b l e XV f i b r e length (mm)  Length D i s t r i b u t i o n distribution  o f lx.012 mm  Rayon F i b r e s  (replicated)  f i b r e length (mm)  distribution  0.00 0.07 0.14 0.21  -  0.07 0.14 0.21 0.28  6.37 3.64 2.76 2.60  3.81 2.94 2.06 2.97  1.41 1.48 1.55 1.62  -  1.48 1.55 1.62 1.69  1.17 0.91 0.80 0.60  1.14 0.77 0.67 0.53  0.28 0.35 0.42 0.49  _  0.35 0.42 0.49 0.56  2.52 2.97 3.17 3.29  3.12 3.45 3.24 3.15  1.69 1.76 1.83 1.90  -  1.76 1.83 1.90 1.97  0. 52 0.42 0.40 0. 32  0. 50 0.42 0. 38 0.31  0.63 0.70 0.77 0.84  3.34 4.32 5.61 7.52  3.20 4; 34 5.51 7.70  1.97 2.04 2.11 2.18  -  2.04 2.11 2.18 2.25  0.25 0.17 0.16 0.13  0.28 0.21 0.17 0.11  0.91 0.98 1.05 1.12  8.98 9.44 9.08 6.95  9.46 10.14 9.60 7. 30  2.25 2.32 2.40  - 2. 32 - 2.40 +  0.12 0.11 0.22  0.09 0.08 0.15  1.20 1.27 1.34 1.41  5.19 2.76 2.10 1. 30  5.54 3.07 2.37 1.40  f i r s t decile f i r s t quartile second q u a r t i l e third quartile ninth decile average w e i g h t e d average  0.07 0.44 0.79 0.98 1.18 0.81 0.97  0.16 0.49 0.81 0.99 1.18 0.81 0.97  0.56 0.63 0.70 0.77 0.84 0.91 0.98 1.05 1.12 1.20 1.27 1.34  -  -  _  _  -  mm  T a b l e XVI  Length D i s t r i b u t i o n  f i b r e length (mm) 0. 00 0. 07 0. 14 0. 21  -  0. 28 0. 35 0. 42 0. 49  _  0. 56 0. 63 0. 70 0. 77  _  0. 84 0. 91 0. 98 1. 05 1. 12 1. 20 1. 27 1. 34  -  -  --  -  ---  distribution  of lx.020 mm  Rayon F i b r e s  (replicated)  f i b r e length (mm)  distribution  0.07 0.14 0.21 0.28  0.15 0.20 0.10 0.05  0.42 0.00 0.23 0.06  1. 39 0.03 0.09 0.16  1.41 1.48 1.55 1.62  -1.48 - 1.55 -1.62 -1.69  5.85 2.29 1.56 0.62  10.45 4.82 3.10 1.03  4.12 1.46 0.91 0.30  0.35 0.42 0.49 0. 56  0.17 0.22 0.18 0.17  0.10 0.14 0.17 0.13  0.20 0.19 0.14 0.12  1.69 1.76 1.83 1.90  -  1.76 1.83 1.90 1.97  0.41 0.20 0.20 0.14  0.68 0.25 0.18 0.10  0.25 0.17 0.14 0.12  0.63 0.70 0.77 0.84  0.13 0.25 0.37 1.19  0.12 0.12 0.19 0.45  0.16 0.28 0.58 1. 59  1.97 2.04 2.11 2.18  -  2.04 2.11 2.18 2.25  0.08 0.06 0.09 0.09  0.09 0.08 0.08 0.07  0.13 0.11 0.07 0.03  0.91 0.98 1. 05 1.12  1.88 4. 68 6.82 13.07  0.70 2.07 3.21 8. 54  2.53 5.90 8.52 14.86  2.25 2. 32 2.40 +  2.32 2.40  0.06 0.03 0. 30  0.06 0.05 0.45  0.02 0.02 0.54  1.20 1.27 1.34 1.41  17 .19 18.04 14.77 8.67  18. 58 17.64 12.98 6.21  f i r s t decile f i r s t quartile second q u a r t i l e third quartile ninth decile average weighted average  0.92 1.03 1.14 1.24 1. 36 1. 14 1.17  1.00 1.10 1.21 1. 32 1.42 1.21 1 i 24  0.87 min 1.00 1.10 1.21 1.31 1. 10 1.14  12.75 17.39 17.83 14.36  Table XVII fibre length (mm) 0.00 0.20 0.41 0.61 0.82 1.02 1.23 1.44  -  -  -  1.64 1.85 2.05 2.26  _  2.47 2.67 2.88 3.08  _  3.29 3.50 3.70 3.91  _  -  -  -  -  -  Length D i s t r i b u t i o n distribution  of p l 0 . r l 4  Kraft  Pulp F i b r e s  f i b r e length (mm)  (replicated) distribution  0. 20 0. 41 0.61 0.82  2.04 1.33 2.35 1.33  1.20 1.29 2.49 1.33  4.11 4.32 4.52 4.73  -  4.32 4.52 4.73 4.94  4.54 3.26 2.66 1.70  4.37 3.31 2.77 1.81  1. 02 1. 23 1. 44 1.64  1.17 1.36 1.70 2.31  1.38 1.45 1.78 2.35  4.94 5.14 5.35 5.55  -  5.14 5.35 5.55 5.76  1.34 0.81 0.65 0. 38  1.40 0.80 0.59 0.32  1. 85 2 .05 2. 26 2 .47  3.15 3.73 4.48 5.03  3.27 4.26 4.57 5.42  5.76 5.97 6.17 6.38  -  5.97 6.17 6.38 6.58  0.27 0.14 0. 13 0. 10  0.24 0.13 0.10 0.06  2 .67 2. 88 3. 08 3 .29  5.81 6.50 6.92 7.59  5.92 7.13 7.42 7.60  6.58 - 6.79 6.79 - 7.00 7 .00 +  0.10 0.09 0. 13  0.05 0.04 0.12  3 .50 3. 70 3. 91 4. 11  7.84 7.36 6.63 5.22  7.49 6.71 6.05 4.88  f i r s t decile first quartile second q u a r t i l e third quartile ninth decile average weighted average  1.08 2.06 2.90 3.59 4.21 2.84 3.31  1.12 2.04 2.84 3.56 4.21 2.79 3.27  mm  Table XVIII fibre length (mm)  Length D i s t r i b u t i o n distribution  of pl4.r28 K r a f t Pulp F i b r e s f i b r e length (mm)  (replicated) distribution  0.00 0.20 0.41 0.61  -  0.20 0.41 0.61 0.82  0.79 1.02 1.55 0.68  0.91 1.30 1.38 1.15  4.11 4.32 4.52 4.73  -  4.32 4.52 4.73 4.94  1.45 0.78 0.64 0.38  1.48 0.78 0.58 0.33  0.82 1.02 1.23 1.44  _  1.02 1.23 1.44 1.64  1.32 2.28 3.55 5.18  1.25 1.87 3.36 5.27  4.94 5.14 5.35 5.55  -  5.14 5.35 5.55 5.76  0.24 0.10 0.10 0.08  0.28 0.18 0.13 0.07  1.64 1.85 2.05 2.26  _  1.85 2.05 2.26 2.47  7.14 8.90 9.46 9.34  7.42 9.23 9.33 9.08  5.76 5.97 6.17 6. 38  -  5.97 6.17 6.38 6.58  0.07 0.04 0.04 0.02  0.07 0.05 0.03 0.01  2.47 2.67 2.88 3.08  _  2 .67 2.88 3.08 3.29  8.97 8.25 7.44 5.91  8.46 8.16 7.59 6.14  6.58 6.79 7.00  - 6.79 -7.00 +  0.02 0.01 0.08  0.00 0.00 0.00  3.50 3.70 3.91 4.11  5.20 3.85 3.20 2.00  5.26 3.75 3.11 1.98  f i r s t decile first quartile second q u a r t i l e third quartile ninth decile average weighted average  1.16 1.68 2.23 2.85 3.45 2.29 2.64  1.16 1.67 2.22 2.86 3.45 2.28 2.64  3.29 3.50 3.70 3.91  -  _  -  mm  it*  T a b l e XIX fibre length (mm) 0.00 0.20 0.41 0.61  - 0. 20 - 0.41 - 0.61 - 0.82  0.82 1.02 1.23 1.44  -  Length D i s t r i b u t i o n  distribution  of K r a f t Pulp F i b r e s f i b r e length (mm)  distribution  7.5 9.2 13.0 6.5  4.11 4.32 4.52 4.73  -  4.32 4.52 4.73 4.94  1.7 1.3 1.0 0.6  1.02 1. 23 1.44 1. 64  5.5 5.1 4.9 4.7  4.94 5.14 5.35 5.55  -  5.14 5.35 5.55 5.76  0.5 0.4 0.3 0.2  1.64 1.85 2.05 2.26  - 1. 85 - 2. 05 - 2. 26 - 2.47  4.6 4.3 4.0 3.7  5.76 5.97 6.17 6.38  -  5.97 6.17 6.38 6.58  0.2 0.1 0.1 0.0  2.47 2.67 2.88 3.08  - 2.67 - 2.88 -3.08 - 3. 29  3.5 3.3 3.0 2.6  6.58 - 6.79 6.79 - 7.00 7 .00 +  0.0 0.0 0.0  3.29 3.50 3.70 3.91  - 3. 50 - 3.70 - 3.91 - 4. 11  2.5 2.1 2.0 1.8  f i r s t decile f i r s t quartile second q u a r t i l e third quartile ninth decile average w e i g h t e d average  0.05 0.32 1.10 2.31 3.43 1.56 2.61  mm  T a b l e XX fibre  length  (mm)  -  0.20 0.41 0.61 0.82  0.82 1.02 1.23 1.44  _  -  1.64 1.85 2.05 2.26  _  2.47 2.67 2.88 3.08  _  3.29 3.50 3.70 3.91  -  _  -  distribution  o f CTMP P u l p F i b r e s fibre  (replicated)  length  distribution  (mm)  0.00 0.20 0.41 0.61  -  Length D i s t r i b u t i o n  7. 83 15. 49 20. 30 11. 68  8.13 16.83 21.33 11.50  4.11 4.32 4.52 4.73  -  4. 32 4.52 4.73 4.94  0.31 0.20 0.16 0.12  0.22 0.15 0.14 0.12  1.02 1.23 1.44 1. 64 ''  9. 60 7. 54 5. 84 4. 40  8.99 6.92 5.47 4.14  4.94 5.14 5.35 5.55  -  5.14 5.35 5. 55 5.76  0.12 0.10 0.07 0.05  0.11 0.09 0.07 0.04  1.85 2.05 2.26 2.47  3. 30 2. 73 2. 11 1. 74  3.20 2.74 2.20 1.75  5.76 5.97 6.17 6.38  -  5.97 6.17 6. 38 6.58  0.05 0.04 0.03 0.01  0.02 0.01 0.00 0.00  2.67 2.88 3.08 3.29  1. 31 1.04 0.96 0. 78  1.33 1.01 0.91 0.72  6.58 6.79 7.00  - 6.79 - 7.00 +  0.01 0.01 0.08  0.01 0.01 0.02  3.50 3.70 3.91 4.11  0. 68 0. 53 0. 49 0. 38  0.64 0.49 0.42 0.29  f i r s t decile f i r s t quartile second q u a r t i l e third quartile ninth decile average w e i g h t e d average  0.02 0.22 0. 52 1.11 1.97 0.88 1.78  0.02 0.20 0.47 1.07 1.92 0.84 1.71  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0058886/manifest

Comment

Related Items