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The forces on pulp fibres during refining Senger, John Jaa 1998

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T H E FORCES ON PULP FIBRES DURING REFINING by J O H N J A A SENGER B.A.Sc. (Engineering Physics), The University of British Columbia, 1995  A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF APPLIED SCIENCE in T H E FACULTY OF G R A D U A T E STUDIES Department of Mechanical Engineering We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH C O L U M B I A January 1998 ©  John Jaa Senger, 1998  In presenting this thesis in partial fulfilment  of the  requirements for an advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department  or  by  his  or  her  representatives.  It  is  understood  that  copying or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  fl&JrlAmCAL  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  ^Jll  ^ 3  ' /??S  ABSTRACT The refining process is widely used in the pulp and paper industry for the production of woodpulps or to develop the papermaking properties of wood fibres through repeated application of strain. The mechanical action of refiners is commonly characterized using energy-based methods, but Page has suggested that characterizing the stress-strain history of fibres would lead to a better understanding of the refining process [Fundamentals of Papermaking, 9th Fundamental Res. Symp., Vol 1, p. 1-38, 1989]. Recent work by Martinez et al. [J. Pulp Paper Sci., 23(1):Jll-18, 1997] and Batchelor et al. [J. Pulp Paper Sci., 23(1):J40-45, 1997] has produced a model of the forces imposed on agglomerates of fibres, called floes, when they are caught between refiner bars. The model assumes a linear stress-strain relationship during floe compression. However, in this work, experiments performed in a laboratory single bar refiner have shown that the stress-strain relationship becomes non-linear at high strain. The present work proposes a new model to predict the normal stress resulting from floe compression between the bars of a refiner. The model accounts for two separate mechanisms to explain the development of this normal stress: fibre bending and radial compression of fibres. The relative importance of the two mechanisms depends on the fibre and floe properties and the level of strain. Experiments have shown that the model accurately predicts the stress-strain behaviour over a wide range of strain and floe properties. For mechanical pulp floes, fibre bending was shown to account for, on average, 65% of the total normal stress, while fibre compression explained the other 35%. For a previously dried kraft pulp, the normal stress could be modeled with good accuracy by accounting for fibre bending  ii  alone. The shear force between the refiner bars was also measured in these experiments, and it was found to be directly proportional to the normal force through a coefficient of friction. Values for the coefficient of friction varied between 0.26 and 0.32 depending on the type of pulp considered.  iii  Contents  ABSTRACT  ii  LIST OF TABLES  vi  LIST OF FIGURES  vii  ACKNOWLEDGEMENT  viii  1  INTRODUCTION  1  2  C H A R A C T E R I Z A T I O N OF T H E REFINING A C T I O N  5  2.1  Characterization of Pulp Refiners  5  2.1.1  Specific edge load  5  2.1.2  Modified edge load  6  2.1.3  Number and Intensity of Impacts  7  2.1.4  C-factor  8  3  2.2  Characterization of Chip Refiners  9  2.3  Force-Based Characterization  11  2.4  Research Objectives  13  EXPERIMENTAL  15  3.1  Single Bar Refiner and the Force Profile  15  3.2  Pulp Preparation  19  iv  4  5  6  7  3.3  Floe Preparation and Handling  21  3.4  Summary of Experimental Conditions  22  STRESS-STRAIN RESULTS  24  4.1  The Stress-Strain Relationship  24  4.2  Discussion of Strain  27  4.3  Applicability of the Compressibility Equation  29  4.4  Discussion of Stress-Strain Results  31  THE FORCE MODEL  35  5.1  Normal Force Component Resulting From Fibre Bending  36  5.2  Normal Force Component Resulting From Fibre Compression  39  5.3  Discussion of the Force Model  41  RESULTS A N D DISCUSSION  45  6.1  Evaluation of K  45  6.2  The C*-W  49  6.3  Predictions of the Normal Stress  51  6.4  Effect of Consistency  55  6.5  Coefficients of Friction  56  c  Relation  CONCLUSIONS A N D RECOMMENDATIONS  58  NOMENCLATURE  60  BIBLIOGRAPHY  64  A P P E N D I X A: INDIVIDUAL F L O C DATA  68  A P P E N D I X B: PROBABILITY OF FIBRE O V E R L A P  76  v  List of Tables 3.1  Bauer-McNett Base Pulp and Fines Free C T M P Fibre Length Distributions  20  3.2  Summary of Experimental Conditions  23  3.3  Summary of Fibre Properties  23  4.1  Comparison of the Constants M and N in the Compressibility Equation . . .  31  6.1  Summary of Regression Estimates for K  48  6.2  Coefficients of Friction  57  c  vi  List of Figures 1.1  Schematic of a Disc Refiner  2  1.2  Schematic of a Chip Refiner Plate  2  3.1  Schematic of Single Bar Refiner  16  3.2  Force Profile of a Floe Compressed in the S B R  18  3.3  Fines Removal Procedure  20  4.1  C T M P Stress-Strain Relationship  25  4.2  Kraft Stress-Strain Relationship  26  4.3  Applicability of the Compressibility Equation  30  4.4  Generation of Normal Forces in a Floe  32  5.1  Incremental Bending Force  38  5.2  Normal Force Component Due to Fibre Compression  40  5.3  Force-Deflection Model for a Single Fibre in Transverse Compression  6.1  a* vs B* for B P C T M P  46  6.2  a* vs B* for F F C T M P  47  6.3  C* vs W  50  6.4  Measured Stress vs Predicted Stress  52  6.5  Measured Stress vs Predicted Stress: B y Pulp Type  53  vii  . . . .  43  ACKNOWLEDGEMENT The author would like to give thanks to the many people who helped bring this thesis to fruition. To Dr. D. Ouellet for many, many helpful discussions and valuable feedback. To Dr. G.S. Schajer for helpful discussions, guidance, and perspective on the entire educational process. To Dr. W . Batchelor for help with the single bar refiner and discussions on experimental procedure. To Dr. R. Thiruvengadaswamy and G . Bygrave for feedback on various ideas. To P. Taylor, K . Wong, T. Paterson, R. Penco, B. Dutka, L . Brandly, G. White, C. Black, and J. Marsden for making the day-to-day tasks both easier and more enjoyable. To the N C E Mechanical and Chemi-mechanical Woodpulps Network for funding for this project. A n d last but certainly not least, to A . Janmaat for continued help and support in many areas over the last two years.  viu  Chapter 1 INTRODUCTION Refining is an energy intensive process that is used in the pulp and paper industry to separate fibres from the wood matrix and develop their papermaking properties through repeated strain. There are many types of refiners but the most common is a disc refiner. A schematic of a disc refiner is given in Fig. 1.1. It consists of a rotating disc (the rotor) and a stationary disc (the stator), both fitted with plates containing bar and groove patterns, and separated by a small gap. Wood fibres in the form of chips or pulp are fed into the center of the discs and are propelled outward by centrifugal forces. When pulp is fed at low consistency, pumping action also plays a major role in moving the suspension through the refiner. As the fibres move between the plates they are compressed and sheared by the opposing bars on either side of the gap. The number of times that an individual fibre is compressed between opposing bars on the rotor and stator is determined by the time that the fibre spends in the refining zone (the residence time), the rotational speed of the refiner, and the number of bars on the refiner plates. The pattern of bars and grooves on the plates is selected according to the use for which the refiner is intended. For a chip refiner, the intended use is to take wood chips and break them down into a pulp suspension. This is accomplished by increasing the number of bars on the plates as the fibres move toward the periphery of the refiner. A schematic of a chip refiner plate is shown in Fig. 1.2. Here, the breaker bar section is used to break down chips into smaller pieces that then enter the intermediate bar zone. The smaller pieces are further refined into pulp as they 1  Plate Segments with Bar and Groove Pattern Stationary Disc  Rotating Disc  Inlet  Motor  Plate Gap  V Outlet 7  Figure 1.1: Schematic of a Disc Refiner  —— F i n e  Bars  I n t e r m e d i a te Bars  -Breaker Bars  Figure 1.2: Schematic of a Chip Refiner Plate. The plate consists of separate regions of alternating bar and groove patterns.  2  travel through the intermediate bar section and finally enter a fine bar section near the outside of the refiner. The fine bar section is intended to flexibilize individual fibres through a rapid succession of strain cycles. In contrast to a chip refiner, a pulp refiner is intended to develop individual fibre properties. In this case, the plate pattern typically contains only one type of bars - the intermediate bars - which extend the whole length of the refining zone. To get an indication of the degree to which fibres are mechanically treated as they pass through a refiner, theories have been developed to characterize the refining action. Most theories of refining in use are based upon a consideration of the energy imparted to individual fibres as they pass through the refiner. This energy is most commonly expressed as the specific energy E , which is simply the ratio of the net instantaneous power of refining divided by the total oven dry (OD) mass flow rate of fibres through the refiner. Energy-based characterizations have their shortcomings in identifying the mechanisms by which refining occurs: for example, internal fibrillation of the fibre wall through transverse compression or fibre bending, external fibrillation through shear forces, or some combination of each of the above. Energy can be expended on pulp fibres in numerous ways and the method of energy application - the forces - will have a substantial influence on the final pulp properties. Hence, an understanding of the forces exerted on fibres as they pass through the refiner may offer greater insight into both controlling the refining process as well as making it more efficient. Giertz was one of the first researchers to comment on the importance of the forces in refining. He suggested that different refining effects could be explained by the relative magnitude of the forces applied [1]. Thirty-two years later, in a review of the beating of chemical pulps, Page suggested that a complete understanding of the refining process would require knowledge of the average stress-strain history of individual fibres [2]. One recent theory, developed by Martinez et ai, considers the forces imparted to an agglomerate of fibres, called a floe, as it is beaten between the passing bars of a refiner [3, 4]. This forcebased characterization of refining shows promise in predicting refining effects as it attempts l  3  to look at the underlying mechanisms involved in the application of energy to the fibres. To determine which forces in refining are beneficial and which simply serve to consume energy, one must first know what the forces are and where they come from. The next chapter reviews current methods of characterizing refining action. This will provide the necessary background to justify the objectives of the present work, which will be stated at the end of the chapter. The following chapters will then present the experimental work that was conducted on a number of different pulp types, and will propose a new model to predict forces on pulp floes in refiners.  4  Chapter 2 CHARACTERIZATION OF T H E REFINING A C T I O N Refiners come in many different types and sizes, and operate under a wide range of conditions. In order to compare one type of refiner to another, in terms of the effect of refining on pulp and fibre properties, it is necessary to have some means of characterizing the action of these refiners. The following sections look at a number of methods of characterizing both pulp and chip refiners, using both energy-based and force-based approaches.  2.1 2.1.1  Characterization of Pulp Refiners Specific edge load  The specific edge load (SEL) is the most widely used theory in practice today. It is a measure of the net power divided by the total length of bar crossings per unit time in the refining zone and is expressed as [5]: SEL =  GEL  =  P  Y.iZ z LiU ri  (2.1)  Si  where C E L is known as the cutting edge length and is defined from the above equation. P is the net power of refining, z , z ri  Si  represent the number of bars on the rotor and stator in a  small radial increment i , Li is the length of increment i , and u is the rotational speed of the refiner. The summation is over the entire length of the refining zone, and the increments are  denned as regions containing an equal number of bars on the rotor and stator. The SEL has units of J / m while the C E L is usually quoted in plate manufacturer's specifications as km/s for a given rotational speed. Once the S E L is known, a two-parameter characterization of refining is given by estimates of E and SEL. Thus, similar pulp properties are expected from fibres subjected to similar E and SEL values. Brecht demonstrated that similar pulp properties could be achieved by refining in various devices of different size and type, at constant E and S E L values. However, care was taken to ensure that the different refiners operated with similar bar width, bar material, and cutting angle [5]. These constraints contribute to shortcomings associated with the SEL characterization: it does not include many of the parameters that are known or seem to have an effect on refining results. In addition to those mentioned above, some of these parameters are consistency, groove depth, rotational speed and others [6]. Thus, although the SEL offers a simple method of characterizing refining effects, it fails to offer a complete picture of the refining process. More parameters are required to reach this goal.  2.1.2  Modified edge load  The modified edge load (MEL) theory is an extension of the SEL theory and is given by the following equation [7]: MEL  = SEL •  2 tan 0  • ^±^B  (2.2)  where B is the bar width, G is the groove width, and <j> is the average bar angle measured relative to a radial line passing through the middle of a plate section. The M E L accounts for fillings parameters such as bar angle and bar and groove width that are absent from the S E L theory. Changes in these parameters will affect the probability that a fibre will be impacted when passing through the refiner and should therefore be taken into account to get a better representation of the actual refining process. Thus, a two-parameter characterization is obtained from an estimate of the M E L along with E , and similar pulp properties are 6  expected from fibres subjected to equal values of M E L and E . Meltzer showed that similar pulp properties could be achieved by refining at constant M E L and E . The M E L did a better job than the S E L of predicting refining effects when bar angle was changed in the refiner, but the results were not conclusive. For properties such as burst, tear, and light scattering coefficient, the M E L did very well in explaining refining effects, while for properties such as freeness and fibre length the results were not much better than those obtained with the S E L theory [7]. In general, the M E L theory is an improvement on the S E L theory but still misses a number of important parameters in the refining process such as consistency, rotational speed, groove depth, and fibre properties. Thus, it is not adequate to explain the wide variability in pulp properties attained by different refiners under different operating conditions. A different approach altogether may be needed.  2.1.3  Number and Intensity of Impacts  Probably the biggest shortcoming of the SEL and M E L theories is that they both consider refining from the perspective of the refiner and not from the perspective of the fibre. A l l the parameters taken into account in the S E L and M E L are refiner parameters: length of bars, width of bars, number of bars, etc. Leider and Nissan took the perspective of a fibre and developed relations indicating the average number of impacts N  m  that a fibre would see  passing through the refiner, as well as the average energy per impact Ei [8]. They expressed these terms in the following equations:  N  m  = z z cjTp r  s  f  E, = ^  (2.3) (2.4)  N where z , z are the number of bars on the rotor and stator respectively, u is the rotational r  s  speed, r is the residence time of a fibre in the refining zone, pf is the probability that a fibre will be impacted, E is the specific energy, and Mf is the average mass of a fibre. 7  They showed that changes in pulp properties correlated well with changes in the number and intensity of impacts for fibres refined in a disc refiner [8]. This approach was later, improved by Kerekes, and adapted to include refiner types other than disc refiners, in the C-factor theory.  2.1.4  C-factor  Kerekes has developed an expression called the C-factor that represents the capacity of a refiner to inflict impacts on fibres passing through it [9]. The C-factor accounts for fibre properties, refiner geometry, and refiner operating conditions and allows estimation of the number of impacts seen by a fibre passing through the refiner as well as the average intensity of impact. For a disc refiner the C-factor is given by: _ 4.ir p Cflfb b m(T 2  w  s  r  + bGD s  s  + b G D )(l + tan</y + tan<ft )(r% - r\) 3w(l + D + T)  s  r  r  r  a  ' '  [  f  where p is the density of water, Cf is the consistency of the suspension, If is the fibre length, w  b is the number of bars per unit arc length, <p is the average bar angle, T is the gap between the rotor and stator, u is the rotational speed, D is the groove depth, G is the groove width, T|,r2 are the inner and outer radii of the refining zone, w is the fibre coarseness, and the subscripts r and s denote rotor and stator respectively. Once the C-factor is known for a given set of conditions, the number of impacts and the average intensity of impact seen by a fibre passing through the refiner are given by the following equations: N  = C/F  (2.6)  / = P/C  (2.7)  m  where N  m  m  is the number of impacts per unit mass, F  m  is the mass flow rate of fibres, / is  the intensity of impact, P is the net instantaneous power of refining, and the product N  m  8  •I  is the specific energy. Thus, the C-factor gives a two-parameter characterization of refining in which the resultant pulp properties are predicted from estimates of both N  m  and I.  The C-factor theory has been used to compare refining effects in different types of refiners under different operating conditions [10, 11]. It has shown that changes in pulp properties can be understood in terms of the number and intensity of impacts experienced by individual fibres. Although the C-factor is useful in giving quantitative predictions about the refining process, it falls short of describing the mechanisms which influence pulp properties. A n understanding of these mechanisms is crucial to the goal of producing a combined qualitative and quantitative view of refining.  2.2  Characterization of Chip Refiners  Chip refiners differ from pulp refiners primarily in the consistency at which they operate. Typically, pulp refiners operate at consistencies below 4%, where the pulp suspension traveling through the refiner behaves very much like a liquid, allowing a straightforward calculation of the residence time using the volumetric flow rate and cross-sectional area. Chip refiners, on the other hand, operate at consistencies above 20% where fibres travel through the refiner as floes, separated from each other by voids, and surrounded by steam. Because pulp behaves as a wet solid at these high consistencies, its flow through the refiner depends on the forces that act to accelerate it. Miles and May have developed a theory to predict the flow of pulp through chip refiners by considering a force balance on an element of pulp as it travels through the refining zone [12]. Their approach considers centrifugal, friction, and steam drag forces acting on a small mass of pulp attached to the rotor, traveling through the gap between the refiner plates. This approach results in a differential equation for the radial velocity of the pulp that needs to be solved numerically to determine the residence time. Miles has simplified  9  their result by proposing that the effects of forward and backward flowing steam cancel each other out over the refining zone. This assumption has allowed the formulation of algebraic equations to predict the residence time, number of impacts, and specific energy per impact seen by a fibre moving through the refining zone [13]. The residence time r is given by: fi  r  aEciL  ']Itufi(L(rl-rl)  + c Erl) i  In  r  2  n  1 2  m  (L-CiE V  L  (2.8)  the number of impacts rij experienced by the pulp is given by: Hi =  OJLU  r  (2.9)  and the specific energy per impact e by: e= — rii  (2.10)  where: \x is the radial coefficient of friction, p is the tangential coefficient of friction, a — 4 T  t  for a single-disc refiner or 2 for a double-disc refiner, E is the specific energy, q is the inlet consistency of the pulp, L is the latent heat of steam, to is the rotational speed of the refiner, r i , T2 are the inner and outer radii of the refining zone respectively, b is the number of bars per unit arc length, and j = 1 for a single-disc refiner or 2 for a double-disc refiner. These equations allow an energy based characterization of the refining process in a chip refiner, similar to that proposed by Leider and Nissan for a pulp refiner, where equivalent pulp properties are expected from fibres subject to equal number of impacts and intensity of impact. Miles and co-workers have shown in numerous studies that the number and intensity of impacts can be used effectively to make quantitative predictions about the refining process [12, 13, 14, 15, 16]. In addition to the specific energy per impact e, Miles has defined a second parameter to represent refining intensity. This is the specific refining power e, which is simply the rate of energy transfer to a unit mass of fibres. Miles has shown that different pulp properties correlate well with either e or e. For example, pulp freeness, handsheet bulk, and breaking length (a measure of the tensile strength of a sheet of paper) were shown 10  to correlate well with specific energy per impact, while pulp rejects, L-factor (a parameter used to characterize average fibre length), and sheet opacity were shown to correlate better with specific refining power [14]. These two measures of impact intensity point to the major drawback of describing the refining process in terms of the energy applied to fibres: it does not say how the energy influences pulp properties. Miles and Karnis have alluded to this drawback in the following passage [15]: "... a qualitative knowledge of the effects of [refining] variables on pulp properties will result in an improved and more uniform quality through better control of the refining process." To obtain this qualitative understanding of the refining process, attention needs to be given to the forces exerted on the pulp fibres, and the effects that these forces have on fibre morphology and stiffness.  2.3  Force-Based Characterization  The preceeding theories have considered the energy imparted to individual fibres as they pass through the refiner. As mentioned earlier, it is the specific forces acting on the fibres, and not simply the total energy applied, that will determine the resulting changes in fibre and pulp properties. Thus, it may be more appropriate to develop theories of refiner characterization that are based on these forces. Page has suggested that the average stress-strain history of an individual fibre is necessary for a complete description of the refining process. He has proposed a theory of refining that considers a typical floe trapped between the bars of a refiner to be acted on by three forces: a normal force, a shear force, and a ploughing force. The ploughing term develops because the leading bar edge has to "plough" through the uncompressed part of the floe in front of it [2]. He has suggested that "further development of such a theory might well 11  explain many of the hitherto unexplained phenomena of [refining]." Martinez took up the challenge of developing a force-based approach to refiner characterization by considering fibres in the refiner to be entangled with each other, forming floes. The floes are then worked between the bars of the refiner as separate units subject to normal and shear forces [17, 18]. This work was expanded by Martinez et al. and Batchelor et al. who developed theories to predict the normal and shear forces exerted on an ideal floe as it passes through the refiner [3, 4]. Their approach considers the floe to be spherical in shape with fibres uniformly distributed throughout. As the floe is compressed between the bars of the refiner there is an initial densification of the floe where the forces are negligible, until a critical thickness is reached at which point all the fibres are in contact with each other. From this point on there is a rise in the normal and shear forces as the floe is compressed further. For a spherical floe compressed from a thickness LQ to a thickness T with a compressed diameter 7L0 less than the width of the refiner bar, the peak normal force produced can be expressed as [3]: (2.11) where F is the peak normal force, 7r(7Z/ ) /4 is the compressed area of the floe, E is the 2  0  b  bulk modulus of elasticity, 7 is the ratio of the diameter of the compressed floe to the uncompressed floe, p is the bulk density of the fibres in the floe, aD is the interfibre spacing, and T is the gap between the refiner bars. This equation has the form: a = Ee b  (2-12)  where a is the normal stress on the floe and e is the strain on the floe. Thus, it assumes a linear stress-strain relationship where the strain is a function of the floe geometry and fibre properties. Note that throughout this thesis, values of stress and strain have been defined as positive when the body involved is under compression. This convention has been adopted because all the stresses considered here are compressive stresses and this avoids carrying 12  around negative signs in the results presented. Experimental results showed that Eqn. 2.11 accurately predicted the stresses on spherical nylon floes subject to strains from 0%-30%, over a range of refiner gaps and floe diameters.  2.4  Research Objectives  In this thesis, a number of interests arise from a consideration of the force model developed by Martinez et al. The first is the validity of the model at strains greater than 30%. Studies have shown that the bulk density p of a thick mat compressed under a static pressure a obeys the 'compressibility equation': p = Ma  N  (2.13)  for a wide range of natural and synthetic fibres, where M and N are empirical constants for a given fibre type [19, 20, 21]. If the action of a refiner trapping a floe between passing bars can be considered analogous to the compression of a pulp mat, as suggested by May et al. [22], then the relation given in Eqn. 2.13 might be applicable in refining theory. Since the strain on a floe is directly related to the compressed floe density, Eqn. 2.13, if applicable over a wide range of strain, implies that the stress-strain relationship is non-linear. This is in contrast to the linear model proposed by Martinez et al. If this wide range of strain is relevant to refiner characterization, then a different model might be needed to determine the forces expected during refining. The second area of interest is whether or not the theory of Martinez et al. can be applied to pulp fibres. The experiments performed by Martinez and co-workers used floes consisting of nylon fibres, but no results were reported for floes consisting of pulp fibres. It is not expected that pulp fibres will behave substantially different than nylon fibres, but this has not been confirmed by experiment. The fact that pulp fibres have hollow lumens may contribute to a behaviour different from that of solid nylon fibres. 13  The third area of interest is the role that fines play in the generation of forces when a mechanical pulp floe is compressed between the bars of a refiner. Fines are small fibre fragments less than 75 jum in size, produced during refining. In a mechanical pulp, fines account for up to 40% of the total fibre mass in suspension. The model proposed by Martinez et al. considers the floe to be made up of fibres with a uniform fibre length. Thus, it is not immediately evident if the presence of a large amount of fines in the floe will alter the stress-strain relationship or not. It might be expected that fines simply fill in voids in the floe and contribute nothing to the generation of forces. However, under higher strains, where the void fraction is significantly reduced, fines may have some influence. The above discussion provides the basis for the objectives of the current research. They are: 1. to determine the stress-strain behaviour of pulp fibre floes compressed between passing bars in a refiner, over a wide range of strain, 2. to test the validity of existing models in explaining this behaviour, 3. to determine the effect of fines on the forces generated during refining, and 4. if necessary, to develop a new model to explain the observed stress-strain behaviour. The following chapters are devoted to meeting these objectives.  14  Chapter 3 EXPERIMENTAL To determine the forces experienced by floes trapped between passing bars of a refiner, and to determine the type of stress-strain behaviour governing these floes, experiments were performed under a wide variety of operating conditions in a laboratory single bar refiner. A description of the single bar refiner, the method of preparing the pulps and floes used in these experiments, and a summary of the experimental conditions is given in the following sections.  3.1  Single Bar Refiner and the Force Profile  A schematic of the single bar refiner (SBR) is shown in Figure 3.1.  It consists of two  opposing, horizontal plates on each of which a single bar is mounted. The bottom plate rests on a stiff turntable that can rotate either clockwise or counter-clockwise at a low speed (<3 rpm) and has an adjustable height. A small cube less than the height of the bar rests on the rotor adjacent to the rotor bar in order to hold a floe in a position to be trapped between the bars on the rotor and stator as they cross. A linear variable differential transformer (LVDT) mounted on the stator measures the small vertical deflection of the stator during floe compression caused by a bar passing. This yields a normal force, while a torque sensor also mounted on the stator measures the torque produced by the event, from  15  Torque Sensor LVDT  5  Stator  Gap i  Floe Floe Holder  Stiff B a s e (Adjustable Height)  Figure 3.1: Schematic of Single Bar Refiner  16  Rotor  which the shear force is obtained. Floes of different pulp types were placed on the floe holder and compressed between the bars on the rotor and stator at varying gap sizes. Both bars were 3 mm wide and made from nickel-hardened steel, a common material used in industrial refiner plates. A l l floes tested were approximately uniform in thickness and always wider than the bars on the SBR. The shear force and normal force experienced by the stator bar during a bar passing were recorded on a personal computer and the results analyzed to determine the stress-strain behaviour of the compressed floes. A typical force profile for a single floe is shown in Fig. 3.2. Here it is seen that as the bars begin to overlap, at an absolute rotor bar displacement of ~ 5.5 mm, the floe is trapped and the normal and shear forces begin to rise until the bars completely overlap, at an absolute rotor bar displacement of ~ 8.5 mm. From this point, the reverse situation occurs as the rotor bar continues past the stator bar and the force drops as the amount of bar overlap decreases to zero. The floe is released at « 11.5 mm. Note that the total width of the force profile is approximately two bars widths (6 mm), with the peak in both the normal and shear forces occuring one bar width (3 mm) into the profile, as expected for the compression of a uniform floe.  17  Normal Force Shear Force  Bar Displacement  [mm]  Figure 3.2: Force Profile of a Floe Compressed in the SBR. The floe is initially trapped when the bars first begin to overlap at ~ 5.5 mm. Both the shear and normal forces rise until complete bar overlap at ~ 8.5 mm, and then decrease until the floe is released at ~ 11.5 mm.  18  3.2  Pulp Preparation  Four different pulp types were tested in the SBR. These included a never-dried T M P , a neverdried C T M P tested as both a base pulp (BP) and a fines free (FF) pulp, and a previously dried bleached kraft pulp. The T M P was made from pure hemlock fibres, while the remaining pulps were a hemlock-balsam fir mix. The T M P was produced at P A P R I C A N ' s T M P pilot plant at the Vancouver laboratory from a single juvenile hemlock bole. The C T M P was obtained from a newsprint mill on Vancouver Island. The kraft pulp was reslushed from dried pulp sheets obtained from a B C coastal mill. In order to determine the effect of fines on the forces produced during refining, it was necessary to remove the fines from a mechanical pulp and compare the forces produced by compressing floes obtained from the base pulp and those forces produced by compressing floes obtained from the fines free pulp. The fines free pulp was obtained by placing 2.5 g of the B P C T M P into the standard British Handsheet Machine (BHM), diluting the sample to « 13 litres, and draining the suspension through the 150 mesh screen at the bottom of the B H M . This procedure was then repeated 29 times on the same sample until almost all of the fines were washed out of the pulp. The percentage by weight of fines retained in the pulp samples were determined using the Bauer-McNett fibre classifier according to C P P A Useful Method C.5U [23]. This apparatus consists of a series of tanks arranged in cascade that are fitted with screens of successively smaller mesh size. It is designed to separate a mechanical pulp sample into a number of fractions, each containing fibres of approximately the same length. Figure 3.3 shows the percent of fines remaining after each dilution/drain pass in the B H M . After 30 passes the fines content has dropped from 35% to 4%. A comparison of the Bauer-McNett fibre length distributions from the B P C T M P and the F F C T M P used in these experiments is given in Table 3.1. It is quite clear from the table that the fibre length distribution of the original pulp has been altered substantially by 19  40  Figure 3.3: Fines Removal Procedure. The plot shows the percent of fines remaining in the sample after each dilution/drain pass in the B H M .  Pulp Type Base Pulp Fines Free  ] 3auer-NIcNett  R14 23 40  14/28 14 17  28/48 13 20  ]faction % of Tota1] 48/100 100/200 P200 35 8 7 4 12 7.  Table 3.1: Bauer-McNett Base Pulp and Fines Free C T M P Fibre Length Distributions. After 30 dilution/drainage passes through the B H M , the fines (P200 fraction) have decreased from 35% to 4% of the total distribution.  20  the method of dilution and drainage in the B H M . Thus, even though the fines could not be removed entirely, any effect that fines have on the forces generated during refining should be detectable.  3.3  Floe Preparation and Handling  In order to determine the influence of various floe and fibre properties on the stress-strain behaviour inside the refiner, it was necessary to produce floes with well-defined geometries so that the strain on the floes could be readily determined. To accomplish this, the B H M was again employed to form a mat of pulp with a roughly constant thickness. This mat was then pressed onto a blotter and lifted off the B H M wire, using a procedure similar to that employed when making standardized handsheets [24]. The consistency of the mat was controlled to a limited extent by changing the number of blotters used in pressing the pulp on the B H M . Individual strips of varying widths were cut from the mat using a razor blade and compressed in the SBR. The compressed floe was then taken from the S B R and the portion of the floe that was actually caught between the bars was cut out using a razor blade and the remainder of the floe discarded. The trapped portion was readily evident by looking at the floe after the bars had crossed and usually approximated a rectangle very well. The length, width, and thickness of the caught portion of the floe were then recorded and the floe was immediately weighed in a Sartorius micro-balance accurate to 10 fj,g. The floe was later placed in a constant temperature and humidity room and allowed to air dry overnight, after which time its air dry (AD) weight was recorded and the floe discarded (the typical A D weight of a floe was around 2 mg). A series of A D floes were placed in an oven overnight and their total oven dry weights measured to obtained an average moisture content for the A D floes. This average moisture content was then used to determine O D floe weights and consistencies.  21  3.4  Summary of Experimental Conditions  A total of 269 floes were tested in the SBR. The majority of the floes tested were from the C T M P in order to establish the effect of fines on the forces produced, while the remainder of the floes tested were from the T M P and kraft pulps in order to determine any noticeable influence of the type of pulp on the forces generated. Floes from all pulps were tested over a range of refiner gaps, floe consistencies, and floe grammages (OD mass per unit area). A summary of the experimental conditions is given in Table 3.2 and a complete listing of all the floes tested by pulp type is given in Appendix A . A l l the results presented throughout this thesis with regard to forces are taken from the peak value of the force profile generated in the S B R - i.e. the point of complete bar overlap. This point was chosen to eliminate the variation in floe width, fixing it at a value of 3 mm (equal to the width of the refiner bars). In addition to testing floes in the SBR, each pulp type was tested in the Kajaani FS200 fibre analyzer to determine average fibre length and coarseness values. Coarseness was obtained by the method of Seth and Chan [25], which allows a precise mass of fibres to be fed to the analyzer for measurement.  The length-weighted fibre length and corresponding  fibre coarseness for each pulp type are listed in Table 3.3.  22  Pulp Type  n  T [mm]  BP CTMP FF CTMP TMP Kraft  85 109 36 39  Range 0.08-0.57 0.08-0.44 0.13-0.31 0.13-0.26  a [kPa] Range 43-228 30-209 41-224 28-351  e[%] Range 32-75 45-78 47-68 25-71  W [g/m ] a  Range 30-210 35-160 40-90 70-120  c [%] Range 9-33 9-31 12-18 15-47 f  Table 3.2: Summary of Experimental Conditions, n = number of floes tested, T = gap, a = normal stress, e = strain, W = floe grammage, and Cf = floe consistency.  Pulp Type BP CTMP FF CTMP TMP Kraft  Fibre Length  Coarseness  [mm] 1.61 1.64 1.52 2.09  [mg/km] 279 279 262 173  Table 3.3: Summary of Fibre Properties. Table shows length-weighted average fibre length and corresponding coarseness values for the four different pulps.  23  Chapter 4 STRESS-STRAIN RESULTS 4.1  The Stress-Strain Relationship  A plot of stress versus strain for both the B P and F F C T M P is shown in Fig. 4.1. From this plot it is evident that fines have no discernible effect on the stresses generated during refining. The scatter in both data sets is significant and the points overlap virtually throughout the entire range of strain tested. A similar plot is shown in Fig. 4.2 for kraft floes. Both Fig. 4.1 and Fig. 4.2 exhibit a similar non-linear stress-strain relationship. This is in contrast to the findings of Martinez et al. who indicated that a linear stress-strain relationship exists [3]. One point that may resolve this discrepancy is a consideration of the range of strain used in the experiments of Martinez et al. compared with the range used here. They tested nylon floes under strains of 0%-30% while the floes tested in this thesis were strained from 25%-75%; hence, the strain levels of Martinez and co-workers show up at the lower end of the strain levels used here. In this lower range, a linear relationship may be quite adequate to explain the behaviour of floes under strain inside a refiner.  This being the case, the immediate  question arises: What is the range of strain occuring in an actual refiner? This question is difficult to answer conclusively because the thickness of floes found in an industrial refiner is not well known; however, the following calculation may provide a fair estimate.  24  250  a B a s e Pulp A Fines Free  200  A  A  ^  150  AU A A  A  A  CO  CO  o CO  A  4> A  100  A£  ^ A A.*AA  *A  A A  A  A  A / a  A  A A  A  A  4  50  0 0.0  0.2  0.4  0.6  0.8  Strain  Figure 4.1: C T M P Stress-Strain Relationship. The plot shows stress vs strain for B P (solid points) and F F (outlined points) C T M P .  25  400  300  CCS  Q_  co 2 0 0 co <D CO  100 +  0  0.0  0.8  Figure 4.2: Kraft Stress-Strain Relationship. The plot shows stress vs strain for previo dried kraft pulp.  26  The mechanical pressure o  m  on a mat of pulp inside a chip refiner can be expressed as: T  ^  T  m  ±  J-  Af p b  where T  m  b  -K(T\ -  m  ^ rf)f p h  b  is the total mechanical thrust on the refiner plates, A is the refining zone area, f  b  is the instantaneous fraction of bars overlapping in the refining zone, p is the probability of b  a bar being covered with pulp, and r\,r2 are the inner and outer radii of the refining zone respectively. Weiss has presented results for a chip refiner indicating that f ~ 0.5 [26], and b  Stationwala et al. have reported bar coverage fractions from 0.5 - 0.85 for similar refiners [27]. Taking from Ref. [28] values of T = 59 k N (corresponding to a specific energy of 4.2 MJ/kg), m  7*1= 0.43 m, T2= 0.635 m gives mechanical pressures from 202 to 345 kPa using the values for f and p reported above. These values for mechanical pressure fall in the upper-range of b  b  stress, and therefore strain, observed for wood fibres in this thesis. Given the many different types of refiners, as well as the wide variation in refiner operating conditions, the range of strain in practice may be quite large; thus, the range of strain studied here may be a more appropriate range to consider when referring to the forces on floes in refiners. If this is the case, then a non-linear model must be used to describe the stress-strain behaviour.  4.2  Discussion of Strain  It should be noted that the strain referred to above does not represent the transverse strain on every (or indeed any) individual fibre but simply the nominal strain on the entire floe. To illustrate this point, consider the following floe model. The floe is made up of a series of fibre layers that are stacked on top of each other to form a three-dimensional mat structure. This is similar to models proposed by Kallmes and Corte [29] and Onogi and Sasaguri [30] for the structure of paper sheets. It is assumed that each layer is produced from a random deposition of fibres onto the previous mat structure and that every layer contains the same number of fibres. The total number of fibre layers 27  is given by the relation n = t jh i  )  where h is the height of a single fibre and ti is the floe  thickness. The probability of having i fibres covering any point in the floe area (P(i)) is simply the probability of obtaining exactly i successes in n Bernoulli trials: P{i) = nCi • v • (1 - P) ~ l  n  (4-2)  l  where nCi is all combinations of n objects taken t at a time and p is the probability of success for any single Bernoulli trial. The strain on any point of an individual fibre  is  related to the gap and the number of fibres covering that point: [ 1- £ 6r. = < 0  for ih > T . otherwise  t h  ,. (4.3)  The expected strain E(ef) on any fibre is then given by: 71  E(e ) = E euPitu) f  =  r  E  /TI  1- ^ I  -i  n t t • p* • (1 - P )  n _ <  (4-4)  noting that P(e .) = P{i). f  Eqn. 4.4 shows why the strain on any individual fibre will be much less than the strain on the entire floe: when fibres overlap, the probability of covering a point will be related to the fibre length:diameter (lf/d) ratio. As lf/d —> 1, the floe structure becomes like one of close-packed spheres and p approaches a limiting value of (ird /A)/d 2  2  ?» 0.79. Conversely, as  If/d—>oo, p approaches zero. For wood fibre floes in this thesis, values of p from 0.12 (for chemical pulps) to 0.5 (for mechanical pulps with high fines content) have been estimated, using floe mass balances and fibre projected areas (see Appendix B). Referring back to strain, for a floe 25 layers thick subject to 80% strain with p equal to 0.3, the expected strain on any single fibre given by Eqn. 4.4 is only 27%. This is an important point to keep in mind when discussing strain levels achieved in refiners - in general, the nominal floe strain will be much larger than the transverse strain on individual fibres.  28  4.3  Applicability of the Compressibility Equation  As mentioned in section 2.4, the bulk density of a pulp mat under compression can be related to the applied pressure through the empirical compressibility equation developed by Wilder (see Eqn. 2.13) [19]. Miles and May have suggested that the action of a refiner may be considered similar to the compression of a pulp mat. They have developed a relationship, similar to the compressibility equation, showing that the thickness of a pulp mat in compression is a power function of the applied pressure [22]. If their analogy is correct, it is logical to apply the compressibility equation to the floes studied here and see if the relationship does indeed hold for floes compressed by passing bars in a refiner. To do this we first re-arrange Eqn. 2.13 and take the logarithm of both sides to obtain: (4.5) where, as mentioned earlier, M and N are empirical constants for a given pulp type. Eqn. 4.5 indicates that a plot of log a vs logp should give a straight line with slope 1/N and intercept \og(l/MN).  A plot of loga vs logp is shown in Fig. 4.3 for all four pulp  types studied here. It can be seen from the regression equations in the figure that the data points for each type of pulp do fall relatively well on a straight line. Taking the regression constants from the equations shown, and back-calculating, gives the constants M and N in the compressibility equation. Values for these constants have been compared with values reported by Han [21] for a northern spruce kraft pulp and are listed in Table 4.1. From the table it is evident that the values reported here are in fair agreement with those published in the literature for pulp fibre mats. Note that the M - N correlation observed by Han has also been observed here - i.e. as M increases, N decreases [21]. The difference in absolute values is believed to be due to the different wood species, pulping conditions, and mat thicknesses.  29  Figure 4.3: Applicability of the Compressibility Equation. Plot shows log a vs logp for the four pulps studied. The equations and R values shown are those representing the regression lines through each data set. 2  30  Pulp Type Hemlock-Balsam Hemlock Hemlock-Balsam Northern Spruce kraft  FF CTMP BP CTMP TMP Pr. Dr. B l . kraft raw unbleached bleached  M 1.4 1.6 2.0 4.0 2.6 3.0 4.5  N 0.43 0.41 0.36 0.26 0.40 0.39 0.37  Table 4.1: Comparison of the Constants M and N in the Compressibility Equation p — Ma . Data for northern spruce kraft taken from Han [21]. M has units [kg/m ]/[Newtons/m ] and N is dimensionless. 3  4.4  2  N  Discussion of Stress-Strain Results  In the model proposed by Martinez et al, the primary mechanism responsible for the generation of forces on floes was individual fibre compression. In contrast, the primary mechanism believed to be occuring in situations where the compressibility equation applies is fibre bending. In considering the forces on floes inside a refiner the actual mechanism is most likely to be some combination of both of the above mechanisms. To illustrate this point, consider Fig. 4.4 which shows a vertical cross-section through a floe in both the uncompressed and compressed states. The cross-section is taken to pass through the center of an individual fibre (shown in grey). The ellipses surrounding the grey fibre represent fibres in the floe that cross the plane at an arbitrary angle. For simplicity, the fibres shown all cross the plane at the same angle, and they are shown to lie in specific layers in the uncompressed floe. The floe shown is five fibre diameters in thickness. When the floe is compressed to 60% strain (two fibre diameters thick) the bottom configuration shown in Fig. 4.4 results. Here, two mechanisms contribute to the generation of normal forces: in the region labeled A , a normal force develops through tranverse compression of the fibre wall, in the region labeled B , a normal force develops through fibre bending, and in the regions labeled C, normal forces develop through a combination of fibre bending and transverse compression of the fibre wall. The relative contributions of each of the two mechanisms will depend on the number of 31  Uncompressed  60% Strain  Figure 4.4: Generation of Normal Forces in a Floe. The top part of the figure shows a vertical cross-section through an uncompressed floe, passing through the center of a fibre (shown in grey). The bottom part of the figure shows the same cross-section of the floe compressed to 60% strain. Normal forces develop through different mechanisms. Region A develops a normal force through transverse compression of the fibre wall. Region B develops a normal force through fibre bending. Regions C develop normal forces through a combination of fibre bending and fibre wall compression.  32  layers in the floe and the level of strain. As the number of layers in the floe is increased, the probability that a sufficient number of fibres overlap in a single place to produce transverse compression will become smaller. Conversely, as the strain is increased for a floe with a given number of layers, more points in the floe will contribute to the normal force through fibre compression (for example, in Fig. 4.4 if the strain is increased above 60%, region B will become a region C because the fibre wall will start to compress from this level of strain onwards). Consider again Fig. 4.3. Here, it is seen that the compressibility equation appears to hold for all the pulps studied, however there is a distinct separation between the kraft data points and all the other data points. This might be explained by the fact that the kraft pulp is a chemical pulp, while the others are mechanical pulps, and so it might be expected that the shorter stiffer mechanical pulp fibres behave differently than the comparatively longer more flexible kraft fibres. A n alternative explanation may be found by considering that the kraft fibres have been previously dried. In addition to being longer and more flexible, the kraft pulp fibres might also be expected to have collapsed under drying stresses. For a fibre with a diameter of 30 jim. and a wall thickness of 3 /im, the ratio of the uncollapsed to collapsed fibre height will be 5:1. If this is the case, then for floes of equal thickness, the kraft floe will have roughly five times as many fibre layers as a mechanical pulp floe (where fibres are uncollapsed). Thus, the proportion of the total force due to fibre compression for a kraft floe will be significantly less than that for a mechanical floe. This implies that the differences between the data sets of Fig. 4.3 might be attributed to the relative amount of fibre compression force, in addition to fibre length and stiffness. It also implies that fibres in floes subjected to similar levels of strain are being treated differently in different pulp types. The role of repeated transverse fibre compression in decreasing fibre stiffness has not been looked into; however, Tarn Doo and Kerekes have demonstrated that repeated lowamplitude fibre flexing does produce effects similar to beating pulp in a P F I mill [31]. This  33  suggests that fibre bending plays a large role in decreasing fibre stiffness during refining. In the next chapter, a new mathematical model that includes both mechanisms of fibre bending and fibre compression will be developed for the forces on floes inside refiners.  34  Chapter 5 THE FORCE MODEL When a floe of fibres is trapped between passing bars in a refiner and the floe thickness is greater than the gap between the bars, there will be a net compressive force and a net shear force exerted on the floe. The shear force S is modeled as a linear function of the normal force F, with the constant of proportionality being the dynamic coefficient of friction fx: (5.1)  S = (j.F  Because of this simple relation between the shear force and the normal force, this chapter will be concerned only with the formulation of the normal force. The compressive normal force will have two components: the first component will involve forces resulting from fibre bending, while the second component will involve forces related to fibre compression (see Fig 4.4). The following semi-empirical model is derived under the assumption that these two components can be superimposed to give the net compressive force, and hence compressive stress, on the floe. The resulting expression for the normal force will then be the following: F =F + F b  c  (5.2)  where Fb and F are the bending and compressive components respectively. The development c  of each of these two components will be considered separately.  35  5.1  Normal Force Component Resulting From Fibre Bending  If the floe is considered to be made up of a number of beam segments under various load and support conditions, then the normal force component resulting from fibre bending can be derived using the beam equation: P = ^  (5-3)  where P is the load on a beam of length I with stiffness EI deflected an amount 5, and K is b  a constant that depends on the loading and support conditions - e.g. for a simply supported beam that is centrally loaded K is 48, while for a clamped beam that is centrally loaded K b  b  is 192. In general, K increases with the complexity of the loading. b  As the floe is compressed, the number of contact points per fibre and hence the number of beam segments in the floe, will increase. Limited data indicates that the number of contacts per fibre increases in direct proportion to the floe density [32, 21]. This is expressed here as: n = Cp c  (5.4)  where n is the number of contacts per fibre, p is the bulk density of the floe, and C is a c  constant. Assuming that fibre-fibre contacts are distributed alternately on both sides of a single fibre, the number of beam segments in the fibre n will be given by: s  » . » ^ = f  (5-5)  and each segment will have a length given by: l^ -L l  =  n  s  where If is the average fibre length. 36  ^L Cp  (5.6)  The total number of fibres in the entire floe n / is given by a mass balance: n = ^ wl  (5.7)  f  f  where m is the total OD floe mass and w is the fibre coarseness. To determine the total normal force due to fibre bending, the beam equation is applied to every beam segment of every fibre in the floe as the floe is compressed from its initial thickness to a thickness equal to the gap between the refiner bars. Figure 5.1 shows how a single fibre contributes to the total bending force component. In situation 1, the floe is unstressed and the fibre rests somewhere in the middle of the floe in contact with three other fibres. In situation 2, the floe has been compressed a small distance dy, where y is defined as the difference between the initial floe thickness (U) and the instantaneous floe thickness (t). Here, the fibre bends a small amount rjdy producing a small force dF, and at the same time comes into contact with more fibres (shown lighter in the figure). The parameter rj is a constant between 0 and 1 representing the average fraction of the distance dy that an individual beam deflects when the entire floe is compressed by an amount dy. In the next increment of compression, the fibre will produce three incremental forces instead of one, because of the new contacts created in the previous step. This, of course, is an idealization of what is actually occurring in the floe, since the fibre-fibre contacts will not nicely alternate on both sides of the fibre at fixed intervals, nor will each beam segment deflect the same amount rjdy. It also assumes that fibres are much easier to bend than to collapse. However, given that the floe consists of thousands of fibres it is hoped that, on average, the situation depicted in Figure 5.1 will result in similar forces to those actually produced. Applying the beam equation to every beam segment in the floe, gives the following incremental expression for the bending component: dF = n n b  f  s  -qdy  (5.8)  Because both the number of contacts per fibre and the length between contacts depend 37  Figure 5.1: Incremental Bending Force. Situation 1: individual fibre in a floe and its contacts with other fibres. Situation 2: the same fibre after the floe has been compressed a distance dy. Here, the fibre has been bent a small amount r/dy producing a small force dF and the number of contacts with other fibres has increased (new contacts shown lighter).  38  on the instantaneous density (and therefore thickness) of the floe, the total bending force can be obtained by integration. Expressing the density of the floe, number of contacts per fibre, and average segment length, in terms of the compressed distance y, allows Eqn. 5.8 to be expressed as: ,„ C K EImW , b = , 4 / , -nVdy A  A  b  dF  (5.9)  where W is the floe grammage (mass/area). Integrating Eqn. 5.9 from 0 to ij — T gives the total component of the normal force due to fibre bending: •nC*K EImW  1 1 7* ~  A  b  F  h  (5.10)  Eqn. 5.10 can be re-written in terms of stress by dividing through by the floe area: T]C K EIW 4  Ob =  5  b  _1_ _ 1  4&wlj  (5.11)  where a is the component of the floe normal stress due to fibre bending. b  5.2  Normal Force Component Resulting From Fibre Compression  To determine the component resulting from fibre compression the floe is considered to be made up of a series of n layers, each layer one fibre thickness in height. Thus, for a floe with unstressed thickness U there will be n = U/h layers where h is the height of a single fibre. For a fibre modeled as an uncollapsed tube, h will simply be the fibre diameter d, while for a fibre modeled as a collapsed tube h will be equal to twice the fibre wall thickness 2t . w  Each layer is made up of fibres that are considered to behave as springs when under transverse compression. The combination of all the springs in a single layer acting in parallel produces an average spring stiffness per unit area K  c  (see Fig 5.2). The combination of all  the layers then acting in series results in an equivalent spring stiffness for the entire floe  39  Each layer has a stiffness per unit area, K ^ c  2L  Compressed  Uncompressed  Figure 5.2: Normal Force Component Due to Fibre Compression. The floe as viewed as a layered structure where each layer consists of many springs acting in parallel.  40  equal to K Ao/n c  (recall that springs in series add like resistors in parallel), where A is the 0  total nominal area of the floe. Using the familiar linear spring relation F = kx, the total force resulting from fibre compression, for a floe compressed from a thickness £; to a thickness T, is given by:  =m^ii  Fc  .  (5 12)  n  Note that K has units of N / m / m = N / m . 2  3  c  Eqn. 5.12 can be re-written in terms of stress: K (U - T)  (5.13)  C  n where a is the component of the nominal floe stress due to fibre compression. c  5.3  Discussion of the Force Model  Expanding Eqn. 5.2 using Eqns. 5.10 and 5.12 gives the complete expression for the normal force exerted on a floe compressed between passing bars of a refiner: rjC K EImW A  F =  1  4  b  7^3  +  K A {U-T) C  (5.14)  0  n  which can be re-written in terms of the floe normal stress a: r]C K EIW A  a =  1  5  b  T  3  1 ~ i  3  +  K {U - T)  (5.15)  C  n  This expression contains unknown parameters rj, C, K , EI, and K that need to be b  c  determined experimentally. To determine values for these parameters, Eqn. 5.15 can be re-arranged in the following manner: na (U-T)  r]C K EIW n 4  5  b  ASwlj{U-T)  41  1 ^3  1  (5.16)  Letting a* = na/(U - T), C* = r]C K EI 4  h  and B* = W n(T~ 5  3  - £~ )/[48w/)(t - T)] 3  z  allows Eqn. 5.16 to be expressed in a simpler form: (5.17)  <j* = C*B* + K  c  Eqn. 5.17 indicates that a plot of a* vs B* should give a straight line with slope C* and intercept K . But are the parameters C* and K constants or do they depend on other c  c  variables, such as pulp type, degree of fibre collapse, floe grammage, consistency, etc.? Consider the constant K first. This parameter will be related to the transverse stiffc  ness of an individual fibre. A conceptual model of the force-deflection relationship for an individual fibre is shown in Fig. 5.3. Here, the force rises steadily with fibre deflection until collapse of the fibre lumen occurs, at which point the fibre stiffness increases dramatically. If a fibre is modeled as an uncollapsed tube, the strain at which lumen collapse occurs e is c  given by: (5.18) For a fibre of diameter d ~ 30 /jm and wall thickness t  w  ~ 3 /im Eqn. 5.18 gives e equal to c  0.8. As mentioned earlier, the strain on an individual fibre in a floe is much less than the nominal strain on the entire floe. This means that an assumption of K equal to a constant c  should be relatively safe for a wide range of nominal floe strains (e < 0.8 for example) in which fibres are in the uncollapsed state. For fibres that are modeled as collapsed tubes - for example a previously dried kraft pulp - the fibres start off with a stiffness in the later region of Fig. 5.3 and again the assumption of a constant K is reasonable, although the value of K c  c  will be much larger in this case than for the case of uncollapsed fibres. Difficulties may arise with the model if intermediate degrees of fibre collapse occur in a single floe. Experiments are needed to determine if this potential difficulty will need to be addressed. Next, consider the parameter C*. This parameter depends on the individual fibre bending stiffness (EI), the relation between the number of contacts per fibre and the floe 42  Deflection [Arbitrary Units]  Figure 5.3: Force-Deflection Model for a Single Fibre in Transverse Compression. The fibre stiffness increases dramatically after lumen collapse.  density (C), the beam deflection constant (77), and the loading/support conditions within the floe (Kf,)- If one assumes that the effects of fibre bending stiffness and number of contacts per fibre at least partially cancel each other out - since, for a given floe density, a more flexible fibre will have a larger number of contacts per fibre - then the variation in C* might best be described by the variations in Kb and 77. One possible variable that might explain the behaviour of these parameters is the floe grammage W. Since the grammage, for a given floe thickness, specifies how close together the fibres are packed, it would determine how far a fibre could be deflected before coming into contact with other fibres. As well, for two floes of equal thickness but different grammage, the floe with the smaller grammage will carry the load on the floe in a smaller number of places - or stress chains - than the floe with the larger grammage. If the number of stress chains in the floe in some sense determines the degree to which individual fibres - i.e. beams - are simply supported as opposed to clamped for example, then the smaller grammage floe can be expected to have a different Kb than the floe with larger grammage, at a given strain and initial thickness. Keeping in mind this  43  intuitive description of what might be occurring in the floe, Eqn. 5.17 can be expressed as: a* = C\W)B*  (5.19)  + K  c  where the parameter C* is now a function of the floe grammage. If the relationship between C* and W can be established, then this relation can be inserted back into Eqn. 5.15 to give: C\W)W  5  a  J_ T3  _  _1 if  K (U - T) C  n  (5.20)  and the normal stress on any given floe can be predicted from measurable floe and fibre parameters and refiner operating conditions. The experiments performed in the S B R have allowed estimates of C\W)  and K  c  and these estimates have been used to compare the  predicted stresses from Eqn. 5.20 with the stresses measured by experiment. These results are presented in chapter 6.  44  Chapter 6 RESULTS A N D DISCUSSION Two parameters in the model developed in the previous chapter cannot be predicted a priori and need to be determined by experiment. These are the compressive stiffness parameter K and the bending component parameter C*. This chapter will go over the evaluation of c  each of these parameters, discuss the predicted stress results from Eqn. 5.20, and conclude with experimental results on coefficient of friction data.  6.1  Evaluation of K  c  The compressive spring stiffness per unit area K can be determined from a plot of a* vs B* c  at constant floe grammage. This is shown in Fig. 6.1 for the B P C T M P and in Fig. 6.2 for the F F C T M P . Tests on the T M P and kraft pulps did not include enough points at constant floe grammage to produce meaningful plots. From the figures, it is clear that the linear relationship predicted by Eqn. 5.19 holds quite well for a wide range of floe grammages. Linear regressions have been performed on each of the data sets of Figs. 6.1 and 6.2 and the average floe grammages and corresponding regression intercept estimates are shown in Table 6.1. Because the presence of fines did not have a significant effect on the stress-strain relationship for the floes tested here, it was expected that the B P C T M P and F F C T M P would have similar compressive stiffness constants.  45  1E+10  CO  JE  6E+09  • 40 g/m 60 g/m  2  80 g/m  2  o  90 g/m  2  x  180 g/m  2  • 200 g/m  2  o A  2E+09 0.0E+00  5.0E+26  1.0E+27  1.5E+27  . 4 / _ 1 71 n  B* [kgVm ']  Figure 6.1: a* vs B* for B P C T M P . The lines shown are linear regressions through each set of points at constant grammage.  46  7E+09 A  o / •  A  o  1  A  o  Oo la  o o  /&  / /•  */ A  /  /  u  I•  1*/  o  o/  o  /  / /o /  A  I  o  /  A  /•(/y  • /  A /  /  / A//  / / /*  4E+09 A  / *IA/  /?* 1  n  •  • 40 g/m  2  70 g/m  2  o A  o  1E+09 0E+00  2E+26  4E+26  80 g/m 155 g/m  6E+26  2  2  8E+26  B* [kg /m ] 4  17  Figure 6.2: a* vs B* for F F C T M P . The lines shown are linear regressions through each set of points at constant grammage.  47  Pulp  W  c  [N/m ] • 10~ 1.4 0.3 1.6 2.0 2.0 1.1  2  BP C T M P  Pulp  K  [g/m ] 40 60 80 90 180 200  3  9  K  W  c  [N/m ] • 101.6 0.9 2.0 3.9  [g/m ] 40 70 80 155  3  2  FF CTMP  9  Table 6.1: Summary of Regression Estimates for K . c  From the table it can be seen that a fair amount of scatter exists in the estimates for K , but the values for the B P and F F pulps do not show any consistent difference, which c  agrees with the earlier results. The combined values range from 0.3 • 10 — 3.9 • 10 N / m 9  9  3  with an average value of 1.7 • 10 N / m . More tests would be needed over a larger range of 9  3  floe grammages to obtain a better estimate for this parameter and to determine conclusively if any differences exist between whole and fines free pulps; however, it seems safe to say that a value for K from 1 — 2 • 10 N / m is a reasonable estimate. For the results that follow, 9  3  c  including the determination of a relationship between C* and W as well as the predictions of Eqn. 5.20, K will be taken as the average of the values reported above - i.e. 1.7 • 10 N / m . 9  3  c  Because the compressive spring stiffness per unit area is a new parameter introduced in this work, no reference is available for what its value should be. However, a rough estimate can be obtained. Using the model for a layered floe described in section 4.2, the contribution to the total normal stress due to fibre compression can be expressed in terms of the individual fibre stiffness per unit area. Limited work has been done in the area of transverse compression of individual fibres that may enable a comparison with the values obtained here. Let the individual fibre stiffness per unit area be denoted K f. c  The contribution of  the total normal stress due to fibre compression in a floe n layers thick compressed to a gap thickness T with a fibre height h, will be the summation of the compressive stresses  48  generated at each point in the floe covered by i fibres: c=  E  CT  K^^—^-nCi-v'-^-vT^  (6.1)  This stress should be equivalent to that given in Eqn. 5.13, which uses the compressive floe stiffness per unit area K . Thus, K may also be expressed as: c  c  Kn  ih — T  n  cf  (6.2)  T which is highly sensitive to the probability of fibre overlap p.  Nyren has studied the transverse compression of individual latewood spruce fibres and has reported that the average force per unit length required to collapse a fibre is 0.164 N / m m [33]. Taking the average diameter of a spruce fibre to be 27 /jm [34] gives a value of K f ranging from 1 — 4 • 10 c  11  N / m , depending on the value chosen for the fibre 3  wall thickness. If these values of K f are substituted into Eqn. 6.2, using a floe that is 25 fibre c  layers thick undergoing 60% strain, with p ranging from 0.2 - 0.4, then values of K ranging c  from 10 — 10 N / m are obtained, using round numbers. A comparison of the values of K 8  10  3  c  calculated here, with those estimated from experiment given in Table 6.1, shows that they are in reasonable agreement.  6.2  The C*-W Relation  As mentioned in section 5.3, the parameter C* might best be described as a function of grammage only. To determine if this is the case, a well-defined relation between C* and W must be found to exist. A glance at the slopes of the lines in Figs. 6.1 and 6.2 indicates that such a relationship may indeed exist: the slopes decrease as grammage increases. In order to define this relationship, the slope regression estimates are plotted against the average floe grammages in Fig. 6.3, where the regression lines have been forced through an intercept of  49  1.7 • 10 (the estimated value of K ). A power series expression has been fit to the points of 9  c  Fig. 6.3, indicating the desired relationship between C* and W: C* = 7- 10" IF 19  (6.3)  M  This relationship holds very well over the range of grammages studied here and the implications stemming from it are discussed below.  6E-17 --  £  3E-17 --  -K  O  O E + O O -I 0  1  1  0.05  1  0.1  0.15  h0.2  W [kg/m ] 2  Figure 6.3: C* vs W. The plot shows the regression estimates for C* vs W for the C T M P data of Figs. 6.1 and 6.2.  50  6.3  Predictions of the Normal Stress  To determine the validity of the proposed model in predicting the normal stress on a floe inside a refiner, the C*—W relation determined in section 6.2 was substituted into Eqn. 5.20 to give the final form of the stress equation for a floe compressed between the bars of a refiner: 7 • 10~ W 19  a—  3A  1 1 T " i 3  3  Ml^Il  .4)  (6  n  Since the bending stiffness parameter C* has been shown to depend primarily on grammage, the first term on the right hand side of Eqn. 6.4 should be valid for any pulp whatsoever. If this is the case, then any differences in normal stress between pulps should be attributable only to differences in the second term on the right hand side of Eqn. 6.4. For the pulps studied here, the never-dried T M P should have a K  value comparable to that  c  of the never-dried C T M P , since both pulps are from similar wood species and have similar coarseness values; however, the kraft pulp should have a higher K value than both the T M P c  and C T M P because it consists of collapsed fibres. But in the case of the kraft floes, the area coverage probability (see page 28) is expected to be low because the kraft fibres have high lf/d ratios. In addition, the kraft pulp floes will contain many more layers than the mechanical pulp floes of similar thickness. This means that for the kraft pulp floes studied here, the contribution of the total normal stress due to fibre compression is expected to be negligible in comparison to the component due to fibre bending. Fig. 6.4 shows the measured stresses versus the stresses predicted by Eqn. 6.4 for all of the floes studied in this thesis. For the T M P and C T M P data, K was taken as 1.7-10 N / m , 9  3  c  while the second term on the right hand side of Eqn. 6.4 was set to zero for the kraft data. Clearly, the data fall quite well on the ideal line of y=x, as indicated by the regression equation shown in the figure: y=1.02x with an R value of 0.78. The same data are shown 2  again in Fig. 6.5 but separated by pulp type.  51  400  Figure 6.4: Measured Stress vs Predicted Stress. The plot shows the stresses measured by experiment vs the stresses predicted by Eqn. 6.4 for all floes of the four different pulp types.  52  400  0  100  200  300  Predicted Normal Stress [kPa] Figure 6.5: Measured Stress vs Predicted Stress: B y Pulp Type. The plot shows the stresses measured by experiment vs the stresses predicted by Eqn. 6.4 for each of the four different pulp types.  53  Here the line in the figure represents the ideal predictive model with slope equal to unity. It can be seen from the figure that each pulp type individually holds to the prediction of Eqn. 6.4 quite well, indicating that the C* — W relation determined for the C T M P does indeed apply to the T M P and kraft floes as predicted. Two apparent discrepancies should be noted here. For higher stresses (a > 200 kPa), the kraft data consistently lie above the y=x line. This indicates that the model is under predicting the stress values for kraft pulp in this area. One reason for this, is that the second term on the right hand side of Eqn. 6.4 was set to zero for the kraft floes. Higher stresses would indicate higher floe strains which means that fibre compression may no longer be insignificant compared to fibre bending in this region. Adjusting the predictions to include fibre compression might resolve this discrepancy. A similar trend is also evident in the T M P data: the model appears to under predict the stresses above 100 kPa. It is difficult to say exactly why this is occurring. One reason may simply be that not very many floes have been tested for T M P and it is simply chance that they fall above the line in Fig. 6.5. Another more complicated reason may come from the fact that the T M P was derived from juvenile wood. This would indicate that the T M P fibres have thin walls that may have collapsed during refining. If this is the case, then the value of K used in Eqn. 6.4 would be smaller than its actual value, but likewise, the number c  of fibre layers would also be too small. These two effects would tend to cancel each other out depending on how much greater the collapsed fibre spring stiffness would be compared to the increase in number of fibre layers; in any event, these thoughts are very speculative. To identify the true reason for the discrepancy, more detailed knowledge of the fibre dimensions, degree of collapse, and corresponding fibre stiffness values would be required. Overall, the model shows good agreement with experiment and indicates that both mechanisms of fibre bending and fibre compression are needed to accurately describe the forces produced during refining. Substituting the relevant data for individual floes from  54  Appendix A into Eqn. 6.4 allows a comparison of the relative contribution to the normal stress from fibre bending and from fibre compression. For the mechanical pulp floes studied here, the compressive component accounts for an average of 35% of the total normal stress, while the bending component accounts for an average of 65% of the total normal stress. Depending on the individual floe and level of strain, the bending component can account for 45% to 81% of the total normal stress. The proportion of each component is determined by the floe grammage, the level of strain, and the floe stiffness. More experiments are needed to determine the full range of grammage over which Eqn. 6.3 is valid, as well as whether it is indeed independent of fibre stiffness.  Likewise,  better estimates of the stiffness of floes and/or fibres in transverse compression would help to explain more conclusively the small discrepancies found in the data for T M P and kraft floes. Such estimates would also be useful in determining the precise role of fines in the forces generated in refining: from the data taken here, it appears that fines do not produce any noticeable effect.  6.4  Effect of Consistency  The consistency of the pulp suspension does not show up anywhere in the proposed model. This implies that consistency does not have any effect on the normal forces produced during refining.  In the experiments performed here, this is indeed the case.  Over the range of  floe consistency studied (9% - 47%), there were no differences between the normal forces produced in floes of similar thickness and strain but with dissimilar consistency. However, it should be noted that this model does not include hydrodynamic effects that could become important at high strain rates and lower consistencies. In such circumstances where water may be rapidly expelled from the floe, there may be an important contribution to the normal force from hydrodynamic forces.  55  6.5  Coefficients of Friction  In chapter 5 it was suggested that the shear force on a floe was related to the normal force through the coefficient of friction /x. This was substantiated by the force profiles generated during the S B R tests, which showed that the shear force profile has a shape that is almost identical to that of the normal force profile (see Fig. 3.2). To determine coefficient of friction values for the different pulps, the ratio of the shear to normal force was taken for thirty points around the peak of the force profiles. These thirty points were then averaged to get one data point for each floe. Multiple points were chosen from each profile to reduce errors due to noise in the signals; they were chosen around the peak because the signal to noise ratio was highest in this area. Then the values from all the floes were averaged to determine the coefficient of friction for a given pulp type. Table 6.2 shows the average values and standard deviations obtained by this method. The presence of fines does not influence the coefficient of friction as shown by the identical values of 0.32 for both the B P and F F C T M P . However, the method of pulping does have some influence: there is almost a 20% drop in the coefficient of friction for the T M P and kraft pulps compared with the C T M P . This effect is probably due to differences in the surface properties of fibres in these different pulps. Miles and Karnis have indicated that fibre morphology can affect the value of the friction coefficient [15] but little work has been done in this area. In the case of the bleached kraft pulp, the lignin content on the fibre surface will be much lower than that for the unbleached C T M P . In the case of the T M P , it may be simply the lack of balsam fir fibres that contributes to fibre surface properties different from the C T M P but a detailed analysis of the fibre chemistry would be needed to determine conclusively if this is true. Given that the value of the friction coefficient will determine the amount of energy consumed in the refining process, a better understanding of the exact properties that influence this parameter could be of great benefit to the industry.  56  Std.  Pulp Type BP CTMP FF CTMP TMP kraft  0.32 0.32 0.27 0.26  0.03 0.03 0.02 0.02  Table 6.2: Coefficients of Friction. Table shows the average coefficient of friction /j and corresponding standard deviation for each of the four pulp types.  57  Chapter 7 CONCLUSIONS A N D RECOMMENDATIONS Most methods currently in use to characterize the mechanical action of refiners consider the energy imparted to individual fibres as they pass through the refiner. Although these methods are useful to characterize refiners based on energy-quality relationships, for the most part they do not get at the physical mechanisms which underlie the refining process. These physical mechanisms - the forces - may offer greater insight into refiner characterization by indicating the manner in which energy is being applied to the pulp fibres. Knowing which forces are the important ones for fibre development and which ones are simply benign or even detrimental to fibre development, may enable researchers to further improve refining efficiency and pulp quality. A new model has been developed here to relate the normal and shear forces on a floe compressed between two passing bars in a refiner to fibre and Hoc properties. Experiments have demonstrated that, over a large range of strain (25%-75%), floes display a non-linear stress-strain relationship, and calculations have indicated that the range of strain found in refiners in practice may be quite large. The model assumes that the normal stress can be divided into two components: one component is a result of fibre bending and the other is a result of transverse fibre compression. Calculations have indicated that, for mechanical pulp floes, the bending component accounts  58  for 65% of the total normal stress on average, but this fraction can range from 45% to 81% depending on the individual floe and level of strain.  For a previously dried kraft pulp,  bending was shown to account for nearly all of the total normal force produced. The most important parameter in determining the bending component of the normal force is the floe grammage, while the most important parameter governing the compressive component is the transverse fibre stiffness. The model has been shown to hold for a T M P , a fines free C T M P , a whole C T M P , and a previously dried bleached kraft pulp, all made from similar softwood fibres. The presence or absence of fines in the floe did not have any discernible effect on the forces generated during refining, and similarly, at the very low strain rates studied here, floe consistency in the range of 9% to 47% did not have any influence. The shear force measured in these experiments was directly proportional to the normal force: the constant of proportionality being the coefficient of friction.  The coefficient of  friction was around 0.3 for the floes studied, and the type of pulp had a slight influence on this parameter. Differences in fibre surface properties between pulps probably explain the differences in coefficient of friction. The presence or absence of fines in the C T M P pulp did not have any effect on the coefficient of friction. Further work is required to determine the full range of grammage over which the relation for the bending component of the normal force holds, as well as whether this relation holds for all pulp types as suggested here. Finally, the experiments have indicated that the compressive stiffness per unit area is in the order of 10 N / m for never-dried mechanical pulp floes. 9  3  More work is needed to determine independently the transverse stiffness of floes and their constituent fibres, and to explain how these two stiffnesses are related through a more detailed knowledge of the floe structure.  59  NOMENCLATURE aD  interfibre spacing in a spherical floe, where D is the fibre diameter  a  constant equal to 2 for a double-disc refiner or 4 for a single-disc refiner  A  refining zone area  A  nominal floe area  b  number of bars per unit arc length  B  bar width  B*  parameter related to bending force  Ci  inlet consistency  C  C-factor  C*  parameter related to fibre bending stiffness  Cf  consistency  CEL  cutting edge length  d  fibre diameter  D  groove depth  e  specific energy per impact  e  specific refining power  E  specific energy  0  E  average energy per impact  EI  fibre bending stiffness  e  nominal floe strain  t  60  e  fibre  c  collapse strain  tf  individual fibre strain  fb  fraction of bars overlapping in the refining zone  F  normal force  dF  incremental change in force  Fb  normal force component due to fibre bending  F  normal force component due to fibre compression  F  mass flow rate  G  groove width  7  ratio of the compressed to uncompressed spherical floe diameter  c  m  fibre  h  height  /  intensity of a bar impact  j  constant equal to 2 for a double-disc refiner or 1 for a single-disc refiner  Kb  bending stiffness constant  K  floe compressive spring stiffness per unit area  c  Kf c  fibre  compressive spring stiffness per unit area  I  length of a fibre segment  //  length-weighted average fibre length  L  latent heat of steam  Li  length of refining zone increment  LQ  diameter of a spherical floe  TO  oven dry mass of a floe  TO/  mass of fibres in a layer of a floe  M  empirical constant  Mf  average mass of a fibre  MEL  modified edge load  61  coefficient of friction average coefficient of friction n  number of fibre layers in a floe  n  number of contacts per fibre  n  f  number of fibres in a floe  ni  number of fibres in a layer of a floe  n  number of beam segments in a fibre  N  empirical constant  c  s  N  number of bar impacts per unit mass of pulp  V  (fibre bending deflection) to (floe compressive deflection) ratio ( 0 < 77 < 1)  P  probability of fibre overlap in a floe  Pb  probability of a refiner bar being covered with pulp  P  net instantaneous power of refining  P  load on a beam  4>  average bar angle  r\  inner radius of the refining zone  m  outer radius of the refining zone P  bulk density of a compressed floc/pulp mat  Pw  density of water  S  shear force  SEL  specific edge load  a  normal stress on a floc/pulp mat  a*  parameter related to the normal stress on a floe  <?b  normal stress component due to fibre bending  o  normal stress component due to fibre compression  0~m  mechanical pressure  c  62  ti t  w  T  uncompressed/initial floe thickness fibre  wall thickness  gap between the bars of the rotor and stator  T  mechanical thrust load on a refiner plate  r  residence time  w  fibre coarseness (mass/length)  W  grammage (mass/area)  ui  refiner rotational speed  y  difference between initial floe thickness and instantaneous floe thickness  dy  incremental change in floe thickness  z  number of refiner bars  m  63  BIBLIOGRAPHY [1] H.W. Giertz. The effects of beating on individual fibres. In F . Bolam, editor, Fundamentals of Papermaking Fibres, Transactions of the Symposium held at Cambridge, pages 389-409. Technical Section, British Paper and Board Makers' Association, September 1957. [2] D.H. Page. The beating of chemical pulps - The action and the effects. In F. Bolam, editor, Fundamentals of Papermaking: Transactions of Fundamental Research Symposium held at Cambridge, volume 1, pages 1-38. Fundamental Research Committee, British Paper and Board Makers' Association, September 1989. [3] D . M . Martinez, W . J . Batchelor, R . J . Kerekes, and D. Ouellet. Forces on fibres in lowconsistency refining: Normal force. Journal of Pulp and Paper Science, 23(1):Jll—18, 1997. [4] W . J . Batchelor, D . M . Martinez, R . J . Kerekes, and D. Ouellet. Forces on fibres in lowconsistency refining: Shear force. Journal of Pulp and Paper Science, 23(l):J40-45, 1997. [5] W . Brecht. A method for the comparative evaluation of bar-equipped beating devices. TAPPI, 50(8):40-44A, 1967. [6] S. Hietanen and K . Ebeling. Fundamental aspects of the refining process. Papen ja Puu, 72(2):158-170, 1990.  64  [7] F.P. Meltzer and P.-W. Sepke. New ways to forecast the technological results of refining.  In Third International Refining Conference, Atlanta, G A , March 1995. P I R A  International. [8] P.J. Leider and A . H . Nissan. Understanding the disk refiner.  TAPPI, 60(10):85-89,  1977. [9] R . J . Kerekes. Characterization of pulp refiners by a C-factor. Nordic Pulp and Paper Research Journal, 5(1):3—8, 1990. [10] R . J . Kerekes, M . Clara, S. Dharni, and M . Martinez. Application of the C-factor to characterize pulp refiners. Journal of Pulp and Paper Science, 19(3):J1253-130, 1993. [11] L . V . Welch and R . J . Kerekes. Characterization of the P F I mill by the C-factor. Appita Journal, 47(5):387-390, 1994. [12] K . B . Miles and W . D . May. The flow of pulp in chip refiners. Journal of Pulp and Paper Science, 16(2):J63-71, 1990. [13] K . B . Miles. A simplified method for calculating the residence time and refining intensity in a chip refiner. Paperi ja Puu, 73(9):852-857,1991. [14] K . B . Miles. Refining intensity and pulp quality in high-consistency refining. Paperi ja Puu, 72(5):508-514, 1990. [15] K . B . Miles and A . Karnis. The response of mechanical and chemical pulps to refining. Tappi Journal, 74(1)157-164, 1991. [16] K . B . Miles, W . D . May, and A . Karnis. Refining intensity, energy consumption, and pulp quality in two-stage chip refining. Tappi Journal, 74(3):221-230, 1991. [17] D . M . Martinez and R . J . Kerekes. Forces on fibres in low-consistency refining. Tappi Journal, 77(12)119-123, 1994. 65  [18] D . M . Martinez. The energy expended on pulp fibres during low consistency refining. PhD thesis, Department of Chemical Engineering, University of British Columbia, Vancouver, B . C . , 1995. [19] H.D. Wilder. The compression creep properties of wet pulp mats. TAPPI, 43(8) :715720, 1960. [20] R . L . Jones. The effect of fibre structural properties on compression response of fibre beds. TAPPI, 46(l):20-28, 1963. [21] S.T. Han. Compressibility and permeability of fibre mats. Pulp and Paper Magazine of Canada, 70(2):65-77, 1969. [22] W.D. May, M . R . McRae, K . B . Miles, and W . E . Lunan. A n approach to the measurement of pulp residence time in a chip refiner. Journal of Pulp and Paper Science, 14(3): J47-53, 1988. [23] Canadian Pulp and Paper Association, Useful Method C.5U. "Fibre classification Bauer-McNett method". [24] Canadian Pulp and Paper Association, Standard Testing Method C.4. "Forming handsheets for physical tests of pulp". 1950. [25] R.S. Seth and B . K . Chan. Measurement of fibre coarseness with optical fibre length analyzers. Tappi Journal, 80(5):217-221, 1997. [26] R. Weiss. Nonlinear axial vibrations on the rotor assembly of a wood-chip refiner. Technical report, U B C Pulp and Paper Centre, June 1992. [27] M.I. Stationwala, D. Atack, and A . Karnis. Distribution and motion of pulp fibres on refiner bar surface. Journal of Pulp and Paper Science, 18(4): J131-137, 1992.  66  [28] K . B . Miles and W . D . May. Predicting the performance of a chip refiner; a constitutive approach. Journal of Pulp and Paper Science, 19(6):J268-274, 1993. [29] O. Kallmes and H . Corte. The structure of paper. TAPPI, 43(9):737-752, 1960. [30] S. Onogi and K . Sasaguri. The elasticity of paper and other fibrous sheets.  TAPPI,  44(12):874-880, 1961. [31] P.A. Tarn Doo and R . J . Kerekes. The effect of beating and low-amplitude flexing on pulp fibre flexibility. Journal of Pulp and Paper Science, 15(l):J36-42, 1989. [32] T . C . Elias. Investigation of the compression response of ideal unbonded fibrous structures. TAPPI, 50(3): 125-132, 1967. [33] J. Nyren. The transverse compressibility of pulp fibres. Pulp and Paper Magazine of Canada, 72(10):81-83, 1971. [34] I.H. Isenberg, M . L . Harder, and L. Louden, editors. Pulpwoods of the United States and Canada, volume I. The Institute of Paper Chemistry, Appleton, Wisconsin, 3  rd  1980.  67  edition,  A P P E N D I X A: INDIVIDUAL F L O C DATA  68  BP CTMP Individual Floe Data Average Fibre Coarseness: 279 mg/km. Length-weighted Average Fibre Length: 1.61 mm. Peak Floc#  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40  Nominal  Nominal  Area Normalized  Air Dry  Oven Dry  Oven Dry  Compressed  Number  Normal  Normal  Length  Width  Thickness  Volume  Area  to Bar Width  Wet Mass  Mass  Mass  Consistency  Density  of Fibre  Grammage  Force  Gap  Strain  Stress  [mm] 4.91 5.38 4.44 4.89 4.47 5.72 4.69 4.52 5.05 5.65 8.35 7.47 8.16  [mm] 2.60 3.02 2.64 2.82 2.42 2.78 2.48 2.71 2.91 2.60 3.01 3.15 2.76 2.72 2.56 2.70 3.43 2.92 3.01 3.28 2.87 3.16 2.50 2.80 3.12 2.94 3.44 2.86 3.18 2.77 2.77 2.99 2.85 2.40 3.03 3.08 3.26 3.23 3.49 3.25  [mm] 0.22 0.21 0.19 0.24 0.17 0.26 0.21 0.18 0.28 0.20 0.43 0.38 0.45 0.37 0.32 0.41 0.46 0.35 0.69 0.67 0.66 0.43 0.69 0.69 0.70 0.68 0.76 0.76 0.72 0.70 0.68 0.58 0.66 0.63 0.73 0.82 0.71 0.83 0.81 0.70  [mm ] 2.8 3.4 2.2 3.3 1.8 4.1 2.4 2.2 4.1 2.9 10.8 8.9 10.1 11.2 4.5 8.7 13.8 7.3 13.9 23.3 12.7 10.7 8.7 17.4 20.2 12.2 19.3 17.6 18.0 13.0 14.1 14.5 13.7 5.2 19.9 23.1 19.4 27.4 30.2 19.7  [mm ] 12.8 16.2 11.7 13.8 10.8 15.9  [mm ] 14.7 16.1 13.3 14.7 13.4 17.2 14.1 13.6 15.2 17.0 25.1 22.4 24.5 33.5 16.5 23.6 26.2 21.5 20.1 31.7 20.1 23.6 15.2 27.0 27.8 18.3 22.1 24.3 23.6 20.1 22.4 25.1 21.8 10.4 26.9 27.5 25.1 30.7 32.0 26.0  [mg] 1.25 2.30 1.62 2.28 1.34 2.31 1.26 1.59 2.42 1.08 7.70 5.56 6.86 8.96 3.45 7.46 9.96 5.68 13.60 26.68 13.03 10.22 8.26 19.17 22.53 12.62 20.75 17.39 19.48 13.44 15.50 13.61 14.09 5.10 21.13 21.86 21.23 28.20 34.17 16.59  [mg] 0.43 0.61 0.45 0.53 0.42 0.62 0.46 0.49 0.59 0.62 1.44 1.35 1.33 1.89 0.89 1.36 1.99 1.44 1.64 2.97 1.69 2.19 1.16 2.34 2.69 1.67 2.37 2.16 2.34 1.75 1.97 2.39 1.98 0.80 2.67 2.78 2.70 3.29 3.72 2.85  [mg] 0.39 0.55 0.41 0.48 0.38 0.56 0.41 0.44 0.53 0.56 1.30 1.22 1.20 1.70 0.80 1.22 1.79 1.30 1.48 2.67 1.52 1.97 1.04 2.11 2.42 1.50 2.13 1.94 2.11 1.58 1.77 2.15 1.78 0.72 2.40 2.50 2.43 2.96 3.35 2.57  [%] 31 24 25 21 28 24 33 28 22 52 17 22 17 19 23 16 18 23 11 10 12 19 13 11 11 12 10 11 11 12 11 16 13 14 11 11 11 11 10 15  [kg/m ] 381 418 423 422 439 428 440 445 439 458 283 283 291 302 313 313 321 334 282 230 303 413 392 317 250 353 233 292 295 354 357 223 398 467 336 283 310 248 248 236  Layers  [g/m] 30 34 35 35 35 35 36 36 36 38 52 52 53 56 57 58 60 62 73 77 79 79 83 83 84 84 84 84 84 85 86 86 86 87 88 89 89 90 90 91  [N] 1.0 1.4  [mm] 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.18 0.18 0.18 0.19 0.18 0.18 0.19 0.19 0.26 0.34 0.26 0.19 0.21 0.26 0.34 0.24 0.36 0.29 0.29 0.24 0.24 0.38 0.22 0.19 0.26 0.31 0.29 0.36 0.36 0.39  0.64 0.61 0.57 0.66 0.53 0.68 0.61 0.55 0.71 0.58 0.58 0.52 0.59 0.50 0.43 0.55 0.60 0.47 0.62 0.50 0.61 0.55 0.69 0.62 0.52 0.65 0.53 0.62 0.60 0.66 0.65 0.34 0.67 0.70 0.64 0.62 0.59 0.56 0.55 0.45  [kPa] 68 87 120 116 75 99 100 103 119 118 48 59 53 63 62 79 88 97 77 46 91 170 149 97 57 134 54 98 84 148 141 43 174 228 93 94 100 51 54 50  11.16 5.51  7.85 8.74 7.16 6.71 10.58 6.71 7.86 5.05 9.01 9.25 6.09 7.38 8.09 7.85 6.71 7.47 8.38 7.26 3.45 8.98 9.15 8.36 10.22 10.67 8.68  3  2  11.6  12.2 14.7 14.7 25.1 23.5 22.5 30.4 14.1 21.2 30.0 20.9 20.2 34.7 19.3 24.8 12.6 25.2 28.9 17.9 25.4 23.1 25.0 18.6 20.7 25.1 20.7 8.3 27.2 28.2 27.3 33.0 37.2 28.2  2  3  6 6 5 7 5 7 6 5 8 6 12 11 13 11 9 12 13 10 20 20 19 12 20 20 21 20 22 22 21 21 20 17 19 18 21 24 21 24 24 21  !  1.6  1.7 1.0 1.7 1.4 1.4 1.8 2.0 1.20 1.32 1.30 2.11 1.02 1.85 2.31 2.09 1.55 1.46 1.83 4.00 2.26 2.63 1.57 2.45 1.20 2.38 1.98 2.98 3.15 1.07 3.79 2.36 2.51 2.58 2.51 1.57 1.73 1.30  BP CTMP Individual Floe Data (cont'd) Peak Floc#  41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85  Nominal  Nominal  Area Normalized  Length  Width  Thickness  Volume  Area  to Bar Width  [mm] 9.84 8.48 10.65 8.51 9.16 10.77 9.73 7.13 6.57 9.35 9.61 9.12 9.75 7.54 7.47 5.97 5.33 5.00 5.08 7.05 5.77 6.07 6.47 6.28 5.30 5.58 5.41 5.48 5.61 8.78 6.21 10.80 6.03 7.55 5.30 7.97 6.57 5.72 5.82 5.59 9.10 6.99 9.67 6.87 5.56  [mm] 3.02 3.10 3.35 3.11 2.99 3.21 2.89 2.66 2.87 2.81 3.58 3.13 3.07 3.17 2.86 3.24 2.80 2.93 3.28 2.89 3.20 2.90 3.07 3.04 2.90 3.18 3.08 3.20 3.01 3.32 3.26 3.11 3.06 3.12 3.13 2.83 2.83 2.98 3.04 3.09 3.50 2.91 3.03 2.99 3.21  [mm] 0.77 0.73 0.75 0.78 0.61 0.81 0.73 0.78 0.78 0.68 0.57 0.69 0.84 0.65 0.62 1.86 1.47 1.86 1.47 1.51 1.31 1.36 1.53 1.35 1.51 1.42 1.37 1.71 1.42 1.41 1.55 1.32 1.67 1.44 1.45 1.49 1.42 1.49 1.47 1.74 1.70 1.53 1.46 1.44 1.55  [mm ] 22.9 19.2 26.8 20.6 16.7 28.0 20.5 14.8 14.7 17.9 19.6 19.7 25.1 15.5 13.2 36.0 21.9 27.2 24.5 30.8 24.2 23.9  [mm ] 29.7 26.3 35.7 26.5  [mm ]  3  30.4  25.8 23.2 25.2 22.8 30.0 24.0 41.1 31.4 44.3 30.8 33.9 24.1 33.6 26.4 25.4 26.0 30.1 54.1 31.1 42.8 29.6 27.7  2  27.4  34.6 28.1 19.0 18.9 26.3 34.4 28.5 29.9 23.9 21.4 19.3 14.9 14.7 16.7 20.4 18.5 17.6 19.9 19.1 15.4 17.7 16.7 17.5 16.9 29.1 20.2 33.6 18.5 23.6 16.6 22.6 18.6 17.0 17.7 17.3 31.9 20.3 29.3 20.5 17.8  2  29.5 25.4 32.0 25.5 27.5 32.3 29.2 21.4 19.7 28.1 28.8 27.4 29.3 22.6 22.4 17.9 16.0 15.0 15.2 21.2 17.3 18.2 19.4 18.8 15.9 16.7 16.2 16.4 16.8 26.3 18.6 32.4 18.1 22.7 15.9 23.9 19.7 17.2 17.5 16.8 27.3 21.0 29.0 20.6 16.7  Air Dry  Oven Dry  Oven Dry  Compressed  Number  Wet Mass  Mass  Mass  Consistency  Density  of Fibre  Grammage  Force  Gap  [mg] 24.87 20.32 31.55 21.79 14.81 33.55 24.58 14.44 13.69 16.22 22.29 23.49 27.45 13.86 13.86 34.57 21.58 23.90 25.32 31.45 27.98 27.57 30.02 28.05 24.25 29.34 24.45 26.60 27.80 47.03 33.53 56.02 33.21 39.47 26.58 37.35 29.35 28.11 28.45 28.97 54.67 34.36 48.84 34.46 31.09  [mg] 3.01 2.67 3.69 2.74 2.85 3.60 2.94 1.99 1.99 2.79 3.66 3.05 3.33 2.70 2.48 3.40 2.82 2.88 3.30 4.07 3.73 3.56 4.02 3.92 3.16 3.70 3.48 3.68 3.55 6.19 4.30 7.20 3.99 5.14 3.62 4.94 4.08 3.75 3.90 3.82 7.16 4.62 6.70 4.74 4.29  [%]  [kg/m ] 291 377 276 297 242 259 280 431 439 247 247 332 318 262 269 336 326 339 378 377 348 347 347 353 354 398 359 360 400 333 404 334 412 342 374 343 415 418 346 419 350 356 356 362 378  Layers  [g/m ] 91 91 93 93 94 94 94 94 95 96 96 96 100 102 104 156 168 175 176 178 180 180 180 183 183 186 186 187 187 189 189 191 192 194 194 195 195 196 196 197 200 202 204 205 214  [N] 2.36 3.77 2.21 2.36 1.74 1.58 1.62 4.56 3.76 1.75 1.75 3.04 2.70 1.80 2.26 2.51 2.34 2.21 2.75 4.09 2.55 2.88 3.02 2.91 2.55 2.70 2.72 2.94 3.01 2.66 3.20 3.44 2.86 2.39 3.14 2.85 3.73 3.26 2.34 3.70 3.38 2.71 3.51 2.57 2.17  [mm]  [mg] 2.71 2.40 3.32 2.47 2.57 3.24 2.65 1.79 1.79 2.51 3.29 2.75 3.00 2.43 2.23 3.03 2.51 2.56 2.94 3.62 3.32 3.17 3.58 3.49 2.81 3.29 3.10 3.28 3.16 5.51 3.83 6.41 3.55 4.57 3.22 4.40 3.63 3.34 3.47 3.40 6.37 4.11 5.96 4.22 3.82  11 12 11 11 17 10 11 12 13 15 15 12 11 18 16 9 12 11 12 12 12 11 12 12 12 11 13 12 11 12 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12  3  23 21 22 23 18 24 21 23 23 20 17 20 25 19 18 55 44 55 44 45 39 40 45 40 45 42 41 51 42 42 46 39 50 43 43 44 42 44 44 52 51 45 43 43 46  Normal  2  Normal  0.31 0.24 0.34 0.31 0.39 0.36 0.34 0.22 0.22 0.39 0.39 0.29 0.31 0.39 0.39 0.47 0.52 0.52 0.47 0.47 0.52 0.52 0.52 0.52 0.52 0.47 0.52 0.52 0.47 0.57 0.47 0.57 0.47 0.57 0.52 0.57 0.47 0.47 0.57 0.47 0.57 0.57 0.57 0.57 0.57  Strain  Stress  0.59 0.67 0.55 0.60 0.37 0.55 0.54 0.72 0.72 0.43 0.32 0.58 0.63 0.40 0.37 0.75 0.65 0.72 0.68 0.69 0.61 0.62 0.66 0.62 0.66 0.67 0.62 0.70 0.67 0.60 0.70 0.57 0.72 0.61 0.64 0.62 0.67 0.69 0.61 0.73 0.66 0.63 0.61 0.61 0.63  [kPa] 80 148 69 92 63 49 55 213 191 62 61 111 92 80 101 140 146 147 180 193 147 158 156 154 160 161 168 179 179 101 172 106 158 106 197 119 189 190 134 221 124 129 121 125 130  FF CTMP Individual Floe Data Average Fibre Coarseness: 279 mg/km. Length-weighted Average Fibre Length: 1.64 mm.  Floc#  1 2 3 4 5 6 7 8  9 10 11 12  13 14 15 16 17 18  19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40  Nominal Area  Area Normalized to Bar Width  Length  Width  Thickness  Nominal Volume  [mm]  [mm]  [mm]  [mm ]  [mm ]  [mm ]  5.49 5.74 6.07 5.32 7.75 6.16 5.06 5.32 4.58 7.81 7.28 7.63 8.74  2.71 2.91 3.09 3.04 3.34 2.76 2.84 3.23 2.70 3.02 3.25 2.64 3.10 3.08 3.35 3.17 3.22 . 3.04 2.92 3.16 3.20 3.13 3.23 2.96 2.89 3.34 2.74 2.84 2.82 2.83 3.06 3.20 3.11 2.51 3.02 3.13 3.06 2.98 3.18 2.93  0.22 0.38 0.28 0.36 0.35 0.16 0.27 0.31 0.27 0.31 0.39 0.33 0.40 0.37 0.52 0.57 0.44 0.55 0.52 0.44 0.65 0.62 0.52 0.66 0.61 0.66 0.77  3.3 6.3 5.3 5.8 9.1 2.7 3.9 5.3 3.3 7.3 9.2 6.6 10.8 7.8 15.0 15.5 12.3 13.4 10.3 9.9 19.2  14.9 16.7 18.8 16.2 25.9 17.0 14.4 17.2 12.4 23.6 23.7 20.1 27.1  16.5 17.2 18.2 16.0 23.3 18.5 15.2 16.0 13.7 23.4 21.8 22.9 26.2 20.6 25.8 25.7 26.0 24.1 20.3 21.4 27.7 36.5 24.9 26.0 25.3 27.2 12.1  6.86 8.59 8.57 8.66 8.04 6.78 7.14 9.24 12.18 8.30 8.68 8.42 9.08 4.02 8.34 6.54 5.82 9.08 8.13 9.64 5.15 6.58 7.38 6.45 9.92 11.13 6.41  0.45 0.55 0.89 0.64 0.66 0.73 0.58 0.85 0.68 0.59 0.72 0.72 0.74  3  23.6 13.9 17.0 14.8 20.0 8.5 10.7 10.1 14.7 17.8 17.2 21.9 7.5 16.9 15.7 11.6 21.3 25.5 13.9  2  21.1 28.8 27.2 27.9 24.4 19.8 22.6 29.6 38.1 26.8 25.7 24.3 30.3 11.0 23.7 18.4 16.5 27.8 26.0 30.0 12.9 19.9 23.1 19.7 29.6 35.4 18.8  2  25.0 19.6 17.5 27.2 24.4 28.9 15.5 19.7 22.1 19.4 29.8 33.4 19.2  Wet Mass [mg] 1.46 2.70 2.33 2.40 4.25 2.58 1.89 3.29 2.26 5.00 6.21 5.53 7.90 6.33 7.76 9.57 10.22 12.71 9.93 7.56 17.65 23.02 15.71 15.57 15.80 19.80 7.48 7.79 5.84 11.78 19.53 17.24 21.12 4.38 14.04 15.24 11.46 20.97 26.20 11.44  Air Dry Mass  Oven Dry Mass  Oven Dry Consistency  Compressed Density  Number of Fibre  [mg] 0.53 0.68 0.80 0.70 1.14 0.75 0.64 0.77 0.58 1.13 1.30 1.15 1.67  [mg] 0.48 0.61 0.72 0.63 1.03 0.68 0.58 0.69 0.52 1.02 1.17 1.04 1.50 1.22 1.67 1.62 1.67 1.49 1.22 1.44 1.98 2.56 1.82 1.77 1.68 2.11 0.77  [%]  [kg/m ]  Layers  33 23 31 26 24 26 30 21 23 20 19 19 19 19 22 17 16 12 12 19 11 11 12 11 11 11 10 21 22 10 10 11 10 21 10 11 13 11  400 438 470 475 220 484 477 486 504 494 273 281 300 313 314 322 324 331 333 348 320 316 363 327 294 295 377 371 334 276 270 305 279  6 11 8 10 10 4 8 9 8 9 11 9 12 11 15 17 13 16 15 13 19 18 15 19 18 19 23 13 16 26 19 19 21 17  1.35 1.86 1.80 1.86 1.66 1.35 1.60 2.20 2.84 2.02 1.97 1.87 2.34 0.85 1.83 1.43 1.28 2.16 2.08 2.41 1.04 1.61 1.88 1.65 2.49 3.00 1.62  1.65 1.29 1.15 1.94 1.87 2.17 0.94 1.45 1.69 1.49 2.24 2.70 1.46  10 13  3  346 262 346 358 319 292 368  25 20 17 21 21 22  Grammage [g/m ] 32 37 2  38 39 40 40 40 40 42 43 49 51 55 58 58 60 60 61 61 64 67 67 68 69 69 69 69 70 70 70 70 72 72 72 73 73 75 76 76 78  Peak Normal Force [N] 1.2 2.2 1.6 1.7 0.7 1.7 2.3 2.0 2.2 3.2 0.9 1.4 1.9 1.7 2.0 2.0 2.1 1.96 1.76 1.6 1.80 2.63 2.46 2.31 1.71 1.93 1.78 2.7 1.76 1.32 1.44 2.00 1.63 1.76 1.26 2.41 2.05 2.48 2.03 2.33  Gap  Strain  [mm] 0.08 0.08 0.08 0.08 0.18 0.08 0.08 0.08 0.08 0.09 0.18 0.18 0.18 0.18 0.19 0.19 0.19 0.18 018 0.18 0.21 0.21 0.19 0.21 0.24 0.24 0.18 0.19 0.21 0.25 0.26 0.24 0.26 0.21 0.28 0.21 0.21 0.24 0.26 0.21  Normal Stress [kPa]  0.64 0.78 0.71 0.77 0.48 0.49 0.69 0.73 0.69 0.72 0.54 0.45 0.54 0.50 0.64 0.68 0.58 0.66 0.65 0.58 0.68 0.66 0.64 0.68 0.61 0.64 0.76 0.58 0.62 0.72 0.60 0.64 0.64 0.64 0.67 0.69 0.64 0.67 0.64 0.71  73 128 88 107 30 92 152 125 160 137 41 61 72 83 78 78 81 81 87 75 65 72 99 89 68 71 148 108 90 76 53 82 56 114 64 109 106 83 61 121  FF CTMP Individual Floe Data (cont'd) Peak Nominal  Area Normalized  Air Dry  Oven Dry  Oven Dry  Compressed  Number  Normal  Normal  Length  Width  Thickness  Volume  Area  to Bar Width  Wet Mass  Mass  Mass  Consistency  Density  of Fibre  Grammage  Force  Gap  [mm]  [mm]  [mm]  [mm ]  [mm ]  [mm ]  [N]  [mm]  31.8 17.2 14.0 23.0 17.3 24.8 17.2 27.5 19.7  51  10.04  53  11.52  54  6.17 7.40 10.37 8.89 8.58 6.29 8.39 8.41 7.99 6.46 6.08 10.91 9.40 4.68 8.54  29.8 18.0 15.4 23.3 18.6 24.0 18.2 25.6 19.2 23.7 22.8 30.1 34.6 18.5 22.2  5.86 17.08 7.87  1.70 3.47 2.09  23 24 23 22 17 21 28 25 21 25 16 21 28 27 26 25 16 15 24 19 18 24 26 25 21 20 18 23 20 19 20 18 21  10.18 13.68 13.90 19.74  2.36 3.11 2.95 3.15 2.57 1.75 2.29  78 79 80 80 80 80 80 80 81 81 81 81 82 82 82 83 83 83 83 83 83 85 85 85 87 88 89 90 91 92 94 95 95 96 96 96 97 97 97 97  1.96 2.36 2.21 1.78 2.17 2.10 1.63 1.73 1.41 1.66 2.47  52  25.1 13.9 11.1 17.0 9.8 18.1 16.2 23.7 14.4 21.7 14.0 22.7 39.3 15.7 18.8 31.1 14.4 12.3 15.3 17.3 18.5 21.1 15.2 15.1 25.7 20.0 7.4 22.5 16.5 12.6 10.9  [%) 10 10 10 10 19 10 10 11 11 10 18 26 10 10 11 10 19 17  [g/m ]  0.79 0.81 0.79 0.74 0.57 0.73 0.94 0.86 0.73 0.84 0.54 0.71 0.95 0.91 0.87 0.85 0.54 0.51 0.82 0.64 0.63 0.82 0.87 0.85 0.72 0.69 0.61 0.78 0.67 0.64 0.67 0.61 0.73 0.62 0.61 0.70 0.76 0.66 0.64 0.66  [mg] 2.49 1.35 1.12 1.84 1.38 1.98 1.38 2.21 1.59 2.10 2.11 2.60 3.38 1.41 1.78 3.02 2.21 1.99 1.55 2.25 2.44 2.19 1.49 1.52 3.09 2.54  Layers  3.20 2.86 2.74  [mg] 2.77 1.50 1.24 2.04 1.53 2.20 1.53 2.46 1.77 2.33 2.34 2.89 3.75 1.57 1.98 3.36 2.45 2.21 1.72 2.50 2.71 2.43 1.66 1.69 3.43 2.82 1.20 2.89 2.51 2.00  [kg/m ]  9.94 6.01 5.12 7.78 6.21 8.01 6.06 8.52 6.40 7.89 7.61  [mg] 25.95 13.52 11.35 17.54 7.35 19.02 14.15 20.95 14.86 20.91 11.86 9.91 33.14 14.56 16.93 29.86 11.85 11.90 14.84 17.71 14.51 21.83 16.03 15.11 20.62 15.70 3.78 18.29 10.87 8.02  0.26 0.21 0.21 0.28 0.21 0.28 0.25 0.31 0.30 0.31 0.21 0.39 0.31 0.21 0.28 0.31 0.22 0.21 0.26 0.21 0.21 0.28 0.19 0.26 0.39 0.38 0.24 0.39 0.31 0.29 0.24 0.32 0.27 0.29 0.31 0.31 0.38 0.27 0.24 0.29  Floc#  41 42 43 44 45 46 47 48 49 50  55 56 57 58  to  Nominal  59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80  9.08 7.16 6.07 11.55 6.80 7.97 10.03 9.56 7.85 7.81 6.07 7.90  2.96 2.78 3.09 2.84 3.23 3.08 3.28 3.40 3.18 3.59 2.80 2.92 3.53 3.00 2.80 2.97 3.23 3.49 3.22 2.71 2.93 3.27 3.08 2.60 3.38 2.72 2.74 2.67 2.85 2.90 2.79 2.92 2.90 3.74 3.06 2.68 2.69  3  20.1  14.4 13.8 17.9 19.4 22.3 15.8 10.4 14.0  2  25.9 25.9 31.9 41.4 17.3 21.6 36.6 26.7 24.0 18.7 27.1 29.4 25.7 17.5 17.8 35.7 29.0 12.2 28.9 24.7 19.6 16.2 32.9 19.7 22.2 29.3 27.7 29.4 23.9 16.3 21.3  2  31.1  26.7 25.7 18.9 25.2 25.2 24.0 19.4 18.2 32.7 28.2 14.0 25.6 27.2 21.5 18.2 34.7 20.4 23.9 30.1 28.7 23.6 23.4 18.2 23.7  9.58 5.53 9.03  1.08 2.60 2.26 1.80 1.53 3.12 1.88 2.12 2.80 2.66 2.84 2.31 1.58 2.06  10 13 17 10 9 10 15 16 29 14 21 22 26 18 24 21 20 19 14 24 28 23  3  300 372 377 284 379 284 314 263 265 265 385 211 265 383 293 269 384 386 325 388 387 302 444 334 223 228 373 233 291 318 390 299 359 330 303 305 251 364 399 335  18 18 21 22 19 19 19  2  1.40 2.28 3.03 2.17 2.08 3.43 3.31 1.78 3.07 3.37 2.07 4.07 1.79 1.91 1.05 2.60 1.58 2.56 2.75 3.77 3.40 3.27 2.93 2.82 2.62 1.13 3.47 3.81 3.00  Strain  Stress  [kPa] 0.67 0.74 0.73 0.62 0.63 0.61 0.73 0.64 0.58 0.64 0.61 0.46 0.68 0.77 0.68 0.64 0.60 0.58 0.69 0.67 0.66 0.66 0.78 0.70 0.46 0.44 0.61 0.50 0.53 0.55 0.64 0.48 0.64 0.53 0.48 0.55 0.49 0.60 0.62 0.56  66 131 144 76 116 87 90 68 73 70 108 46 66 164 98 67 129 129 94 122 134 86 210 98 58 37 185 62 94 128 207 98 160 123 94 91 48 148 209 127  FF CTMP Individual Floe Data (cont'd) Peak Nominal  Nominal  Area Normalized  Air Dry  Oven Dry  Oven Dry  Compressed  Number  Normal  Normal  Length  Width  Thickness  Volume  Area  to Bar Width  Wet Mass  Mass  Mass  Consistency  Density  of Fibre  Grammage  Force  Gap  [mm]  [mm]  [mm]  [mm ]  [mm ]  [mm ]  [mg]  [mg]  [%]  [kg/m ]  Layers  [g/m ]  [N]  [mm]  81  5.58  2.59  0.70  10.1  14.5  16.7  5.91  [mg] 1.56  1.40  24  370  21  97  2.36  0.26  0.63  141  82  9.20  2.77  0.59  15.0  25.5  27.6  11.55  2.78  2.50  22  338  17  98  3.20  0.29  0.51  116  83  8.42  2.94  0.65  16.1  24.8  25.3  10.77  2.71  2.44  23  369  19  99  3.74  0.27  0.59  148  84  7.31  2.98  0.67  14.6  21.8  21.9  12.83  2.39  2.15  17  256  20  99  1.17  0.39  0.43  53  85  5.25  2.76  0.61  8.8  14.5  15.8  5.41  1.60  1.44  27  414  18  99  3.20  0.24  0.61  203  86  9.60  3.25  0.81  25.3  31.2  28.8  25.03  3.54  3.19  13  262  24  102  2.33  0.39  0.52  81  87  7.81  2.98  0.93  21.6  23.3  23.4  10.11  2.79  2.51  25  276  27  108  2.80  0.39  0.58  120  88  8.13  3.41  1.02  28.3  27.7  24.4  21.51  3.40  3.06  14  283  30  110  2.53  0.39  0.62  104  89  10.67  2.80  0.72  21.5  29.9  32.0  23.73  3.83  3.45  15  296  21  115  2.58  0.39  0.46  81  90  8.57  3.12  1.53  40.9  26.7  25.7  32.73  4.13  3.72  11  333  45  139  3.26  0.42  0.73  127  91  5.83  3.24  0.90  17.0  18.9  17.5  14.99  2.92  2.63  18  336  27  139  2.24  0.41  0.54  128  92  6.22  2.99  1.37  25.5  18.6  18.7  21.93  2.94  2.65  12  322  41  142  2.62  0.44  0.68  140  93  6.36  4.28  1.42  38.7  27.2  19.1  37.66  4.41  3.97  11  351  42  146  2.74  0.42  0.71  144  94  8.34  3.00  1.29  32.3  25.0  25.0  31.75  4.13  3.72  12  336  38  149  2.92  0.44  0.66  117  95  7.39  2.81  1.37  28.4  20.8  22.2  27.25  3.43  3.09  11  336  41  149  3.02  0.44  0.68  136  96  6.80  2.96  1.20  24.2  20.1  20.4  24.86  3.33  3.00  12  338  36  149  2.48  0.44  0.63  122  97  8.57  3.18  1.54  42.0  27.3  25.7  36.89  4.51  4.06  11  356  46  149  3.45  0.42  0.73  134  98  9.02  3.08  1.28  35.6  27.8  27.1  34.31  4.61  4.15  12  337  38  149  3.07  0.44  0.65  113  99  8.42  3.34  1.29  36.3  28.1  25.3  35.05  4.71  4.24  12  340  38  3.32  0.44  0.66  131  100  8.17  3.13  1.63  41.7  25.6  24.5  35.27  4.38  3.94  11  347  48  151 154  3.43  0.44  0.73  140  101  8.47  3.32  1.42  39.9  28.1  25.4  41.56  4.84  4.36  10  369  42  155  3.78  0.42  0.70  149  102  6.63  3.07  1.26  25.6  20.4  19.9  27.92  3.51  3.16  11  373  37  155  2.86  0.42  0.67  144  103  6.66  2.87  1.49  28.5  19.1  20.0  27.77  3.32  2.99  11  375  44  156  3.22  0.42  0.72  161  104  6.68  3.24  1.30  28.1  21.6  20.0  28.56  3.76  3.38  12  354  39  156  2.81  0.44  0.66  140  105  8.33  3.24  27.0  25.0  37.82  4.70  4.23  11  373  39  157  3.99  0.42  0.68  160  6.10  3.01  1.31 1.52  35.4  106  27.9  18.4  18.3  25.48  3.22  2.90  11  358  45  158  2.60  0.44  0.71  142  107  7.59  3.58  1.39  37.8  27.2  22.8  40.76  4.85  4.37  11  383  41  161  3.69  0.42  0.70  162  108 109  7.29  3.00 3.50  1.25  27.3 42.2  21.9  21.9 24.4  29.51 43.22  3.92  3.53 4.63  365 387  37  5.14  12 11  161 162  2.98 3.77  0.44 0.42  0.65 0.72  136 154  Floc#  8.14  1.48  3  2  28.5  2  3  44  2  Strain  Stress [kPa]  TMP Individual Floe Data Average Fibre Coarseness: 262 mg/km. Length-weighted Average Fibre Length: 1.52 mm.  Floc#  1 2 3 4 5 6 7 8  9 10 11  -J  12 13 14 15 16 17 18  19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36  Nominal Area  Area Normalized to Bar Width  Length  Width  Thickness  Nominal Volume  [mm]  [mm]  [mm]  [mm ]  [mm ]  [mm ]  7.48 8.75 6.35 9.69 9.03 8.70 6.35 8.52 10.14 7.05 8.64 7.44 9.88 11.71 8.04 9.38 5.00 5.90 7.83 9.32 9.76 7.10 7.48 8.68 8.69 10.20 7.77  2.73 2.96 2.86 2.72 2.75 2.80 2.86 2.93 2.80 2.98 2.81 2.84 2.90 2.80 3.00 2.88 2.92 2.82 3.00 2.94 2.92 2.93 2.84  0.32 0.31 0.30 0.30 0.45 0.36 0.35 0.43 0.41 0.37  6.5 8.0 5.4 7.9  20.4 25.9 18.2 26.4 24.8 24.4 18.2 25.0 28.4 21.0 24.3 21.1 28.7 32.8 24.1 27.0 14.6 16.6 23.5 27.4 28.5 20.8 21.2 26.9 26.7  22.4 26.3  5.40 8.84 9.05 10.55 7.94 6.07 9.84 11.40 7.47  3.10 3.07 2.85 2.94 2.86 2.86 3.01 3.08 2.95 2.88 3.04 3.14 2.90  0.40 0.33 0.35 0.37 0.34 0.33 0.58 0.53 0.51 0.55 0.63 0.58 0.58 0.57 0.57 0.64 0.61 0.61 0.55 0.54 0.67 0.58 0.51 0.68 0.67 0.54  3  11.2 8.8 6.4 10.7 11.6 7.8 9.7 7.0 10.0 12.1 8.2 8.9 8.5 8.8 12.0 15.1 18.0 12.1 12.3 15.3 15.2 18.6 13.9 9.4 13.9 14.7 21.8 13.6 8.9 20.3 24.0 11.7  2  29.1 22.8 15.4 25.3 27.2 32.5 23.4 17.5 29.9 35.8 21.7  2  19.1 29.1 27.1 26.1 19.1 25.6 30.4 21.2 25.9 22.3 29.6 35.1 24.1 28.1 15.0 17.7 23.5 28.0 29.3 21.3 22.4 26.0 26.1 30.6 23.3 16.2 26.5 27.2 31.7 23.8 18.2 29.5 34.2 22.4  Wet Mass [mg] 4.46 6.26 3.71 7.49 8.30 7.44 4.62 8.66 10.58 5.42 8.05 5.91 9.57 11.77 6.82 7.99 6.18 7.72 11.20 14.71 15.91 10.62 10.62 14.51 13.34 16.43 12.12 6.93 13.18 14.17 18.84 12.18 8.01 17.63 21.95 10.97  Peak Normal Force  Gap  [g/m ]  [N]  [mm]  36 36 38 41 41 42 44 44 44 45 45 45 45 47 47 47 75 77 77 78 79 80 80 81 81 81 81 82 83 83 83 84 84 86 87 88  1.52 2.06 2.30 2.07 1.10 1.73 3.22 1.38 1.49 4.25 2.07  0.13 0.13 0.11 0.16 0.18 0.16 0.11 0.18 0.18 0.12 0.16 0.12 0.16 0.18 0.14 0.14 0.21 0.26 0.24 0.29 0.31 0.26 0.24 0.29 0.24  Air Dry Mass  Oven Dry Mass  Oven Dry Consistency  Compressed Density  Number of Fibre  Grammage  [mg] 0.81 1.03 0.76 1.19 1.14 1.15 0.88 1.21 1.40 1.04 1.21 1.06 1.44  [mg] 0.73 0.93 0.68 1.07 1.03 1.04 0.79 1.09 1.26 0.94 1.09 0.95 1.30 1.54 1.13 1.28 1.09 1.29 1.82 2.14 2.25 1.66 1.70 2.17 2.15 2.35 1.85 1.26 2.09 2.26 2.71 1.97  [%]  [kg/m ]  Layers  16 15 18 14 12 14 17 13 12 17 14 16 14  270 267 342 255 227 269 385 239 242 381 282 388 281 255 342 338 350 297 322 271 253 305 334 281 333 259 284 379 312 312  9 9 9 9 13 10 10 12 12 11 12 9 10 11 10 9 17  1.71 1.26 1.42 1.21 1.43 2.02 2.38 2.50 1.84 1.89 2.41 2.39 2.61 2.06 1.40 2.32 2.51 3.01 2.19 1.64 2.85 3.45 2.13  1.48 2.57  3.11 1.92  13 17 16 18 17 16 15 14 16 16 15 16 14 15 18 16 16 14 16 18 15 14 17  3  266 348 390 296 275 401  15 15 16 18 17 17 17 17 19 18 18 16 16 20 17 15 20 20 16  2  4.11 2.50 1.71 2.99 3.67 2.88 1.74 3.21 2.57 1.95 2.04 3.05 2.33 3.72 2.15 2.02 3.48 2.96 3.34 2.29 3.65 3.82 3.14 2.98 5.02  0.31 0.29 0.22 0.26 0.27 0.31 0.24 0.22 0.29 0.32 0.22  Strain  Normal Stress [kPa]  0.59 0.57 0.63 0.47 0.60 0.56 0.68 0.57 0.55 0.68 0.60 0.65 0.54 0.50 0.60 0.58 0.63 0.51 0.53 0.48 0.51 0.55 0.59 0.50 0.58 0.51 0.53 0.65 0.52 0.51 0.53 0.58 0.58 0.57 0.53 0.59  68 78 121 71 41 66 169 54 49 201 80 184 84 49 124 130 192 98 137 92 67 96 136 89 143 70 87 215 112 123 72 153 210 106 87 224  Kraft Individual Floe Data Average Fibre Coarseness:  173mg/km.  Length-weighted Average Fibre Length: 2.09 mm.  Peak Nominal  Nominal  Area Normalized  Air Dry  Oven Dry  Oven Dry  Compressed  Number  Normal  Normal  Length  Width  Thickness  Volume  Area  to Bar Width  Wet Mass  Mass  Mass  Consistency  Density  of Fibre  Grammage  Force  Gap  [mm]  [mm]  [mm]  [mm ]  [mm ]  [mm ]  [%]  [kg/m ]  Layers  6 7  11.15  8  7.89 7.63 8.35 4.79 9.82 11.10 10.88 11.97 9.82 10.82 9.99 10.84 10.84 7.15 3.99 5.05 3.99 4.75 7.92 5.92 8.44 7.83 5.28 5.13 7.17 5.11 7.86 9.19 10.04 8.17 5.30 10.21  0.31 0.27 0.30 0.27 0.28 0.28 0.30 0.30 0.30 0.32 0.32 0.30 0.32 0.32 0.31 0.34 0.37 0.35 0.36 0.33 0.59 0.48 0.57 0.48 0.47 0.53 0.53 0.64 0.65 0.54  5.7 8.3 8.6 5.3 7.9 8.2 10.2 6.9 6.7  18.5 30.7 28.6 19.7 28.2 29.2 33.9 22.9 22.2 25.4  10.8 9.7 11.2 10.1 13.5 10.2  17.0 29.3 29.3 20.5 29.6 28.7 33.5 23.7 22.9 25.1 14.4 29.5 33.3 32.6 35.9 29.5 32.5 30.0 32.5 32.5 21.5 12.0 15.2 12.0 14.3 23.8 17.8 25.3 23.5  1.33 2.31 2.20 1.52 2.21 2.29 2.70 1.84 1.78 2.06 1.07 2.38 2.81 2.53 3.02 2.50 3.08 2.48 2.67 2.56 2.01 0.99 1.36 1.07 1.37 2.26  47 41 40 48 41 40 36 45 44 46 48 41 39 37 35 40 39 41  77 67 75 67 70 70 75 75 75 80 80 75 80 80 77 85 92 87 90 82 147 120 142 120 117 132 132 160 162  [N] 2.97 1.64 1.98 3.87 2.54 1.93 1.39 3.27 3.58 3.30 2.48 1.99 1.64 1.01 1.02 1.85 2.02 2.97 1.52 1.12 2.04 1.77  0.56 0.62 0.58 0.56 0.58 0.59 0.66 0.55 0.65  8.5 13.9 8.6 12.9 16.8 16.8 16.4 7.8 18.8  524 409 416 550 485 424 383 491 575 496 601 443 399 360 361 403 402 522 363 389 417 543 604 631 641 500 456 495 413 564 573 466 578 517 430 470 434 538 446  [g/m ] 72 75 77 77 78 78 80 80 80 81 82 82 83 84 84 84 84 85 85 91 98 100 101 105 107 107 107 107 108 108 110 110 111 111 112 113 113 114 117  [mm]  3.27 3.15 2.92 2.88 2.86 3.05 3.04 2.90 2.91 3.04 2.74 2.95 3.04 2.78 3.01 3.02 3.37 2.93 2.90 2.60 2.85 2.48 2.67 2.55 2.69 2.66 2.75 3.07 3.29 2.93 2.96 3.12 2.91 2.92 3.15 2.84 3.04 2.67 2.83  [mg] 1.48 2.57 2.44 1.69 2.45 2.54 3.00 2.04 1.98 2.29 1.19 2.64 3.12 2.81 3.36 2.78 3.42 2.76 2.97 2.84 2.23 1.10  [mg]  5.66 9.76 9.78 6.83 9.87 9.56  [mg] 2.82 5.62 5.46 3.19 5.37 5.65 7.59 4.08 4.04 4.52 2.23 5.78 7.17 6.86 8.52 6.27 7.98 6.08 7.71 7.53 13.18 5.18 6.68 5.23 6.71 12.78 10.05 16.37 17.63 8.60 9.28 14.63 8.39 14.97 21.64 19.61 17.69 9.02 20.85  Floc#  1 2 3 4 5  9 10  11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39  3  8.1  4.2 8.7  11.3 9.3 12.0 4.7 7.7 4.9 6.0 11.2  8.6 16.6 16.7 8.4  2  13.1  29.0 33.7 30.2 36.0 29.7 36.5 29.3 31.4 28.2 20.4 9.9 13.5 10.2 12.8 21.1 16.3 25.9 25.8 15.5 15.2 22.4 14.9 23.0 28.9 28.5 24.8 14.2 28.9  2  15.8 15.4 21.5 15.3 23.6 27.6 30.1 24.5 15.9 30.6  1.51 1.19 1.52 2.51 1.94 3.09 3.08 1.85 1.85 2.74 1.83 2.83 3.60 3.57 3.13 1.80 3.77  1.75 2.78 2.77 1.67 1.67 2.47 1.65 2.55 3.24 3.21 2.82 1.62 3.39  35 34 15 19 20 20 20 18 17 17 16 19 18 17 20 17 15 16 16 18 16  3  135 140 155 145 140 145 147 165 137 162  2  4.25 4.20 4.29 3.27 1.74 3.96 1.87 3.70 3.81 2.19 3.89 3.30 1.85 3.11 2.15 2.84 2.61  0.14 0.18 0.18 0.14 0.16 0.18 0.21 0.16 0.14 0.16 0.14 0.18 0.21 0.23 0.23 0.21 0.21 0.16 0.23 0.23 0.24 0.18 0.17 0.17 0.17 0.21 0.24 0.22 0.26 0.19 0.19 0.24 0.19 0.21 0.26 0.24 0.26 0.21 0.26  Strain  Stress  [kPa] 0.56 0.32 0.38 0.48 0.43 0.34 0.31 0.46 0.53 0.49 0.58 0.38 0.35 0.27 0.25 0.38 0.43 0.54 0.35 0.29 0.60 0.62 0.71 0.65 0.64 0.60 0.56 0.66 0.60 0.65 0.66 0.62 0.67 0.62 0.55 0.59 0.60 0.61 0.60  175 56 67 189 86 67 42 138 156 132 173 68 49 31 28 63 62 99 47 34 95 148 281 351 301 138 98 156 80 234 248 102 254 140 67 103 88 179 85  A P P E N D I X B: P R O B A B I L I T Y OF FIBRE OVERLAP If a floe of fibres is modeled as a series of n layered sheets, then the probability that any single fibre will cover a given point can be estimated by a mass balance on the floe. The mass of fibres in each layer mi is simply the total mass of the floe divided by the number of layers m/n. The number of fibres in any given layer ni is then given by: ni =  mi — wl f  Using the projected area of a fibre, the area covered by these n\ fibres, Af, is: Af =  nilfd  This gives the probability that any point will be covered when a single layer is deposited on the floe as: A  Wd  f  p=-L  = AQ  nw  Assuming an average fibre diameter of 0.030 mm, and taking grammage, number of fibre layers, and fibre coarseness values from Appendix A , gives values of p from as low as 0.12 for kraft pulp to as high as 0.5 for the C T M P . It should be noted that these estimates are likely to be higher than the true values. This is because the projected fibre area is larger than the actual area of contact for two fibres under moderate levels of strain. In addition, given the results presented in the main body which indicate that fines do not play a role in generating stress, the mass of fibres used in the above calculations might be adjusted to include only fibres over a certain length, which would also lower the values of p calculated above. 76  

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