Rheology of fibre suspensions in papermaking: An overview of recent research

Transcription

1 Rheology of fibre suspensions in papermaking: An overview of recent research Richard J. Kerekes, The University of British Columbia, Vancouver, Canada KEYWORDS: Fibre suspensions, Rheology, Flocculation, Flocs, Formation, Formation aids, Forming SUMMARY: Recent research on fibre suspension rheology with a focus on papermaking has been reviewed. Topics include: regimes of fibre behaviour in shear flows, contacts and forces between fibres, floc formation and dispersion, flow properties of suspensions, fluidization, and the effect of chemical additives. Applications of these findings in headboxes, jet impingement, and forming zones of paper machines are discussed. Several areas requiring further work have been identified. ADDRESS OF THE AUTHOR: Richard J. Kerekes (kerekes@chml.ubc.ca): The University of British Columbia, Pulp and Paper Centre, 2385 East Mall, Vancouver, BC, Canada V6T 1Z4. The rheology of fibre suspensions plays a key role in almost all unit operations of papermaking. Given this importance, many studies of fibre suspensions have been carried out over the years. The early work has been well described in several reviews, for example by Norman et al. (1978), Kerekes et al. (1985), Norman (1990), Kerekes (1996), Norman and Söderberg (2001), and Sampson (2001). There have also been related studies on the rheology of macromolecules and rod-like particles. These too have been described in several reviews, such as those by Ganani and Powell (1985) and Petrie (1999). The objective if this paper is to review recent studies on the rheology of suspensions of pulp fibres with emphasis on applications to papermaking. Earlier work in the field and studies of other suspensions will be referred to where appropriate. General Fibre suspensions are found over a very wide range of consistency (mass concentration) in papermaking. For example, laboratory handsheets are formed at 0.017%; commercial paper is formed at 0.5-1%; pulp is mixed and refined at 3-4%; pulp is often stored at 10-15%. The rheological properties of fibre suspensions vary greatly over this consistency range. An additional factor of great importance is the existence of flocs (mass concentrations of fibres) within the suspensions. The behaviour of these flocs and fibres within in them is governed by contacts between fibres and forces at contacts. Accordingly, we begin this review by discussing these factors. Regimes of Fibre Suspension Behaviour Background Papermaking fibres have length to diameter ratios in the range As a consequence, in shear flow they collide in rotation as well as translation. Several regimes of fibre behaviour have been defined on the basis of collisions induced by fibre asymmetry and suspension concentration. Mason (1950) was the first to do so by defining a dilute regime as one in which there was less than one fibre within a volume swept out by the length of a single fibre. The upper limit of this regime was called the critical concentration. At larger concentrations, Meyer and Wahren (1964) defined a regime having 3 or more contacts per fibre. At this level, fibres are fully constrained in rotation and flexible fibres become locked into networks in a bent configuration upon cessation of shear. Thalén and Wahren (1964) estimated the onset of this condition experimentally by a sedimentation concentration, defined as the concentration of a sediment formed by gravity settling of fibres from a dilute suspension. Crowding number Kerekes et al. (1985) generalized Mason s criterion to encompass behaviour over the full range of fibre suspensions found in papermaking by a crowding number, N. This is defined as the number of fibres in a volume swept out by the length of a fibre. The concept is illustrated in Fig 1. Fig 1. Illustration of crowding number concept. This dimensionless number is readily calculated from the suspension volumetric concentration C v (fraction), fibre length, L, and diameter, d as shown below: More conveniently for swollen pulp fibres, N can be calculated from suspension mass consistency C (%), length L(m), and fibre coarseness, ω (kg/m) as shown in Eq 2 [1] [2] 100 Nordic Pulp and Paper Research Journal Vol 21 no. 5/2006

2 It is apparent that Mason s critical concentration is the special case N = 1. For networks having 3 or more contacts per fibre, N can be related to the number of contacts per fibre, by a theoretical expression derived by Meyer and Wahren (1964) and simplified Kerekes and Schell (1992) to: Soszynski (1987) defined three regimes of fibre suspension behaviour shown in Table 1. Table 1. Fibre suspension regimes. Regimes Type of Fibre Contact N Dilute Chance Collisions N < 1 Semi-Concentrated Forced Collisions 1 < N < 60* Concentrated Continuous N > 60* Contacts * Value assigned in Kerekes & Schell (1992) Typical values for N in papermaking are: 1 < N < 5 for standard handsheet forming and 20 < N < 60 for headbox consistencies. In recent work, Martinez et al. (2001) identified a subregime within 1 < N < 60 defined by a gel crowding number having the value N = 16. Below this value, fibre suspensions exhibit essentially dilute behaviour while above it they interact but are not completely immobilized. The influence of these differences in fibre mobility was observed by positron emission tomography of gravity settling of fibres and in paper formation (Martinez et al. 2001). The gel crowding number has been used to explain some findings in paper forming described later in this paper. The influence of fibre length distribution on crowding number has been examined in recent work. Using a theoretical approach, Kropholler and Sampson (2001) investigated the influence of lognormal length distribution on crowding number. They showed that a true crowding number differed from N by a factor which depended on the coefficient of variation of the lognormal fibre length distribution. Huber and Martinez (2003) also estimated the influence of lognormal distributions for softwoods and hardwoods and compared theoretical estimates to measurements of the number of fibres in Jacquelin flocs (described later). They found that a corrected crowding number, N T, where N T = 1.5 N, gave closest agreement with measured values for both hardwoods and softwoods. They cautioned, however, that the fibre concentration in Jacquelin flocs was likely to be much larger than those found in papermaking. Huber et al. (2003) examined the influence of a general fibre length distribution on the crowding number. They proposed an expression to describe flocculation based on a modified crowding number and flow speed, and confirmed the relevance of this approach by experiment. In more recent work, Yan et al. (2006) measured flocculation and paper formation for mixtures [3] of hardwood and softwood pulps at a common consistency. They found that fibre length represented by the crowding number to be the dominating effect in fibre suspension flocculation. Alternative approaches to regime characterization It is useful at this point to draw attention to other approaches in the scientific literature similar to the crowding number. Some past studies of suspensions of rods and macromolecules have used a crowding number based on number of fibres in a cube rather than a sphere. To facilitate comparisons in the following discussion, these have been converted to N as defined in Eq 1. Doi and Edwards (1978a, 1978b) were the first to characterize regimes of dynamic behaviour of rod-like macromolecules in flowing systems. They defined a semi concentrated regime by the range: Bibbo et al. (1985) considered another upper limit to be when fibres are aligned parallel to one another: Petrie (1999) has provided a good summary of the concepts and physical meaning of these ranges. They are based on an estimated mean space between rods being larger than a fibre diameter and smaller than a fibre length for a random distribution of fibres(eq 4) and for aligned fibres(eq 5). We may note that the semi-dilute range defined by Eq 4 is analogous in concept to the semi-concentrated range in Table 1, but with L/d rather than 60 as an upper limit. For a papermaking fibre of 2.5 mm length and 25 µm diameter, the upper limit of Eq 4 is about 50. Keep and Pecora (1985) found that fibre restraint in rotation began at value larger than N = 1, specifically somewhere in the range 10 < N < 25. This observation and range is similar to the gel crowding number described earlier. It was further pointed out that this applied to rigid rods and that flexible rods introduced major differences. The number of contacts per fibre, n c, is another approach to characterizing regime behaviour. Using statistical geometry and assuming fibres to be randomly arranged in space, Dodson (1996) showed n c to be Pan (1993), also using statistical geometry, obtained Eqs 3, 6, 7 and 8 may be compared by a numerical example for C v = 0.01 and L/d = 70. They give, respectively, values of 2, 1.4, and 1.4, which are reasonably close given the many approximations made in the estimates. [4] [5] [6] [7] Nordic Pulp and Paper Research Journal Vol 21 no. 5/

3 The number of contacts per fibre has also been used to characterize caging of fibres the condition at which fibre motion in a network is prevented in all directions except along the fibre axis. This has been employed for the packing of fibres in static networks. For example, Philipse (1996) measured random packing by sprinkling rigid rods fibres in a vessel and then shaking the sediment. He found the limiting density to occur when n c = 5.4 where n c is given by [8] Surprisingly, there have been few attempts to measure n c in fibre networks. The only one known to this author was performed by Soszynski (1987) on networks of nylon fibres in sucrose solutions. The suspending liquid was evaporated to create bonding at contacts, then the networks were broken apart and the broken contacts counted. The measured values of n c were all significantly less than the predicted number, for example by a factor of one half for C v = 0.01 and L/d = 82. Clearly, further experimental work is needed to confirm predictions of fibre contacts in networks. Another approach to network characterization has been proposed by Björkman (1999) in the form of a fibre centre span number, Ncs, defined as the number of fibre center spans in the reach of a single fibre. Björkman related this to the crowding number as shown below: In summary, a number of approaches may be employed to characterize regimes of fibre suspension behaviour. Directly or indirectly they all describe restraint imposed on translational and rotational motion. Given the large range of consistencies found in papermaking and the benefit of avoiding assumptions which may not hold, the crowding number appears to be the useful means of characterizing fibre suspensions for this application. Forces at Contacts Forces at fibre contacts govern suspension rheology. Kerekes et al. (1985) described these as: electrochemical, surface tension, bending, and hooking. Electrochemical forces Up until the late 1940s, colloidal forces were thought to dominate in papermaking fibre suspensions. The early work of Mason and co-workers changed this. As recounted later by Mason (1979): After several years hard work, we concluded that with particles as big as fibres, under the conditions of flow in paper machines, colloidal forces were only of secondary importance. Some chemical additives may change this condition, and these will be discussed later in the paper. Surface tension Air bubbles trapped in the interstices of fibre networks [9] Fig 2. Illustration of mechanical forces caused by bending and friction (a) and hooking (b). cause fibres adhere from surface tension. This force is large in wet webs, and may also be significant in papermaking suspensions in causing flocculation. For this and other reasons, papermaking suspensions are de-aerated before headboxes. Mechanical forces Mechanical forces causing fibres to cohere may be of two types: hooking and friction. These are illustrated in Fig 2. Hooking forces resist an applied force by a reaction force normal to a fibre surface. The force arises from fibre curl, kinks, or highly fibrillated surfaces. Hooking forces are important in the dilute regime, causing fibres to adhere instead of sliding over one another in shear flow. Friction forces oppose an applied force by a normal force acting upon a surface and a coefficient of friction. The normal force typically comes from fibre bending when fibres are locked into a fibre network by 3 or more contacts, as illustrated in Fig 2a. This force is found in the concentrated regime, i.e. when N > 60. Bending forces were first identified by Wahren and coworkers as the source of cohesion in fibre networks formed upon cessation of agitation. The existence of bending forces was verified by Soszysnki and Kerekes (1988) in a stress relaxation experiment in which heattreated flocs were found to disperse readily when compared to untreated flocs. Bending forces require a coefficient of friction to inhibit sliding of fibres over one another. These coefficients depend on several factors, a major one being surface roughness. In cases of extreme roughness, for example from large external fibrillation caused by beating, friction forces become hooking forces. Estimates of bending forces The magnitude of bending forces, f n, in fibre networks 102 Nordic Pulp and Paper Research Journal Vol 21 no. 5/2006

4 has been estimated by a number of workers. Wahren (1979) estimated a range f n = 7-20 µn for softwood at 3% consistency; Farnood et al. (1994) f n =1µN for a 1% consistency suspension; Ringnér and Rasmuson (2001) estimated 0.5 µn to 50 µn for consistencies 4 to 10% from simulations using finite element analysis. In later work Hansson and Rasmuson (2004a) updated these predictions to be larger by approximately an order of magnitude. Values of coefficient of friction Coefficients of friction of fibres have been measured in recent work by Andersson and Rasmuson (1997) and Andersson et al. (2000). The latter found µ = 0.6 for dry fibres and µ = 0.6 to 0.8 for wet fibres, decreasing with decreasing kappa number and the addition of NaCl. In addition to friction, Anderson et al. (2000) found an adhesive force which did not depend on normal force. It was obtained by extrapolating friction data to zero normal force. This adhesive force did not appear to be due to hooking as it was unaffected by beating. It increased with ionic strength and therefore may be due to an electrochemical effect. The force is sizeable (20-60 µn) relative to the bending forces and therefore is a potentially important force at the low consistencies employed in paper forming (Anderson et al., 2000). This finding clearly deserves further study. Coefficients of friction may also be affected by chemical additives and will be discussed in a later section. Floc Formation Thus far, we have considered fibre suspensions as homogeneous networks. However, in practice fibre suspensions are never uniform. Fibres form into flocs which may exist as isolated entities or as mass concentrations within a network. In both cases, flocs exert a profound effect on suspension rheology. Accordingly, we now discuss fibre flocs, commencing with how they form. Simple shear flow Mason (1948) described the essential components of the floc-forming process in dilute suspensions as follows: fibres are brought together as a result of relative motion in translation and rotation; mechanical entanglement gives rise to cohesive forces; if flocs are weak, hydrodynamic forces also disperse flocs; in a resulting dynamic equilibrium, transient flocs form and disperse; the size of transient flocs decrease with increasing levels of shear; at low levels of shear, or large floc strength, large rolling, coherent flocs may form, leaving few free fibres in the suspension. Klingenberg and colleagues investigated this floc forming process in simple shear flow in a series of investigations using computer simulations. Ross and Klingenberg (1998) showed that flocs form in shear flow, Fig 3. Simulation of floc forming in simple shear flow (from Schmid and Klingenberg, 2000a). but lack coherence in the absence of short-range attractive forces between fibres. Schmid and Klingenberg (2000a) considered both attractive forces and friction forces in simulations, and found that friction was essential to obtain elastic interlocking of fibres. They found bending forces in the range f n = 1-10 µn. An example of floc formation is shown in Fig 3. Schmid et al. (2000) found that the shape of fibres exerted a strong effect on flocculation. Irregular equilibrium shapes greatly increased flocculation. For example, curled fibres flocculated at N < 1.5 while straight stiff fibres remained uniformly dispersed even at N = 50. They also confirmed that fibres aggregated as a result of inter-fibre friction caused by fibre bending without the need of attractive forces, and that coherent fibre networks formed at about N = 50. The influence of fibre stiffness was also strong. However, they were only able to model very flexible fibres and therefore had to use large coefficients of friction, for example 20 as opposed to measured values of about 0.5. Switzer et al. (2004) extended the fibre network simulations to investigate the response of planar 3-D planar networks subjected to elongational deformation. Qualitative agreement was found with experiment, but quantitative agreement was lacking because of the limitations in fibre stiffness that could be modelled. Dodson and Serafino (1993) used another simulation approach to simulate floc formation based on particle attraction and repulsion without specifying the nature of the forces (e.g. friction). They simulated families of dynamic and dispersing flocculating processes that cover much of the range of variability for stock approach flows and paper structure. Nordic Pulp and Paper Research Journal Vol 21 no. 5/

5 Decelerating-turning flows In the 1960s, Jacquelin (1966) observed the formation of strong flocs in the flow of a half-filled, horizontal rotating cylinder. Using a similar apparatus and nylon fibres, Soszynski and Kerekes (1988) identified the conditions at which coherent flocs formed, with. coherent defined as flocs which persist as identifiable entities in the flow in which they form. They noted that coherent flocs first appeared from transient flocs in the portion of flow where deceleration and turning took place and postulated that flocs likely arose form local crowding. Kerekes (1995) later elaborated upon a postulate for the mechanism of floc formation. He postulated that it occurred from local network crowding caused by cumulative forces acting on fibres in decelerating flow where the network is unable to turn with the fluid. In this case the network must obey the law of conservation of mass by local densification. Local crowding, aided by bending from flow turning, causes fibres to wedge into networks, thereby creating strong bending forces which impart coherence to the floc. Other necessary conditions are low hydrodynamic drag on individual fibres (large fibre Reynolds number) to prevent affine fibre-fluid flow and sufficient decelerating strain rate and duration to overcome forces resisting crowding (Kerekes, 1995). Such floc forming by local densification may be illustrated by hand-patting nylon fibres together as one would make a snowball (Soszynski, Kerekes 1988). The above postulate, though based on some experimental evidence, remains speculative. There remains a need for a detailed mechanistic understanding of how flocs form, even in simple shear flow. Floc formation in decaying turbulence Decaying turbulence is the most common floc-forming flow in papermaking. Turbulence is employed in headboxes to disperse pulp, but re-flocculation occurs rapidly as the turbulence decays in the flow downstream. Kerekes (1983b) postulated the floc forming mechanism to be one of transient flocs in dynamic equilibrium being transported to zones downstream of lower shear insufficient to disperse flocs. Coherent flocs form, grow, and densify. The growing large-scale inertial eddies downstream (d Incau, 1983a) may be source of decelerations and turning described above. Some key aspects of this flocforming process were observed in high-speed cine films (Kerekes et al., 1985). The process is very rapid; coherent flocs in a 1% suspension appear within 0.1 s in flow downstream from a grid (Kerekes 1995). Steen (1989, 1991) modelled floc formation in decaying turbulence by transport equations for consistency variations based on the rate of floc rupture caused by turbulent intensity and rate of floc mass growth. He defined floc mass as a proportion of floc consistency to surrounding consistency. An everyday example of decaying turbulence occurs in standard handsheet forming when plunger action ceases. For the dilute conditions of the standard method, fibre hooking rather than bending is the likely source of cohesive forces. This was demonstrated by Stoere et al. (2001). At standard conditions, (about N = 3) the uniformity of handsheets produced from fibres flexibilized by refining showed no change from the unrefined case, but fibres externally fibrillated by refining gave much poorer formation. In contrast, all handsheets formed at headbox consistency (N = 70) had much poorer formation than standard handsheets. At this consistency, flexibilization by refining gave slightly improved formation whereas external fibrillation made it even poorer. All comparisons were made at equal fibre length. Floc Disperson We now consider how flocs disperse in shear flows. Here too, seminal work was carried out by Mason and coworkers. Kao and Mason (1975), examining rupture of flocs in simple shear flow and pure extensional flows, found that in both cases dispersion occurred in a tensile mode. In shear flow, it occurred at the position of a floc s rotational orbit where maximum tension was exerted on the floc. In extensional flow, it occurred along the elongational axis. Thus, somewhat surprisingly, flocs did not shear apart as one might expect in shear flow. Indeed, long elastomer filaments coiled up whereas they stretched out in extensional flow. From these observations, Kao and Mason concluded that extensional flows having little or no rotation were superior to shear flows for dispersing flocs. Recent work by Switzer and Klingenberg (2003b) has added to these findings. Simulations of floc dispersion showed that extensional flows disrupt flocs much faster than simple shear flow. However, floc fragments from the main floc remain intact. In contrast, shear flow acts more slowly, but it breaks up flocs completely by shredding the clumps extracted from the main floc. Several workers have explored the application extensional flow in dispersing pulp in contracting channels. Duffy and Norman (1979) found that extensional flow could rupture weak mechanical pulp flocs, but not stronger chemical softwood pulp flocs. Kerekes (1983a) investigated dispersion of flocs of softwood kraft of consistency 0.5% using high strain rates created by large contractions. He found that flocs could be stretched but not always ruptured even at large extensional strain rates. However, the large step contractions necessary to produce large strains imposed physical restraint of flocs at entry edges. This changed the mode of deformation from tension caused by flow elongation to shear caused by relative fluid velocity acting on a physically restrained floc. This edge contact may be seen in Fig 4. In recent work, James et al. (2003) examined the rupture of individual flocs in suspensions of low consistency (0.01%) softwood kraft pulp in extensional flow. They found that about 60% of the softwood kraft flocs ruptured. They also developed a theoretical model to estimate tensile stress within a floc in extensional flow. In recent work, Yan and Norman (2006) observed flocs of 0.5% softwood kraft in a 2:1 contraction. They found that about 20% of the flocs ruptured. Li et al (1995) examined suspension behaviour through a 1.7:1 tubular contraction 104 Nordic Pulp and Paper Research Journal Vol 21 no. 5/2006

6 strength properties of the suspensions, τ, where related to consistency by a power law of the form [10] Fig 4. Flocs of softwood kraft pulp at 0.5% consistency entering a constriction (moving left to right). The flocs are restrained by contact with the edges of the constriction entry. (from Kerekes (1983a) using NMR imaging and found extensional flow to be highly disruptive to the network. The role of extensional strain in turbulent flows has also been examined. Shah et al. (2000) measured the influence of turbulent stresses on floc dispersion in a 4:1 contraction and found that turbulent stresses were sufficiently large to rupture flocs in tension. Network Structure and Strength Network structure We now consider the structure and properties of fibre suspensions. Both are strongly influenced by the presence of flocs and consequently much effort has been devoted to measuring the state of flocculation in fibre suspensions. Newer methods of measuring flocculation have generally exploited new developments in sensing technology such as high power laser sources, fast digital cameras, and powerful methods of image analysis. Digital imaging and image analysis have been used by several workers, for example fractal analysis of flocculation (Kaji et al 1991); floc size distributions (Kellomäki et al.1999); frequency analysis by Fourier transforms (Beghello et al., 1996); image analysis of digital images (Raghem-Moayed, Kuhn 2000; Huber et al. 2003). Other approaches have used NMR imaging (Li, Ödberg 1997); X-ray computed tomography (Ringnér, Rasmuson 2000); positron emission tomography (Martinez et al. 2001). A recent approach has been the use of wavelets to characterize flocs in suspensions to provide information on inner floc structure as well as floc number (Yan, Söderberg 2006). In non-flowing suspensions, Hansson and Rasmuson (2004b) studied structure of freeze-dried suspensions using X-ray tomography and image analysis. Other workers have used traditional light-based methods, for example to show the effect on fibre flocculation of fibre length and coarseness for single species and mixtures of species (Kerekes, Schell 1995). Network strength Many measurements of fibre network strength have been made over the years. Early work on this topic was summarized by Kerekes et al. (1985). The various with b having a typical value 2 to 3. Given the strong dependence of network strength on consistency evident in Eq 10, flocs in suspensions are stronger than the zones around them. Thus, rupture in flocculated fibre suspensions first takes place in zones around flocs. Björkman (2003a, 2003b) considered fibre networks as systems of closely packed, non-adherent compressible flocs and initiation of flow to occur from the opening of network-free voids. In further studies, Björkman (2005) treated fibre suspensions as a particulate system composed of compressible flocs suspended for the ranges 13 < N < 487 and shear strain rates s -1. Yield stress Yield stress is the stress at which a medium adopts continuous strain at constant stress. This is a particularly important property for fibre suspension rheology, but it is difficult to measure for several reasons. First, network rupture takes place in weak zones around flocs. Andersson et al. (1999) showed that non-flocculated fibre suspensions had significantly greater network strength than flocculated suspensions. A second issue is measurement of yield stress within the body of a suspension rather than at its interface with a solid wall. Fibres and flocs press against a wall and therefore a measured yield stress may reflect the friction of a network plug sliding over this surface rather than a true suspension property (Duffy 2000). Several approaches have been employed to measure yield stress in fibre suspensions. One is by imposing stress within a suspension through the tips of rotor vanes. This approach was employed by Gullichsen and Härkönen (1981); by Bennington et al. (1990) for consistencies up to 30% and Bennington et al. (1995) for consistencies up to 50% with high gas content; by Wikström and Rasmuson (1998) for differing fibre properties, processing conditions, and mixtures of fibre length. Most recently, Dalpke and Kerekes (2005) measured yield stress of flocculated suspensions for a grid of long, short, coarse, and fine pulps. They found, as did others, that suspension yield stress is proportional to consistency to approximately the third power. The constant a in Eq 10 depended primarily on fibre length. Another approach to overcome the wall effect is by roughened walls in a parallel plate rheometer. Damani et al. (1993) measured yield stress in this manner. Slippage was avoided by gluing fine sand ( µm) to the wall. However, the authors cautioned that slippage still occurs along the cylindrical surfaces of the reservoir. The measured yield stresses are somewhat lower than those of Bennington. Swerin et al. (1992) used this method to measure dynamic viscoelasticity of fibre suspensions as well as yield stress. Various attempts have been made to model yield stress Nordic Pulp and Paper Research Journal Vol 21 no. 5/

7 from fibre properties and bending forces. Bennington et al. (1990) developed a model which showed yield stress to depend on consistency to the third power. Andersson et al. (1999) developed model for non-flocculated suspensions incorporating fibre length distribution and adhesive force as well as bending force. They found yield stress to depend on power 2 for adhesive force between fibres and a larger power for friction force between fibres. Farnood et al. (1994) estimated tensile and shear strengths of individual flocs based on fibre bending in a network. They found shear strength to vary as consistency squared and tensile strength to vary as consistency cubed. Switzer and Klingenberg (2003a) modelled yield stress and found it to increase approximately to the third power of consistency. Flow Properties of Fibre Suspensions Shear viscosity Once yield stress is exceeded, fibre suspensions flow at a strain rate determined by the applied stress and suspension viscosity. However, defining a meaningful viscosity for fibre suspensions is complex. Fibres and flocs may be large relative to the channel size and therefore the suspension cannot be considered a continuum. Fibres in shear flow may migrate away from walls, leaving a fibredeficient zone near the wall over which most of the shear takes place. Duffy (2000) has described these various factors and pointed out the hazards of modeling pipe flow as a simple non-newtonian fluid. Meaningful viscosities may be measured over limited ranges of conditions. Much of this past work has been summarized in several papers, for example by Ganani and Powell (1985), Bennington and Kerekes (1996), and Petrie (1999). Over wide ranges of consistency and shear rates, the measurement becomes complex, as illustrated in early work by Steenberg and Johansson (1958) and later by Horie and Pinder (1979). More recently, Chen et al. (2002) showed this as well in measurements of shear stress of hardwood bleached kraft pulp over a range of consistency 0.03 to 0.32% and shear rates 0.1 to 100 s -1. They found Newtonian behaviour at low shear rates, unstable behaviour at medium shear rates due to formation of flocs, and then Newtonian behaviour again at high shear rates which dispersed flocs. Chaouche and Koch (2001) examined the role of flocs and adhesive forces between fibres on shear and interpreted shear thinning in terms of floc formation and rupture caused by competition between colloidal attractive forces and hydrodynamic forces. Petrich et al. (2000) measured the effect of suspending liquid viscosity on fibre suspension behaviour and related viscosity to suspension microstructure, specifically fibre orientation. Switzer and Klingenberg (2003a) modelled the viscosity of fibre suspensions by the simulations described earlier. They showed viscosity to be strongly influenced by fibre equilibrium shape, inter-fibre friction, and fibre stiffness. The influence of fibre shape and coefficient of friction on suspension viscosity is shown in Fig 5 by a plot of specific viscosity against the inverse of effective Fig 5. The influence of flocculation on shear viscosity for increasing shear rates. Suspensions A, B, and C have equal crowding number and aspect ratio, but differing coefficients of friction and shapes. At low shear rates, suspensions B and C remain homogeneous while suspension A flocculates (from Switzer and Klingenberg, 2003a). stiffness, a dimensionless parameter reflecting the amount a fibre bends in flow from torque produced by the fluid shear. Specifically, the inverse effective stiffness consists of the product of fluid shear rate, fluid viscosity, fibre length to the fourth power divided by fibre stiffness. Fig 5 shows that at for a given fibre, the specific viscosity increases with decreasing shear, in this case by about an order of magnitude. As shear rate increases, the viscosities of flocculated suspensions decrease to the non-flocculated values. The strong influence of fibre shape (curl) accords with early observations of the importance of this variable (Blakeney 1966). Falling-ball rheometry has also been employed to measure viscosity of fibre suspensions. Mondy et al. (1990) and Milliken et al. (1989) employed this technique. The latter found a sharp transition at N = 33, below which viscosity increased linearly with concentration, and above it increased as the third power of concentration. Another approach to overcome continuum and wall effects is by indirect measurement based on viscous dissipation in turbulent flow. Bennington and Kerekes (1996) employed this approach for high consistency suspensions. They found, as did Milliken, that suspension viscosity increased with the third power of consistency for C > 1% and strain rates estimated to be in the range 10 3 s -1. However, this approach requires assumptions in defining the dissipation scale and estimating the strain rates, and is therefore approximate. Some recent work has addressed the question of viscosity in channels much smaller than a fibre length. For this case, Roux et al. (2001) introduced the concept of a shear factor a parameter consisting of velocity divided by a gap size. This was employed, for example, to model fibre suspension behaviour in gaps between bar crossings in pulp refiners which are only a few fibre diameters in size and support large compressive loads. Strain rates As indicated earlier, fibre suspension rheology is dependent upon strain rate. Accordingly, estimates of strain rates have been made for various unit operations in 106 Nordic Pulp and Paper Research Journal Vol 21 no. 5/2006

8 papermaking. Van de Ven and Mason (1981), d Incau (1983b), and Tam Doo et al. (1984) estimated values ranging from 10 3 to 10 5 s -1, depending on the assumptions made and the flow components selected for the estimates. In addition to flow strain rates, Tam Doo et al. (1984) estimated strain rates on fibre surfaces to determine shear levels on fibres. Large surface strain rates were obtained when fibres were physically restrained relative to flow, as opposed to being in flows having large strain rates. Extensional viscosity and viscoelasticity Extensional viscosity refers to the resistance of a fluid to elongation. Mewis and Metzner (1974) measured resistance of fibre suspensions to extensional deformation (apparent extensional viscosity) in the range N > 59 and found levels one to two order of magnitude greater than the value of the suspending fluid. There do not appear to have been further measurements since this early work. Fibre suspensions may also exhibit viscoeleastic behaviour. In early work, Nawab and Mason (1958) observed the Weissenberg effect: the climbing of the suspension up the rotor of a viscometer. Interestingly, this was found was when N > 56, that is, in the concentrated regime as described in Table 1. Swerin et al. (1992) measured viscoelastic behaviour of bleached kraft pulp fibres at high concentration (3-8%) in oscillatory shear. Below a critical level of strain, the suspension showed linear viscoelasticity almost independent of consistency, suggesting that network breakdown occurred in zones around flocs. Above the critical strain, fibre networks showed strong non-linear viscoleastic behaviour, suggesting that flocs were being disrupted as well. Damani et al. (1993) measured viscoelasticity in medium consistency suspensions and found it to be very dependent on strain, particularly at lower consistencies. The reason was postulated to be a change from elastic strain to a regime in which breakages occur in the suspension. Switzer et al. (2004) explored the mechanical response of planar, 3D networks of entangled fibres subjected to elongational deformation. The observed effects of fibre shape and length agreed with measurements of dry and wet handsheets. The trends with coefficient of friction and fibre stiffness were consistent with elastic interlocking, but quantitative agreement with experiment was lacking. One suggested reason was force introduced by surface tension from water in the network menisci. Chemical Additives Thus far, this review has focused on mechanical factors that affect fibre suspension rheology. However, chemical additives also may have profound effects. These may be unwanted, for example increased fibre flocculation induced by retention aids, even after short addition times (Solberg and Wågberg, 2003). However, in some cases chemicals are deliberately added to influence the flocculation of fibres as well as the rheology of fibre suspensions. The following discussion will focus on this aspect of chemical addition. Formation aids Formation aids are chemicals added to reduce flocculation and thereby improve mass uniformity (formation) in paper. Lee and Lindström (1989) provide a good review of the early work in this field. Beghello and Lindström (1998) defined these aids as being in two categories: gums and mucilages believed to decrease the friction between fibres high molecular weight polymers which affect the rheological properties of the suspending fluid. Fibre surface friction It has long been known that certain vegetable extracts deflocculate pulp. As summarized by Lee and Lindstrom(1989), many early workers attributed the effect to reduced friction between fibres. The effect may be quite large as shown by the example in Fig 6 for karaya gum. Fig 6. Suspensions of softwood kraft fibres in water alone (left) and with karaya gum added (right). Recent work on formation improvement has focused on Na-CMC. Beghello and Lindström (1998) found that floc size and yield stress of fibre suspensions decreased with the addition of Na-CMC. They attributed this to decreased friction between fibres caused by the creation of gelatinous layers on their surface. The reduced friction was evident in a slimy feeling of the suspension kneaded by hand. Lower friction was also suggested by Laine et al. (2002). Direct measurements of the effect of chemical additives on friction have been made by some workers. Zauscher and Klingenberg (2001 using colloidal probe microscopy found friction to exhibit stick-slip behaviour influenced by surface roughness. Small amounts of high molecular weight polyelectrolytes significantly decreased sliding friction between cellulose surfaces. Amelina et al. (1998) examined friction coefficient with chemical additions. In some cases, friction was reduced by what appears to be a change in surface charge, reaching a minimum, increasing, then decreasing again with charge change. The maximum was explained by a decrease in electrostatic repulsion. Beghello and Lindström (1998) have suggested that colloidal forces and friction may be indistinguishable since all electrochemical forces are expected to affect the surface friction of fibres. Nordic Pulp and Paper Research Journal Vol 21 no. 5/

9 Extensional viscosity of suspending medium Wasser (1978) observed a stringiness in polymer solutions that were most effective as formation aids and from this concluded that a rheological property of the suspending fluid was the likely source of dispersion. In a study of formation aids, Lee and Lindström (1989) concluded that reduced surface friction could not explain the action of all polymeric formation aids because the trace amounts needed (e.g. 10 ppm) were insufficient for substantial coverage of fibre surfaces. They postulated the cause to lie in the rheological properties of the suspending medium, specifically increased extensional viscosity. Specifically, they postulated that this reduced intensity of turbulence in the suspension, resulting in less fibre bending and consequently smaller bending forces among fibres, which allowed flocs to be more easily disrupted. Shear viscosity of suspending medium Increasing shear viscosity of the suspending medium may also diminish fibre flocculation. Steenberg et al. (1966) observed that sugar solutions having shear viscosities in the range of 60 mpa.s reduced the shear modulus of suspensions of perlon fibres to about 10% of their original value. The cause was postulated to be dissipation of elastic bending energy before fibres could lock into bent configurations in networks upon cessation of shear. In later work, Soszynski and Kerekes (1988) found that coherent flocs could be avoided altogether at shear viscosities of 13 mpa.s in a rotating cylinder. Zhao and Kerekes (1993) found that in suspensions of softwood kraft pulps at 0.5%, flocs could be eliminated altogether at viscosities of 60 mpa.s. Strong fibre alignment was also observed in the flow. The decreased flocculation was attributed to fewer accelerations and decelerations to cause crowding and greater drag forces on fibres to cause affine flow rather than crowding. In recent work, Yan et al. (2006b) increased viscosity by a lowering temperature and found reduced flocculation. Comparisons of effects Several studies have compared various means of formation improvement. Beghello (1998) compared surface friction and suspending fluid viscosity for fibres suspended in CMC and sugar solutions. He found comparable levels of floc size with 1% CMC and 30% sugar. These also had comparable levels of apparent shear viscosity. However, changing the viscosity by temperature did not have a substantial effect, which suggested that reduced friction, not viscosity, was the cause of formation improvement in both cases. Giri et al. (2000) examined torque exerted on pulp suspensions in a rheometer. They found dispersion to be more closely related to the amount of CMC absorbed on fibres than to the amount in solution, again suggesting the effect of CMC was one of lowering friction between fibres. Yan et al. (2006b) showed that xyloglucan reduced flocculation by decreased friction. They also showed that Na-CMC grafted on fibre surfaces reduced flocculation, but when added in solution had no effect. These findings all suggest that for CMC, reduced surface friction of fibres rather than changes in rheology of the suspending medium is the cause of reduced flocculation. In unpublished work, Kerekes, Zhao, and James compared the effects of extensional viscosity and shear viscosity on flocculation of 0.5% suspensions of softwood kraft fibres. The pulp was suspended in solutions of sugar and various natural (e.g. locust bean gum) and synthetic (e.g. Accurac 61) polymers. The shear and extensional viscosities of the solutions were measured for concentrations which gave nearly uniform dispersion of pulp fibres, approximately ppm for polymers and 30% for sugar. The shear viscosity of the sugar solutions was greater than that of the polymers by an order of magnitude. However, the apparent extensional viscosities of both were at a comparable threshold level. Thus, although this comparison is very approximate, it too suggests that extensional viscosity plays a key role in formation improvement. This author speculates that it does so by inhibiting local crowding through diminished extensional accelerations and decelerations in flow. Effect of chemicals on friction loss in flow Chemicals may also affect the friction loss of flowing fibre suspensions. Zauscher et al. (2000) added various water-soluble polymers to high consistency (45%) fibre suspensions to reduce friction in a screw-feed extruder. They found Na-CMC to be the most effective. Scott and Zauscher (1997) attributed this effect to the binding of water to fibres by the polymers thereby adding lubricity to the pulp. Paul et al. (2000) examined fibres suspended in CMC solutions at shear viscosities up to 20 mpa.s. The disruptive shear stress of the fibre suspensions in these highly viscous solutions was found to decrease significantly. They also found friction loss behaviour in pipe flow to differ significantly from equivalent pulpwater curves. In essence, increasing liquid viscosity had the same effect as decreasing suspension consistency. Both caused the suspension to behave more like a homogeneous liquid. Chemical additives may also affect drag reduction of fibre suspensions. The phenomenon of drag reduction occurs when the friction loss of solution or suspension is less that that of water alone flowing at the same rate. It is produced by the addition of certain long chain polymers to water and may also occur with some solid-liquid suspensions, fibre suspensions being the most notable example. In the case of solutions, the mechanism has often been attributed to increased extensional viscosity or viscoelasticity. For fibre suspensions, Kerekes and Douglas (1972) showed that elasticity was not required and proposed a visco-intertial mechanism based on diminished near-wall radial momentum transfer. Recent work by Paschkewitz et al. (2004) seems to confirm this mechanism for suspensions of rigid fibres. Because of these differing mechanisms, long chain polymers added to fibre suspensions produce a synergistic effect, achieving drag reductions larger than the sum of those obtained with either polymer of fibre alone (Paschkewitz et al., 2004). 108 Nordic Pulp and Paper Research Journal Vol 21 no. 5/2006

10 Applications We now consider applications of fibre suspension rheology in some flows of importance in papermaking. Pipe flow Fibre suspensions are transported in pipe flow throughout the papermaking process. Chemicals such as retention aids are frequently mixed into fibre suspensions during pipe flow. In their classic work, Robertson and Mason (1957) identified the basic flow regimes of fibre suspensions in pipe flow as: plug, mixed, and turbulent. They also determined the corresponding friction loss behaviour. Since that time, a number of workers have added to this knowledge, most notably Duffy and co-workers. In recent years, work has focused on small channels, open channels, and high consistency. Duffy and Ramachandra (2005) found that for pipe sizes in the range 4-29 mm, pulp suspensions exhibited extrusion-like flow either as a single long floc in the case of long fibres, or as multiple end-on-end flocs in the case of short fibres. The elongated floc structures were found to migrate away form the wall, giving a thin water annulus between the flocs and pipe wall over the entire range of flow rates. Duffy and Abdullah (2003) measured friction losses in small diameter pipes (3.8 to 7.5 mm) and showed that, for consistencies below 1%, friction losses of suspensions were similar to water, even though classical laminar and turbulent flow could not be observed. Between 1 and 2%, friction loss was less than water at higher flow rates. Thus, this friction loss behaviour in small pipes differs significantly from that in large-diameter pipes. In other work, Duffy et al. (2003) measured heat transfer to flowing pulp suspensions and showed that both heat transfer and frictional pressure loss reflect changes in fibre characteristics. Develter and Duffy (1998) measured friction losses in open channels and found that the logarithmic resistance formula could be used successfully. Fluidization Fibre suspensions may be described as fluidized when they adopt the properties of a fluid, for example, undergo continuous strain under a shear stress. To attain this sate in fibre suspensions, the yield stress must be exceeded. The strain rates necessary to do so occur in the turbulent regime. Some properties exhibited in the fluidized state are recovery of pressure energy from kinetic energy, which enables centrifugal pumping, and obeying the power law relationship for fluids in mixing vessels (Bennington, Kerekes 1996). Duffy (1995) has questioned the use of the term fluidization when applied to flows having parts that are not in motion, and therefore care must be exercised to avoid this misapplication. He has suggested using turbulent flow in place of fluidization. Owing to the presence of flocs in suspensions, fluidization may occur at a floc-level as well as a fibre-level. Floc-level fluidization consists of random motion of flocs and has been observed, for example, by Kerekes (1983b), Bennington et al. (1991) and Hietaniemi and Gullichsen (1996). There may also be fibre level fluidization consisting of movement between individual fibres. Given the difficulty of measuring velocities in pulp suspensions, quantification of fluidization is difficult. As a consequence, this has been accomplished by indirect means, most commonly by power dissipation per unit volume introduced by Wahren (1979). This parameter reflects shear in small scale turbulence, which induces relative motion among fibres and flocs.. Various workers have measured power dissipation for the onset of fluidization employing an apparatus similar to that used by Gullichsen and Härkönen (1981) in their pioneering work in developing MC pumps. Bennington et al. (1991) showed the strong effect of device geometry arising from large gradients of shear in the radial direction, even for gap sizes between the rotor and stator as small as 5 mm. This gradient may be reduced by a smaller gap size, but then the suspension may not be considered a continuum because gap size approaches a fibre length. To reconcile the need for a small gap size to minimize gradients, and a large gap size to create continuum conditions. Bennington and Kerekes (1996) employed differing sizes of large gaps and extrapolated to zero gap size. Their estimate is therefore one for fluidization at rotor tip, which is likely to be a high level of fluidization, perhaps at the fibre level, though this is not proven. Hietaniemi and Gullichsen (1996) measured power dissipation by temperature rise and expressed this as a ratio of input power measured from torque and speed. They found this ratio to be about 75% for suspensions up to 10% consistency. They also presented a model for floc size based on a turbulence model for power dissipation. In other recent work, Wikström et al. (2002) measured onset of fluidization in a vaned rotor, narrow gap viscometer, defining the onset of fluidization as the condition at which the power number becomes constant with Reynolds number (RPM) as required by turbulent flow of fluids in mixing vessels. They developed a new correlation and found values similar to those of Gullichsen and Härkönen (1981), but smaller than those of Bennington et al by a factor of about 1/4 at 10% consistency. There is no obvious explanation for this latter difference other than differences in geometry and interpretation of what constitutes the fluidization point. In other recent work, using the principle of fluidization Cichoracki et al. (2001) have developed a former to produce fibrous webs from 5-12% consistency fibre suspensions. Headbox flows Research on fibre suspension rheology in headbox flows during the 1990s has been well described in the review of Norman and Söderberg (2001). Only recent work will be reviewed here along with some earlier work for context. Headboxes on paper machines disperse pulp by turbulence created in the wake of hydraulic elements. This turbulence decays in the flow downstream, during which reflocculation occurs. Fibre behaviour in decaying turbulence was described by Kerekes (1983b), Kerekes et al. (1985), and d Incau (1983a). In recent work, Salmela Nordic Pulp and Paper Research Journal Vol 21 no. 5/