web forming

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size, microflow, and colloidal interactions are important.

- Small-scale covers the range of 0.1 to 20 mm, in which range fiber flocculation andhydrodynamic conditions during forming are the main causes for irregularity. Formation describesthe local basis weight variations in this range and will be discussed further in a later section.

- Medium-scale covers the range of 20 mm to 10 m and is affected mainly by instabilities inheadbox flow and wire section dewatering.

- Macro-scale variations are those in excess of 10 m and are caused mainly by the variabilityin the incoming thick stock. The variations are then mainly in the MD (machine direction). Suchvariations will not be treated in this chapter.

6.1.1 The power spectrum

To quantify the variations at different scales in a stochastic signal, the power spectrum is oftenapplied. Already during the 1930s, the autocorrelation and its Fourier transform, the frequencypower spectrum, were introduced, initially to characterize the energy content within differentfrequency bands for electrical signals. The power spectral density P(v) describes how the

variance σ2 (square of standard deviation) of a signal is distributed on different frequency rangesdv.

¾2 =1R 0

P (v)dv (1)

The frequency power spectrum has since been applied to characterize the structure of turbulence for more than 60 years3. The frequency power spectrum has also been used for along time to characterize variations of basis weight and moisture at the dry end of the paper machine. An analysis of the distribution of variance on different frequency ranges is a useful toolto trace the origin of the variations.

Turbulence, flocculation, and formation represent stochastic variations in local flow velocity,local fiber suspension concentration, and local basis weight in the small-scale range,respectively. To describe such variations, it is useful to use geometrical scale instead of frequency for the characterization. This method is also applicable to medium and macro scalevariations, since geometrical size rather than frequency often simplifies the tracing of the originsfor variations such as wire lengths, felt lengths, and cylinder circumferences. The frequencyspectrum is therefore transformed into a wavelength spectrum. The wavelength l is calculatedfrom the frequency n, and the scanning speed (or flow velocity) u from using the transformation.

l = un

(2)

The wavelength corresponding to a floc of size L amounts to 2L, since in the analysis one

(sine)wave consists of one "positive" and one "negative" floc. To conserve the basic property of the power spectrum, i.e., to describe the distribution of variance, the frequency spectral densityP(n) has to be transformed into the wavelength spectral density E(l) 4.

E (l) = k un2

P ¡

un

¢ (3)

k is a constant depending on the bandwidth of the incremental wavelength intervals used topresent the spectrum within the wavelength range of interest. Usually logarithmic bandwidths arepreferable, and the width of an individual wavelength interval is then proportional to the meanwavelength of that interval.

From a two-dimensional map, such as a beta radiograph for formation evaluation asdescribed below, the wavelength spectrum can be calculated directly, without using thefrequency spectrum as an intermediate step.

size, microflow, and colloidal interactions are important.

- Small-scale covers the range of 0.1 to 20 mm, in which range fiber flocculation andhydrodynamic conditions during forming are the main causes for irregularity. Formation describesthe local basis weight variations in this range and will be discussed further in a later section.

- Medium-scale covers the range of 20 mm to 10 m and is affected mainly by instabilities inheadbox flow and wire section dewatering.

- Macro-scale variations are those in excess of 10 m and are caused mainly by the variabilityin the incoming thick stock. The variations are then mainly in the MD (machine direction). Suchvariations will not be treated in this chapter.

6.1.1 The power spectrum

To quantify the variations at different scales in a stochastic signal, the power spectrum is oftenapplied. Already during the 1930s, the autocorrelation and its Fourier transform, the frequencypower spectrum, were introduced, initially to characterize the energy content within differentfrequency bands for electrical signals. The power spectral density P(v) describes how the

variance σ2 (square of standard deviation) of a signal is distributed on different frequency rangesdv.

¾2 =1R 0

P (v)dv (1)

The frequency power spectrum has since been applied to characterize the structure of turbulence for more than 60 years3. The frequency power spectrum has also been used for along time to characterize variations of basis weight and moisture at the dry end of the paper machine. An analysis of the distribution of variance on different frequency ranges is a useful toolto trace the origin of the variations.

Turbulence, flocculation, and formation represent stochastic variations in local flow velocity,local fiber suspension concentration, and local basis weight in the small-scale range,respectively. To describe such variations, it is useful to use geometrical scale instead of frequency for the characterization. This method is also applicable to medium and macro scalevariations, since geometrical size rather than frequency often simplifies the tracing of the originsfor variations such as wire lengths, felt lengths, and cylinder circumferences. The frequencyspectrum is therefore transformed into a wavelength spectrum. The wavelength l is calculatedfrom the frequency n, and the scanning speed (or flow velocity) u from using the transformation.

l = un

(2)

The wavelength corresponding to a floc of size L amounts to 2L, since in the analysis one

(sine)wave consists of one "positive" and one "negative" floc. To conserve the basic property of the power spectrum, i.e., to describe the distribution of variance, the frequency spectral densityP(n) has to be transformed into the wavelength spectral density E(l) 4.

E (l) = k un2

P ¡

un

¢ (3)

k is a constant depending on the bandwidth of the incremental wavelength intervals used topresent the spectrum within the wavelength range of interest. Usually logarithmic bandwidths arepreferable, and the width of an individual wavelength interval is then proportional to the meanwavelength of that interval.

From a two-dimensional map, such as a beta radiograph for formation evaluation asdescribed below, the wavelength spectrum can be calculated directly, without using thefrequency spectrum as an intermediate step.

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"A Power spectrum quantifies the product of number and density of flocs in diffrent sizeranges, averaged over the complete sampling area. Wavelet mothods also inform about thelocation of different variations, such as streaky structures. Wavelets can also rely on localvariation shapes different from the sinusoidal (power spectra), such as e.g. rectangular."

6.1.2 Fiber flocculation

A fiber under free rotation in a dilute fiber suspension covers a spherical volume with a maximumdiameter equal to the fiber length. The highest concentration of freely mobile fibers of length L isthen represented by the case of closely packed spheres of diameter L. The correspondingvolume concentration cv of fibers will then depend not only on the fiber length L but also on thefiber diameter d, or rather the slenderness L/d of the fibers. The more slender the fibers are, thelower will be the volume concentration allowable to still give the fibers full freedom of individualmovement.

cv = 1;5

(Ld )2 (4)

For fibers with a slenderness of 100, cv according to Eq. 4, will amount to 0.015% or 0.15 g/L.This could be compared with the concentration used in laboratory sheet forming, where, e.g., 7 Lof water is required to form a 1 g paper sheet, i.e., a concentration of 0.14 g/L. The conclusionthen is that to form a sheet of paper with a negligible amount of disturbing fiber flocculation, thefiber suspension initially has to be so dilute that the fibers are free to move independently. Inreality, however, the fibers in suspension will still contact each other to some extent, since theywill not be evenly distributed in space. A more random distribution will then generate areas withlocal concentrations above and below average concentration respectively.

6.1.2.1 Sediment concentration

A small amount of cellulose fibers is added to a beaker of water, circa 0.5 g fibers per liter water.

If the beaker is left undisturbed, the fibers will gradually settle at the bottom of the beaker under the influence of gravity (density of cellulose 1.5 g/cm3).

When the weight of the added fibers is known, it is possible to calculate the weightconcentration of fibers in the sediment from the height of the sediment, the so-called "sedimentconcentration." The concentration is expressed either as a percentage or in g/L, where 1%corresponds to 10 g/L.

The sediment consists of one mechanically connected fiber floc. The sediment concentrationis actually the lowest concentration at which a connected floc can be formed by the fibers. Anyamount of stirring in the beaker is sufficient to cause the fibers in the sediment to whirl up,however, which indicates that the floc strength in the sediment is very low.

The level of the sediment concentration depends on the slenderness L/d of the fibers. For normal cellulose fibers, the slenderness lies within an interval of 50−300. The higher theslenderness is, the lower the sediment concentration will be.

Table 1 shows the approximate sediment concentration for some different types of pulp.

Table 1. Sediment concentration, g/L.

Softwood fibersHardwood fibersTMPGroundwood pulp

2−33−44−65−9

Table 2 provides typical values of the mix concentration used when forming paper onindustrial paper machines. To avoid excessive fiber flocculation, forming concentration should not

"A Power spectrum quantifies the product of number and density of flocs in diffrent sizeranges, averaged over the complete sampling area. Wavelet mothods also inform about thelocation of different variations, such as streaky structures. Wavelets can also rely on localvariation shapes different from the sinusoidal (power spectra), such as e.g. rectangular."

6.1.2 Fiber flocculation

A fiber under free rotation in a dilute fiber suspension covers a spherical volume with a maximumdiameter equal to the fiber length. The highest concentration of freely mobile fibers of length L isthen represented by the case of closely packed spheres of diameter L. The correspondingvolume concentration cv of fibers will then depend not only on the fiber length L but also on thefiber diameter d, or rather the slenderness L/d of the fibers. The more slender the fibers are, thelower will be the volume concentration allowable to still give the fibers full freedom of individualmovement.

cv = 1;5

(Ld )2 (4)

For fibers with a slenderness of 100, cv according to Eq. 4, will amount to 0.015% or 0.15 g/L.This could be compared with the concentration used in laboratory sheet forming, where, e.g., 7 Lof water is required to form a 1 g paper sheet, i.e., a concentration of 0.14 g/L. The conclusionthen is that to form a sheet of paper with a negligible amount of disturbing fiber flocculation, thefiber suspension initially has to be so dilute that the fibers are free to move independently. Inreality, however, the fibers in suspension will still contact each other to some extent, since theywill not be evenly distributed in space. A more random distribution will then generate areas withlocal concentrations above and below average concentration respectively.

6.1.2.1 Sediment concentration

A small amount of cellulose fibers is added to a beaker of water, circa 0.5 g fibers per liter water.

If the beaker is left undisturbed, the fibers will gradually settle at the bottom of the beaker under the influence of gravity (density of cellulose 1.5 g/cm3).

When the weight of the added fibers is known, it is possible to calculate the weightconcentration of fibers in the sediment from the height of the sediment, the so-called "sedimentconcentration." The concentration is expressed either as a percentage or in g/L, where 1%corresponds to 10 g/L.

The sediment consists of one mechanically connected fiber floc. The sediment concentrationis actually the lowest concentration at which a connected floc can be formed by the fibers. Anyamount of stirring in the beaker is sufficient to cause the fibers in the sediment to whirl up,however, which indicates that the floc strength in the sediment is very low.

The level of the sediment concentration depends on the slenderness L/d of the fibers. For normal cellulose fibers, the slenderness lies within an interval of 50−300. The higher theslenderness is, the lower the sediment concentration will be.

Table 1 shows the approximate sediment concentration for some different types of pulp.

Table 1. Sediment concentration, g/L.

Softwood fibersHardwood fibersTMPGroundwood pulp

2−33−44−65−9

Table 2 provides typical values of the mix concentration used when forming paper onindustrial paper machines. To avoid excessive fiber flocculation, forming concentration should not



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greatly exceed the sediment concentration.

Table 2. Typical fiber concentrations in indust rial forming, g/L.

Sack paper Fine paper LinerboardNewsprint

1.54510

6.1.2.2 Network generation

Carefully add dry, unflocculated fibers (e.g., cut polymer fibers) to a beaker filled with water until itreaches a concentration clearly greater than the sediment concentration. Stir slowly with a spoon,and place it finally in the center. It will immediately fall against the beaker edge.

Add turbulence energy using a small propeller agitator. When the stirring has been stopped,the spoon can be placed in the center of the beaker, without falling against the beaker edge. Thefiber suspension thus no longer behaves as a liquid (a liquid cannot take up shear stresseswithout continuing deformation) but instead as an elastic body, a fiber network, with considerablenetwork strength.

The physics of this network strength is that, during the turbulent stirring process, the fibersare deformed from their natural shapes, which they strive to regain when the stirring ceases.When they then strike adjacent fibers, the springing back is hindered, and the fibers becomeinterlocked in strained shapes in a network. As shown in Fig. 1, at least three contact points withthe surrounding fibers are required for a fiber to be kept in a bent shape.

Figure 1. Mobile fibers (top) and a fixed fiber (bottom).

Meyer and Wahren5 analyzed how the volume concentration cn (really cvn) at an average

number of contact points n with surrounding fibers depends on the slenderness L/d of the fibers.They derived an approximate relationship according to the equation:

cn = 16¼L

( 2Lnd+ 1

n¡1 )3(n¡1)d

(5)

Figure 2. Jacquelin-flocs.

Soszynski and Kerekes6 reported two experiments that confirm the validity of the abovemodel for network generation. They slightly tilted a beaker with fiber suspension and made itrotate. After a period of time, uniform nearly spherical fiber flocs formed, so-called"Jacquelin-flocs" (see Fig. 2).

When flocs had been formed, the fiber suspension was diluted with water, under continuedrotation of the beaker. If the original fiber concentration was low enough, the fiber flocs werebroken up by this dilution.

When the original concentration was progressively increased, conditions were eventuallyreached where the flocs resisted the subsequent dilution. They named this critical originalconcentration the "threshold concentration," and Fig. 3 shows the way in which it varies with theslenderness of the fibers.

In the diagram, a curve has also been drawn according to Eq. 5 with an average of threecontact points between a fiber and the surrounding fibers. It is shown by the figure that there isfair agreement between this curve and the experimentally determined threshold concentration.

Figure 3. Threshold concentration as a function of fiber slenderness. The solid line corresponds

greatly exceed the sediment concentration.

Table 2. Typical fiber concentrations in indust rial forming, g/L.

Sack paper Fine paper LinerboardNewsprint

1.54510

6.1.2.2 Network generation

Carefully add dry, unflocculated fibers (e.g., cut polymer fibers) to a beaker filled with water until itreaches a concentration clearly greater than the sediment concentration. Stir slowly with a spoon,and place it finally in the center. It will immediately fall against the beaker edge.

Add turbulence energy using a small propeller agitator. When the stirring has been stopped,the spoon can be placed in the center of the beaker, without falling against the beaker edge. Thefiber suspension thus no longer behaves as a liquid (a liquid cannot take up shear stresseswithout continuing deformation) but instead as an elastic body, a fiber network, with considerablenetwork strength.

The physics of this network strength is that, during the turbulent stirring process, the fibersare deformed from their natural shapes, which they strive to regain when the stirring ceases.When they then strike adjacent fibers, the springing back is hindered, and the fibers becomeinterlocked in strained shapes in a network. As shown in Fig. 1, at least three contact points withthe surrounding fibers are required for a fiber to be kept in a bent shape.

Figure 1. Mobile fibers (top) and a fixed fiber (bottom).

Meyer and Wahren5 analyzed how the volume concentration cn (really cvn) at an average

number of contact points n with surrounding fibers depends on the slenderness L/d of the fibers.They derived an approximate relationship according to the equation:

cn = 16¼L

( 2Lnd+ 1

n¡1 )3(n¡1)d

(5)

Figure 2. Jacquelin-flocs.

Soszynski and Kerekes6 reported two experiments that confirm the validity of the abovemodel for network generation. They slightly tilted a beaker with fiber suspension and made itrotate. After a period of time, uniform nearly spherical fiber flocs formed, so-called"Jacquelin-flocs" (see Fig. 2).

When flocs had been formed, the fiber suspension was diluted with water, under continuedrotation of the beaker. If the original fiber concentration was low enough, the fiber flocs werebroken up by this dilution.

When the original concentration was progressively increased, conditions were eventuallyreached where the flocs resisted the subsequent dilution. They named this critical originalconcentration the "threshold concentration," and Fig. 3 shows the way in which it varies with theslenderness of the fibers.

In the diagram, a curve has also been drawn according to Eq. 5 with an average of threecontact points between a fiber and the surrounding fibers. It is shown by the figure that there isfair agreement between this curve and the experimentally determined threshold concentration.

Figure 3. Threshold concentration as a function of fiber slenderness. The solid line corresponds



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to Eq. 5 with n = 3. Soszynski and Kerekes 6.

Soszynski and Kerekes6 also demonstrated by another experiment that the mechanicalbending of the fibers is decisive for the strength of the flocs. They produced Jacquelin-flocs frompolymer fibers, and then removed some of the flocs from the rotating beaker. The removed flocs

were placed in water with a temperature above the softening temperature of the polymer. Thetemperature treated flocs were then reintroduced into the rotating beaker, where theyimmediately were broken up. This can be explained by stress relaxation in the fibers at thetemperature treatment, reducing the mechanically interconnecting forces within the flocs.

6.1.2.3 Crowding factor

Kerekes and Schell7 have introduced the concept of Crowding Factor N for the number of fibersof length L and diameter d at a volume concentration of cv, within a given reference volume. Thereference volume was chosen as the volume of a sphere of diameter L, i.e., the sphere createdby a freely rotating fiber of length L. The following relationship is then valid for the crowding factor N.

N = 23

cv ¡Ld ¢2 (6)Experimentally, Kerekes has derived a relationship between the crowding factor and type of

fiber contacts at different concentrations (see Table 3).

Table 3. Fiber contacts at different crowding factor levels7.

Crowding factor N Concentration Type of fiber contactN < 11 < N < 60N > 60

DiluteSemi-concentratedConcentrated

Rare collisionsFrequent collisionsContinuous contact

It should be pointed out that the definition of the crowding factor assumes identical fibers.Normally, a rather wide distribution of fiber lengths will be found in a practical situation. Thismeans that the crowding factor concept has to be treated with some caution in such cases, sinceit is proportional to the square of fiber slenderness.

Since the density of cellulose is approximately 1.5, it would be expected that the volumeconcentration of the fibers is lower than the weight concentration. However, because of theswelling of the fiber wall and lumen volume, etc., concentration can be as high as twice theweight concentration.

By eliminating the concentration between Eqs. 5 and 6, it is possible to express the number of contact points n as a function of fiber slenderness L/d and the crowding factor N.

6.1.2.4 Network st rengthThe assumption that the strength of the fiber network is created by the mechanical interlocking of the individual fibers predicts that the network strength increases with increasing fiber concentration.

With measurements in a rheometer, Thalén and Wahren 8 demonstrated a relationshipbetween the shear failure strength τB of the network and the fiber concentration c according tothe formula:

¿ B = ¿ 0(c ¡ cs)k (7)where τ0 and k are fiber dependent parameters and

cs is the sediment concentration.The network strength is thus zero at the sediment concentration and then increases rapidly

to Eq. 5 with n = 3. Soszynski and Kerekes 6.

Soszynski and Kerekes6 also demonstrated by another experiment that the mechanicalbending of the fibers is decisive for the strength of the flocs. They produced Jacquelin-flocs frompolymer fibers, and then removed some of the flocs from the rotating beaker. The removed flocs

were placed in water with a temperature above the softening temperature of the polymer. Thetemperature treated flocs were then reintroduced into the rotating beaker, where theyimmediately were broken up. This can be explained by stress relaxation in the fibers at thetemperature treatment, reducing the mechanically interconnecting forces within the flocs.

6.1.2.3 Crowding factor

Kerekes and Schell7 have introduced the concept of Crowding Factor N for the number of fibersof length L and diameter d at a volume concentration of cv, within a given reference volume. Thereference volume was chosen as the volume of a sphere of diameter L, i.e., the sphere createdby a freely rotating fiber of length L. The following relationship is then valid for the crowding factor N.

N = 23

cv ¡Ld ¢2 (6)Experimentally, Kerekes has derived a relationship between the crowding factor and type of

fiber contacts at different concentrations (see Table 3).

Table 3. Fiber contacts at different crowding factor levels7.

Crowding factor N Concentration Type of fiber contactN < 11 < N < 60N > 60

DiluteSemi-concentratedConcentrated

Rare collisionsFrequent collisionsContinuous contact

It should be pointed out that the definition of the crowding factor assumes identical fibers.Normally, a rather wide distribution of fiber lengths will be found in a practical situation. Thismeans that the crowding factor concept has to be treated with some caution in such cases, sinceit is proportional to the square of fiber slenderness.

Since the density of cellulose is approximately 1.5, it would be expected that the volumeconcentration of the fibers is lower than the weight concentration. However, because of theswelling of the fiber wall and lumen volume, etc., concentration can be as high as twice theweight concentration.

By eliminating the concentration between Eqs. 5 and 6, it is possible to express the number of contact points n as a function of fiber slenderness L/d and the crowding factor N.

6.1.2.4 Network st rengthThe assumption that the strength of the fiber network is created by the mechanical interlocking of the individual fibers predicts that the network strength increases with increasing fiber concentration.

With measurements in a rheometer, Thalén and Wahren 8 demonstrated a relationshipbetween the shear failure strength τB of the network and the fiber concentration c according tothe formula:

¿ B = ¿ 0(c ¡ cs)k (7)where τ0 and k are fiber dependent parameters and

cs is the sediment concentration.The network strength is thus zero at the sediment concentration and then increases rapidly



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with concentration. At high concentrations, the network strength is approximately proportional tock, where the exponent k lies close to two for most pulps.

At forming concentrations, colloidal phenomena can also influence the network strength. Inthis way, the degree of flocculation in the paper product can be influenced by, e.g., the choice of retention additives.

If a considerable amount of air is present in the system, this interacts with the fibers. Small air bubbles get stuck in the fiber network and can influence the network forming, especially at lowconcentrations.

6.1.2.5 Flocculation measurements

Qualitative studies of fiber flocculation in flowing fiber suspensions are possible using differentoptical setups, but quantitative description of local concentration variations is extremely difficult,due to secondary light-scattering effects. Most investigations have used transmitted light througha transparent pipe or channel, but local reflection measurements have a potential of better geometrical resolution.

Wågberg9 studied effects of chemical additives on flocculation in flowing fiber suspensions in

a pipe with 40 mm diameter. He used a laser light source, focused the illumination on one spot inthe pipe, and recorded the back-scattered light from that same spot. The optics were thus inprinciple the same as those in confocal microscopy. From the signal, he evaluated theflocculation spectrum up to 50 mm wavelength. He described the influence on flocculation of chemical additives by taking the ratio between the recorded wavelength spectrum and areference spectrum without additives.

Beghello10 used a wide, flat channel with a reflecting background, provided light over thewhole area, and took two-dimensional pictures of the reflected light. It was not possible toevaluate absolute concentration variations. Instead the spectrum was evaluated up to 32 mmwavelength, and the mean floc size was calculated from the wavelength dividing the area below

the spectrum into two equal parts. He studied the influence of, e.g., fiber concentration, fiber surface properties, and chemical additives.It should be pointed out that fiber flocculation in a mix is detrimental only to the extent that it

prevails also in the final paper product. Loose flocs, which break apart during the formingprocess, do not have a negative effect. It is therefore necessary to complement the currentoptical methods to evaluate fiber flocculation with methods to also evaluate the strength andrheological properties of the flocs.

A general background within the area of fiber flocculation has been given by Kerekes11,12.

6.1.3 Formation

The formation of a paper sheet, i.e., the local basis weight variations up to about 40 mm

wavelength, determined by the fiber distribution in the plane of the sheet, has a great influenceon many sheet properties; it is therefore desirable to be able to quantify this distribution. At leasttwo parameters, one overall intensity value which quantifies the total amount of local basis weightvariations, and one scale value, describing the distribution between small and large flocs, areneeded for a proper description of a specific paper sample. In analogy with the characterizationof macro scale basis weight variations recorded at the dry end, the coefficient of variation(standard deviation divided by mean value) is a suitable measure of total variability.

In industry, formation evaluation is often done using light transmission methods, which aresensitive to other optical parameters as well as local basis weight. Radiation sources other thanvisible light are therefore required to quantify local basis weight variations.

The geometrical resolution of the basis weight measurement is of decisive importance for theamount of variations recorded. The smaller the measurement area is, the more small-scalevariations can be detected and the larger the total variations recorded.

with concentration. At high concentrations, the network strength is approximately proportional tock, where the exponent k lies close to two for most pulps.

At forming concentrations, colloidal phenomena can also influence the network strength. Inthis way, the degree of flocculation in the paper product can be influenced by, e.g., the choice of retention additives.

If a considerable amount of air is present in the system, this interacts with the fibers. Small air bubbles get stuck in the fiber network and can influence the network forming, especially at lowconcentrations.

6.1.2.5 Flocculation measurements

Qualitative studies of fiber flocculation in flowing fiber suspensions are possible using differentoptical setups, but quantitative description of local concentration variations is extremely difficult,due to secondary light-scattering effects. Most investigations have used transmitted light througha transparent pipe or channel, but local reflection measurements have a potential of better geometrical resolution.

Wågberg9 studied effects of chemical additives on flocculation in flowing fiber suspensions in

a pipe with 40 mm diameter. He used a laser light source, focused the illumination on one spot inthe pipe, and recorded the back-scattered light from that same spot. The optics were thus inprinciple the same as those in confocal microscopy. From the signal, he evaluated theflocculation spectrum up to 50 mm wavelength. He described the influence on flocculation of chemical additives by taking the ratio between the recorded wavelength spectrum and areference spectrum without additives.

Beghello10 used a wide, flat channel with a reflecting background, provided light over thewhole area, and took two-dimensional pictures of the reflected light. It was not possible toevaluate absolute concentration variations. Instead the spectrum was evaluated up to 32 mmwavelength, and the mean floc size was calculated from the wavelength dividing the area below

the spectrum into two equal parts. He studied the influence of, e.g., fiber concentration, fiber surface properties, and chemical additives.It should be pointed out that fiber flocculation in a mix is detrimental only to the extent that it

prevails also in the final paper product. Loose flocs, which break apart during the formingprocess, do not have a negative effect. It is therefore necessary to complement the currentoptical methods to evaluate fiber flocculation with methods to also evaluate the strength andrheological properties of the flocs.

A general background within the area of fiber flocculation has been given by Kerekes11,12.

6.1.3 Formation

The formation of a paper sheet, i.e., the local basis weight variations up to about 40 mm

wavelength, determined by the fiber distribution in the plane of the sheet, has a great influenceon many sheet properties; it is therefore desirable to be able to quantify this distribution. At leasttwo parameters, one overall intensity value which quantifies the total amount of local basis weightvariations, and one scale value, describing the distribution between small and large flocs, areneeded for a proper description of a specific paper sample. In analogy with the characterizationof macro scale basis weight variations recorded at the dry end, the coefficient of variation(standard deviation divided by mean value) is a suitable measure of total variability.

In industry, formation evaluation is often done using light transmission methods, which aresensitive to other optical parameters as well as local basis weight. Radiation sources other thanvisible light are therefore required to quantify local basis weight variations.

The geometrical resolution of the basis weight measurement is of decisive importance for theamount of variations recorded. The smaller the measurement area is, the more small-scalevariations can be detected and the larger the total variations recorded.



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give accurate formation values and also limits the possibilities to evaluate scale size.

Beta radiographyBeta radiography has been used since the early 1970s to evaluate formation 17. With this method,an X-ray film in contact with the paper sample is exposed to the transmitted beta particles. In the

STFI method for beta radiography18, a C-14 beta radiation source with a size of 100 x 150 mm2is used, which requires about 30 minutes of sample exposure, after which conventional filmdevelopment is performed. Figure 4 shows examples of beta radiographs.

Figure 4. Beta radiographs for two kraft paper samples, softwood kraft, 60 g/m2, twin-wire bladeforming. Left: Forming concentration 4 g/L. Right: Forming concentration 10 g/L.

Figure 5. Local basis weight variations along a newsprint sample using 0.1 mm measurementresolution.

Simultaneously, calibration areas of constant basis weights within the range of interest areexposed. After development, the film will show a negative, two-dimensional, gray-scale picture of the basis weight distribution in the sample. The radiographs are analyzed in a standard desktopscanner, using a resolution of 300 dpi (dots per inch), which corresponds to circa 0.1 mmresolution. With the help of the calibration areas, the gray-scale values can be transformed tobasis weight valves. Thus a two-dimensional basis weight map can be generated, and formationcharacteristics can be calculated (see below).

Figure 5 shows variations in the local basis weight along a sample of newsprint, recorded ona beta radiograph. Local basis weight is seen to vary between about 25 and 60 g/m2.

6.1.3.3 Formation characteristics

The term "formation index" is reserved for optical formation meters, which give less well definedmeasures of absolute formation level.

Formation number F denotes the coefficient of variation of local basis weight, that is, standarddeviation σ (w) divided by mean basis weight wm, and it is often expressed as a percentage.

F = ¾(w)=wm (8)

If a paper sheet consists of a number of layers of equal structure, the formation number willbe lower, the higher the number of layers are in the sheet. It is therefore not relevant to compareformation numbers between sheets of different basis weights. Comparisons are however possibleusing normalized formation numbers Fnorm according to Eq. 9,

F norm = F p wm =wn (9)where wn is normalization basis weight and

wm sample basis weight.

Normalization according to Eq. 9 assumes that all layers in paper samples of different basisweights have similar fiber distributions. This will generally not be strictly true, when basis weightis changed on a paper machine. At constant forming concentration, e.g., the total structure willoften improve with increasing basis weight due to a self healing effect during dewatering of additional sheet layers (see further discussion below).

In the STFI method, 60 g/m2 is normally used for normalization basis weight. It could bepointed out that the normalized Ambertec meter values in

p g=m (which is a dimension hard to

interpret) can in fact be interpreted as a dimensionless normalized formation number according to

give accurate formation values and also limits the possibilities to evaluate scale size.

Beta radiographyBeta radiography has been used since the early 1970s to evaluate formation 17. With this method,an X-ray film in contact with the paper sample is exposed to the transmitted beta particles. In the

STFI method for beta radiography18, a C-14 beta radiation source with a size of 100 x 150 mm2is used, which requires about 30 minutes of sample exposure, after which conventional filmdevelopment is performed. Figure 4 shows examples of beta radiographs.

Figure 4. Beta radiographs for two kraft paper samples, softwood kraft, 60 g/m2, twin-wire bladeforming. Left: Forming concentration 4 g/L. Right: Forming concentration 10 g/L.

Figure 5. Local basis weight variations along a newsprint sample using 0.1 mm measurementresolution.

Simultaneously, calibration areas of constant basis weights within the range of interest areexposed. After development, the film will show a negative, two-dimensional, gray-scale picture of the basis weight distribution in the sample. The radiographs are analyzed in a standard desktopscanner, using a resolution of 300 dpi (dots per inch), which corresponds to circa 0.1 mmresolution. With the help of the calibration areas, the gray-scale values can be transformed tobasis weight valves. Thus a two-dimensional basis weight map can be generated, and formationcharacteristics can be calculated (see below).

Figure 5 shows variations in the local basis weight along a sample of newsprint, recorded ona beta radiograph. Local basis weight is seen to vary between about 25 and 60 g/m2.

6.1.3.3 Formation characteristics

The term "formation index" is reserved for optical formation meters, which give less well definedmeasures of absolute formation level.

Formation number F denotes the coefficient of variation of local basis weight, that is, standarddeviation σ (w) divided by mean basis weight wm, and it is often expressed as a percentage.

F = ¾(w)=wm (8)

If a paper sheet consists of a number of layers of equal structure, the formation number willbe lower, the higher the number of layers are in the sheet. It is therefore not relevant to compareformation numbers between sheets of different basis weights. Comparisons are however possibleusing normalized formation numbers Fnorm according to Eq. 9,

F norm = F p wm =wn (9)where wn is normalization basis weight and

wm sample basis weight.

Normalization according to Eq. 9 assumes that all layers in paper samples of different basisweights have similar fiber distributions. This will generally not be strictly true, when basis weightis changed on a paper machine. At constant forming concentration, e.g., the total structure willoften improve with increasing basis weight due to a self healing effect during dewatering of additional sheet layers (see further discussion below).

In the STFI method, 60 g/m2 is normally used for normalization basis weight. It could bepointed out that the normalized Ambertec meter values in

p g=m (which is a dimension hard to

interpret) can in fact be interpreted as a dimensionless normalized formation number according to



9/85

Eq. 9, using a normalization basis weight of 1 g/m2.A more complete characterization of formation is given by the wavelength power spectrum.

The area beneath a power spectrum, as already mentioned above, is equal to the variance of theparameter studied, and the area beneath a formation spectrum is thus equal to the square of theformation number F2.

Because of the logarithmic wavelength scale, spectra presented as variance per unitwavelength have the disadvantage that visually the importance of large flocs is underestimated.To give a more correct picture of the contribution to the real area beneath the spectrum, in spiteof the logarithmic scale of the x-axis, a modified presentation is now used in the STFI method.The variance is then presented for wavelength intervals proportional to the wavelength, instead of intervals of constant wavelength.This means in practice that the original spectral density is multiplied by the wavelength (and aconstant which is dependent on the bandwidth chosen) so that the spectral density at smallwavelengths decreases while, at large wavelengths, it increases.

The information in a complete formation spectrum can be simplified by integration within

different scale ranges. In the STFI method, a small-scale wavelength range of 0.3 to 3 mm and alarge-scale range of 3 to 30 mm are used.

Figure 6. Modified STFI formation spectra for the two samples in Fig. 4. Solid line: Concentration4 g/L, F=13.3%, F(0.3−3)=9.3%, F(3−30)=9.5%. Broken line: Concentration 10 g/L, F=19.1%,F(0.3−3)=9.8%, F(3−30)=16.4%.

Figure 6 shows examples of modified STFI formation spectra. The formation is given for twodifferent forming concentrations. The figure shows clearly the dominating occurrence of largeflocs in the paper with the higher forming concentration. The spectra can be compared with theradiographs in Fig. 4, which represent these two samples.

6.1.3.4 Formation of random sheets

It was suggested by Wrist during the 1960s19 that fiber distribution in a real paper could be moreeven than that of a random sheet. The reason would be that there is an inherent self-healingeffect in the dewatering process. If a hole is present in the web on the wire during the dewateringphase, the local dewatering resistance will be low, and excess fiber suspension will be dewateredat that position. Thus extra fibers will be deposited, and the overall basis weight evened out. Thiswas later studied by Norman et al.20 by calculation of the formation spectrum of a random sheetand comparison using beta radiography with that of a well-formed laboratory sheet. The resultsconfirmed that the real sheet is more even than the random sheet in the small and medium flocsize range. At larger floc sizes, the real sheet is however more uneven, due to fiber flocculation

effects, by definition not present in the random sheet. This result has later been confirmed in aninvestigation21 showing that the real sheet is more even than the random sheet at wavelengthssmaller than about 10 mm (see Fig. 7).

Figure 7. Formation spectra at 60 g/m2 for a laboratory sheet of softwood fibers, F=10.2%, andthe corresponding random sheet, F=14.1%21.

6.1.3.5 Dewatering effects on fo rmation

As mentioned in the previous section, real paper sheets are more even in the small scale thanrandom sheets. This is due to the self-healing effects of the dewatering process. To avoid the

self-healing effect during paper forming, the dewatering rate must be extremely low, which leavestime for considerable fiber flocculation by fiber-fiber interaction and sedimentation. In a

Eq. 9, using a normalization basis weight of 1 g/m2.A more complete characterization of formation is given by the wavelength power spectrum.

The area beneath a power spectrum, as already mentioned above, is equal to the variance of theparameter studied, and the area beneath a formation spectrum is thus equal to the square of theformation number F2.

Because of the logarithmic wavelength scale, spectra presented as variance per unitwavelength have the disadvantage that visually the importance of large flocs is underestimated.To give a more correct picture of the contribution to the real area beneath the spectrum, in spiteof the logarithmic scale of the x-axis, a modified presentation is now used in the STFI method.The variance is then presented for wavelength intervals proportional to the wavelength, instead of intervals of constant wavelength.This means in practice that the original spectral density is multiplied by the wavelength (and aconstant which is dependent on the bandwidth chosen) so that the spectral density at smallwavelengths decreases while, at large wavelengths, it increases.

The information in a complete formation spectrum can be simplified by integration within

different scale ranges. In the STFI method, a small-scale wavelength range of 0.3 to 3 mm and alarge-scale range of 3 to 30 mm are used.

Figure 6. Modified STFI formation spectra for the two samples in Fig. 4. Solid line: Concentration4 g/L, F=13.3%, F(0.3−3)=9.3%, F(3−30)=9.5%. Broken line: Concentration 10 g/L, F=19.1%,F(0.3−3)=9.8%, F(3−30)=16.4%.

Figure 6 shows examples of modified STFI formation spectra. The formation is given for twodifferent forming concentrations. The figure shows clearly the dominating occurrence of largeflocs in the paper with the higher forming concentration. The spectra can be compared with theradiographs in Fig. 4, which represent these two samples.

6.1.3.4 Formation of random sheets

It was suggested by Wrist during the 1960s19 that fiber distribution in a real paper could be moreeven than that of a random sheet. The reason would be that there is an inherent self-healingeffect in the dewatering process. If a hole is present in the web on the wire during the dewateringphase, the local dewatering resistance will be low, and excess fiber suspension will be dewateredat that position. Thus extra fibers will be deposited, and the overall basis weight evened out. Thiswas later studied by Norman et al.20 by calculation of the formation spectrum of a random sheetand comparison using beta radiography with that of a well-formed laboratory sheet. The resultsconfirmed that the real sheet is more even than the random sheet in the small and medium flocsize range. At larger floc sizes, the real sheet is however more uneven, due to fiber flocculation

effects, by definition not present in the random sheet. This result has later been confirmed in aninvestigation21 showing that the real sheet is more even than the random sheet at wavelengthssmaller than about 10 mm (see Fig. 7).

Figure 7. Formation spectra at 60 g/m2 for a laboratory sheet of softwood fibers, F=10.2%, andthe corresponding random sheet, F=14.1%21.

6.1.3.5 Dewatering effects on fo rmation

As mentioned in the previous section, real paper sheets are more even in the small scale thanrandom sheets. This is due to the self-healing effects of the dewatering process. To avoid the

self-healing effect during paper forming, the dewatering rate must be extremely low, which leavestime for considerable fiber flocculation by fiber-fiber interaction and sedimentation. In a



10/85

conventional laboratory sheet former, sugar was therefore added to the dilution water. Theamount of addition was such that the fluid density was equal to that of the fibers, and theviscosity was highly increased. By extremely slow dewatering, thus avoiding the self-healingeffects, it was then possible to manufacture a real sheet with random fiber distribution 22. Thestrength of such a sheet was lower than that of a standard laboratory sheet, which demonstrates

that the self-healing effect has some positive effect on paper strength.Due to the increasing self-healing effect, the formation number compensated for the basis

weight level (see Eq. 9) should improve with increasing mean basis weight. This wasdemonstrated for laboratory sheets formed at standard concentration21. It can then be concludedthat a fourdrinier paper in principle has a better formation potential than a twin-wire formed paper,and maybe also a better strength potential. The reason for this would be that the twin-wire paper in reality consists of two plies, each with half the total basis weight. The self-healing effect is thenlower for each half than for the single sheet in fourdrinier forming.

Figure 8. Strength of single- and double-layered laboratory sheets respectively 21. Laboratorysheets with 50/50 mixture of short/long fibers.

The strength of single- and double-layered laboratory sheets formed at standardconcentration was evaluated (see Fig. 8). From the diagram, it is clear that the strength potentialfor a fourdrinier sheet is higher than that of a twin-wire sheet. In reality, however, many other aspects have to be considered. The trend today is to use twin-wire forming in new paper machines also for the production of strong papers. Main advantages are better control of thedewatering process including medium-scale basis weight variability, especially at high machinespeeds, as well as lower equipment costs and space requirements.

6.1.4 Medium-scale basis weight variations

Maps of the two-dimensional basis weight distribution in the scale above the formation range,

that is, around 20 mm, up to about 10 m has been recorded by STORA using beta ray absorptiontechniques for measurements in a laboratory scale. Figure 9 shows an example of such a basisweight map.

Figure 9. Gray scale picture (original in color) of basis weight of full width paper web. Newsprintquality, with each level curve indicating a deviation of 1 g/m2(23).

Such a map gives a good picture of the medium-scale variations in basis weight and is animportant tool for tracing the origin of different basis weight defects.

Recently, corresponding two-dimensional maps of light transmission have been recordedon-line with the ABB Hyperscan system24. Even if only light transmission variations are recorded,some calibration against actual basis weight variation is possible by comparison with the basisweight signal from the conventional scanning beta meter at the dry end.

6.2 HeadboxesThe main function of the headbox is to distribute the mix evenly across the width of the wiresection. This means, for example, that the flow from a pipe with a diameter of 800 mm shall betransformed into a 10 mm thick and 10 000 mm wide jet, with absolutely the same flow rate andflow direction at all points across the width, as indicated in Fig. 10.

Figure 10. Feed pipe for mix and cross-section of jet from headbox (not to scale).

Table 4. Typical jet thickness [mm] in industrial forming.

conventional laboratory sheet former, sugar was therefore added to the dilution water. Theamount of addition was such that the fluid density was equal to that of the fibers, and theviscosity was highly increased. By extremely slow dewatering, thus avoiding the self-healingeffects, it was then possible to manufacture a real sheet with random fiber distribution 22. Thestrength of such a sheet was lower than that of a standard laboratory sheet, which demonstrates

that the self-healing effect has some positive effect on paper strength.Due to the increasing self-healing effect, the formation number compensated for the basis

weight level (see Eq. 9) should improve with increasing mean basis weight. This wasdemonstrated for laboratory sheets formed at standard concentration21. It can then be concludedthat a fourdrinier paper in principle has a better formation potential than a twin-wire formed paper,and maybe also a better strength potential. The reason for this would be that the twin-wire paper in reality consists of two plies, each with half the total basis weight. The self-healing effect is thenlower for each half than for the single sheet in fourdrinier forming.

Figure 8. Strength of single- and double-layered laboratory sheets respectively 21. Laboratorysheets with 50/50 mixture of short/long fibers.

The strength of single- and double-layered laboratory sheets formed at standardconcentration was evaluated (see Fig. 8). From the diagram, it is clear that the strength potentialfor a fourdrinier sheet is higher than that of a twin-wire sheet. In reality, however, many other aspects have to be considered. The trend today is to use twin-wire forming in new paper machines also for the production of strong papers. Main advantages are better control of thedewatering process including medium-scale basis weight variability, especially at high machinespeeds, as well as lower equipment costs and space requirements.

6.1.4 Medium-scale basis weight variations

Maps of the two-dimensional basis weight distribution in the scale above the formation range,

that is, around 20 mm, up to about 10 m has been recorded by STORA using beta ray absorptiontechniques for measurements in a laboratory scale. Figure 9 shows an example of such a basisweight map.

Figure 9. Gray scale picture (original in color) of basis weight of full width paper web. Newsprintquality, with each level curve indicating a deviation of 1 g/m2(23).

Such a map gives a good picture of the medium-scale variations in basis weight and is animportant tool for tracing the origin of different basis weight defects.

Recently, corresponding two-dimensional maps of light transmission have been recordedon-line with the ABB Hyperscan system24. Even if only light transmission variations are recorded,some calibration against actual basis weight variation is possible by comparison with the basisweight signal from the conventional scanning beta meter at the dry end.

6.2 HeadboxesThe main function of the headbox is to distribute the mix evenly across the width of the wiresection. This means, for example, that the flow from a pipe with a diameter of 800 mm shall betransformed into a 10 mm thick and 10 000 mm wide jet, with absolutely the same flow rate andflow direction at all points across the width, as indicated in Fig. 10.

Figure 10. Feed pipe for mix and cross-section of jet from headbox (not to scale).

Table 4. Typical jet thickness [mm] in industrial forming.



11/85

NewsprintFine paper LinerboardSack paper

8152550

A simple equation that relates the required lip opening h [mm] to form a product of basisweight w [g/m2] from a mix concentration of c [g/L] is given below:

w = Rhc (10)

where R is the retention factor. This equation presumes that jet speed equals wire speed.

The flow transformation by the headbox from the incoming pipe flow to the delivered plane jettakes place in mainly three steps:

- The cross-direction distributor makes a first distribution of the mix across the machinewidth.

- Pressure drop elements are introduced to even out the CD flow profile.

- A headbox nozzle generates the final jet.6.2.1 Cross-direction dis tribution

A modern cross-direction distributor usually consists of a tapered header, a channel that runsacross the whole headbox width, from which discharge takes place successively through holes inthe channel wall25 (see Fig. 11).

Figure 11. CD distributor with main flow Q, discharges Δ Q, and overflow q.

If a perfect headbox jet is to be delivered to the wire section, the mix flow ΔQ through eachdischarge hole must be equal. This means that the static pressure along the CD distribution

channel must be kept constant. The friction pressure drop along the channel must therefore becompensated for by a corresponding pressure rise.

This pressure rise can be achieved by transforming part of the velocity energy in the flowalong the channel into static pressure by successively reducing the flow velocity. The channelthen functions in principle like a diffuser, even though the cross-sectional area A(x) decreases inthe flow direction, in contrast to the case in a conventional diffuser. This is possible since thevolumetric flow along the channel gradually decreases because of the discharge flows ΔQ. Thefollowing equation describes the flow velocity u(x) along the CD channel.

u(x) = Q¡n(x)¢QA(x)

(11)

where n(x) is the number of flows ΔQ discharged before position x. The cross-sectional area A(x)along the channel changes so that, for given values of input flow Q and overflow q, a constantstatic pressure is obtained along the whole channel. It will not be possible, however, to maintainthis constant pressure with other flow rates Q. If there is a pressure difference between the inletand outlet, the overflow rate q can be adjusted so that pressure agreement is attained. Somepressure deviations inside the channel can nevertheless still remain.

The distance between the individual discharge holes should be so large that bridging of fibersacross two adjacent holes is avoided. Such fiber piling would lead to the build-up of detrimentalfiber flocs.

The discharge holes feed a tube bank or drilled plate. The higher the pressure drop is alongthe tubes, the smaller the differences will be between the individual discharge flows ΔQ causedby variations in static pressure along the CD distribution channel. To achieve a high pressuredrop, the local flow velocity must be high, which means that the flow area in the tube bank should

NewsprintFine paper LinerboardSack paper

8152550

A simple equation that relates the required lip opening h [mm] to form a product of basisweight w [g/m2] from a mix concentration of c [g/L] is given below:

w = Rhc (10)

where R is the retention factor. This equation presumes that jet speed equals wire speed.

The flow transformation by the headbox from the incoming pipe flow to the delivered plane jettakes place in mainly three steps:

- The cross-direction distributor makes a first distribution of the mix across the machinewidth.

- Pressure drop elements are introduced to even out the CD flow profile.

- A headbox nozzle generates the final jet.6.2.1 Cross-direction dis tribution

A modern cross-direction distributor usually consists of a tapered header, a channel that runsacross the whole headbox width, from which discharge takes place successively through holes inthe channel wall25 (see Fig. 11).

Figure 11. CD distributor with main flow Q, discharges Δ Q, and overflow q.

If a perfect headbox jet is to be delivered to the wire section, the mix flow ΔQ through eachdischarge hole must be equal. This means that the static pressure along the CD distribution

channel must be kept constant. The friction pressure drop along the channel must therefore becompensated for by a corresponding pressure rise.

This pressure rise can be achieved by transforming part of the velocity energy in the flowalong the channel into static pressure by successively reducing the flow velocity. The channelthen functions in principle like a diffuser, even though the cross-sectional area A(x) decreases inthe flow direction, in contrast to the case in a conventional diffuser. This is possible since thevolumetric flow along the channel gradually decreases because of the discharge flows ΔQ. Thefollowing equation describes the flow velocity u(x) along the CD channel.

u(x) = Q¡n(x)¢QA(x)

(11)

where n(x) is the number of flows ΔQ discharged before position x. The cross-sectional area A(x)along the channel changes so that, for given values of input flow Q and overflow q, a constantstatic pressure is obtained along the whole channel. It will not be possible, however, to maintainthis constant pressure with other flow rates Q. If there is a pressure difference between the inletand outlet, the overflow rate q can be adjusted so that pressure agreement is attained. Somepressure deviations inside the channel can nevertheless still remain.

The distance between the individual discharge holes should be so large that bridging of fibersacross two adjacent holes is avoided. Such fiber piling would lead to the build-up of detrimentalfiber flocs.

The discharge holes feed a tube bank or drilled plate. The higher the pressure drop is alongthe tubes, the smaller the differences will be between the individual discharge flows ΔQ causedby variations in static pressure along the CD distribution channel. To achieve a high pressuredrop, the local flow velocity must be high, which means that the flow area in the tube bank should



12/85

be relatively small. This means that the (relative) open area at the inlet of the tube bank, i.e., theratio of the total area of the discharge holes to the channel wall area is small (in the order of 10percent). To feed a downstream chamber from only 10 percent open area would however generate unacceptable flow instabilities. To improve the stability of the downstream flow, therelative open area at the outlet from the tube bank therefore may be increased considerably.

This can be done in two alternative ways:- The tubes or holes are expanded with gradual or sudden increases in diameter, so that the

flow cross section is successively increased.

- The tube centers are brought together, so that the solid area between the individual jetsdelivered is decreased.

After the tube bank, there may be an equalization chamber, followed by a secondary tubebank to generate a pressure drop with a function to further improve the velocity CD profile.Depending on the design of such a chamber, a headbox is called either an "air-cushion headbox"or a "hydraulic headbox." The latter term is also used if the tube bank directly feeds the headboxnozzle.

6.2.2 Air-cushion headboxes

The air-cushion headboxes are a development of the original, completely open headboxes,where gravity was the only driving force for the outflow through the headbox nozzle.

At high machine speeds, however, too high a mix height would be required in an openheadbox to achieve the required jet speed. A jet speed of 250 m/min requires a mix height of 0.9m. At higher speeds, it was therefore preferable to close the headbox and place a pressurized air cushion over the mix in the equalization chamber, to create the driving forces required for the jetvelocity generation. The compressible air cushion has a damping effect on pressure fluctuationsin the mix flow entering the headbox.

A traditional way of evening out velocity profiles, which is applied in, e.g., wind tunnels, is tolet the flow pass through a number of nets which cause pressure drops and thus generate lateralflow from areas with locally high flow velocities. Unfortunately, nets cannot be applied in a paper machine headbox since fibers would rapidly clog them. Instead, rolls perforated with circular holes are placed in the equalization chamber. Their function is to generate a pressure drop andthereby even out the flow velocity profile across the headbox width. They are kept in slow rotationto reduce the tendency for large fiber flocs to form at the hole edges. Early air-cushionheadboxes could be equipped with up to five perforated rolls, while two are used in modernversions (see Fig. 12).

Figure 12. Air-cushion headbox with two perforated rolls.

The degree of downstream velocity disturbances originating from a perforated roll isdetermined mainly by the size and spacing of the holes. The relative open area of a perforatedroll should not be below 50 percent. This still generates a rather turbulent flow at the entrance tothe headbox nozzle.

Air-cushion headboxes are now used mainly for moderate machine speeds, for themanufacture of different specialty papers, and for some kraft paper machines, which require verylarge jet thickness.

6.2.3 Hydraulic headboxes

Hydraulic headboxes were designed specifically for twin-wire forming. A main requirement wassmall nozzle dimensions to allow a short free jet from the headbox into the gap between the twowires. Hydraulic headboxes lack the traditional air cushion and are available either with or without

be relatively small. This means that the (relative) open area at the inlet of the tube bank, i.e., theratio of the total area of the discharge holes to the channel wall area is small (in the order of 10percent). To feed a downstream chamber from only 10 percent open area would however generate unacceptable flow instabilities. To improve the stability of the downstream flow, therelative open area at the outlet from the tube bank therefore may be increased considerably.

This can be done in two alternative ways:- The tubes or holes are expanded with gradual or sudden increases in diameter, so that the

flow cross section is successively increased.

- The tube centers are brought together, so that the solid area between the individual jetsdelivered is decreased.

After the tube bank, there may be an equalization chamber, followed by a secondary tubebank to generate a pressure drop with a function to further improve the velocity CD profile.Depending on the design of such a chamber, a headbox is called either an "air-cushion headbox"or a "hydraulic headbox." The latter term is also used if the tube bank directly feeds the headboxnozzle.

6.2.2 Air-cushion headboxes

The air-cushion headboxes are a development of the original, completely open headboxes,where gravity was the only driving force for the outflow through the headbox nozzle.

At high machine speeds, however, too high a mix height would be required in an openheadbox to achieve the required jet speed. A jet speed of 250 m/min requires a mix height of 0.9m. At higher speeds, it was therefore preferable to close the headbox and place a pressurized air cushion over the mix in the equalization chamber, to create the driving forces required for the jetvelocity generation. The compressible air cushion has a damping effect on pressure fluctuationsin the mix flow entering the headbox.

A traditional way of evening out velocity profiles, which is applied in, e.g., wind tunnels, is tolet the flow pass through a number of nets which cause pressure drops and thus generate lateralflow from areas with locally high flow velocities. Unfortunately, nets cannot be applied in a paper machine headbox since fibers would rapidly clog them. Instead, rolls perforated with circular holes are placed in the equalization chamber. Their function is to generate a pressure drop andthereby even out the flow velocity profile across the headbox width. They are kept in slow rotationto reduce the tendency for large fiber flocs to form at the hole edges. Early air-cushionheadboxes could be equipped with up to five perforated rolls, while two are used in modernversions (see Fig. 12).

Figure 12. Air-cushion headbox with two perforated rolls.

The degree of downstream velocity disturbances originating from a perforated roll isdetermined mainly by the size and spacing of the holes. The relative open area of a perforatedroll should not be below 50 percent. This still generates a rather turbulent flow at the entrance tothe headbox nozzle.

Air-cushion headboxes are now used mainly for moderate machine speeds, for themanufacture of different specialty papers, and for some kraft paper machines, which require verylarge jet thickness.

6.2.3 Hydraulic headboxes

Hydraulic headboxes were designed specifically for twin-wire forming. A main requirement wassmall nozzle dimensions to allow a short free jet from the headbox into the gap between the twowires. Hydraulic headboxes lack the traditional air cushion and are available either with or without



13/85

an equalization chamber. If disturbing pressure pulsations occur in the approach mix flow, it isnecessary to install a separate air-cushion pulsation damper before the headbox.

In a hydraulic headbox with an equalization chamber, the perforated rolls in the air-cushionheadbox are replaced by a secondary tube bank between the chamber and the headbox nozzle,to improve the velocity CD profile. Although it is impossible in air-cushion headboxes, a stationary

arrangement is applicable in hydraulic headboxes, since the turbulence level is higher (due tohigher flow velocities) so that fiber accumulation at edges on the upstream side of the pipes isavoided. The secondary tube bank is often called "turbulence generator," although its mainobjective is to reduce local flow defects.

As mentioned earlier, the relative open area at the downstream end of the pipe packageshould be as large as possible to stabilize the nozzle flow. In the first hydraulic headboxes, theheadbox nozzle was fed by rather widely spaced tubes, which gave relatively high turbulencelevels. To counteract the generation of large-scale fluctuations, Beloit divided the nozzle intoseveral narrow channels with the help of thin, flexible separation vanes (see Fig. 13), a techniquewhich was introduced at the end of the 1960s26.

Figure 13. Beloit Converflo headbox nozzle with separation vanes.

Voith developed a design for improved flow stability during the 1970s, by modification of theoutlet section of the pipe package feeding the headbox nozzle27. At the inlet side, the pipepackage consisted of widely spaced cylindrical pipes (low open area). Toward the outlet of thepipes, the shape was gradually modified to a hexagonal form. These hexagons could then bepacked closely together, so that a high open area was attained.

Figure 14. Flow pattern in Escher Wyss step diffuser headbox.

An alternative design by Escher Wyss, also from the 1970s, is the so-called "step-diffuser headbox"28, in which there is no equalization chamber (see Fig. 14).

In the tube bank from the CD distributor, area increases take place through suddenexpansions of the pipe diameters. The final stage has a square cross section in order to permitclose packing. Along a pipe wall, a boundary layer of water develops, and vertical walls can thengenerate streaks in the paper if several pipes are located on top of each other. However, asudden increase in flow cross section area means that the boundary layer is broken up. Thisreduces the problems of basis weight streaks when several units are stacked vertically.

A similar principle but with a rectangular discharge shape is now used by Valmet 29. Valmethas chosen to use some sideways displacement between the different rows to avoid basis weightstreaks (see previous paragraph), although this in turn causes some problems at the headbox

edges. To avoid jet flow misalignment, corrective mix additions sometimes are made at theheadbox edges.

6.2.4 Headbox nozzle

In the headbox nozzle, consisting of top and bottom lips, the mix is accelerated and leaves thenozzle outlet in the form of a plane jet. The lip opening determines the initial thickness of the jet.The ideal jet is perfectly flat, which requires that it contains no turbulence. When such a jet landsin the wire section, the wire contact will take place along a straight line, perpendicular to the MD.In reality, however, the jet surfaces are never planar, but deteriorate gradually with the distancefrom the nozzle end. The irregular jet contact with a wire will then cause flow disturbances andcan influence web formation and local fiber orientation.

To generate a jet with the smallest possible velocity variations, feeding the nozzle from alarge relative open area is important, as discussed above. The acceleration of the suspension in

an equalization chamber. If disturbing pressure pulsations occur in the approach mix flow, it isnecessary to install a separate air-cushion pulsation damper before the headbox.

In a hydraulic headbox with an equalization chamber, the perforated rolls in the air-cushionheadbox are replaced by a secondary tube bank between the chamber and the headbox nozzle,to improve the velocity CD profile. Although it is impossible in air-cushion headboxes, a stationary

arrangement is applicable in hydraulic headboxes, since the turbulence level is higher (due tohigher flow velocities) so that fiber accumulation at edges on the upstream side of the pipes isavoided. The secondary tube bank is often called "turbulence generator," although its mainobjective is to reduce local flow defects.

As mentioned earlier, the relative open area at the downstream end of the pipe packageshould be as large as possible to stabilize the nozzle flow. In the first hydraulic headboxes, theheadbox nozzle was fed by rather widely spaced tubes, which gave relatively high turbulencelevels. To counteract the generation of large-scale fluctuations, Beloit divided the nozzle intoseveral narrow channels with the help of thin, flexible separation vanes (see Fig. 13), a techniquewhich was introduced at the end of the 1960s26.

Figure 13. Beloit Converflo headbox nozzle with separation vanes.

Voith developed a design for improved flow stability during the 1970s, by modification of theoutlet section of the pipe package feeding the headbox nozzle27. At the inlet side, the pipepackage consisted of widely spaced cylindrical pipes (low open area). Toward the outlet of thepipes, the shape was gradually modified to a hexagonal form. These hexagons could then bepacked closely together, so that a high open area was attained.

Figure 14. Flow pattern in Escher Wyss step diffuser headbox.

An alternative design by Escher Wyss, also from the 1970s, is the so-called "step-diffuser headbox"28, in which there is no equalization chamber (see Fig. 14).

In the tube bank from the CD distributor, area increases take place through suddenexpansions of the pipe diameters. The final stage has a square cross section in order to permitclose packing. Along a pipe wall, a boundary layer of water develops, and vertical walls can thengenerate streaks in the paper if several pipes are located on top of each other. However, asudden increase in flow cross section area means that the boundary layer is broken up. Thisreduces the problems of basis weight streaks when several units are stacked vertically.

A similar principle but with a rectangular discharge shape is now used by Valmet 29. Valmethas chosen to use some sideways displacement between the different rows to avoid basis weightstreaks (see previous paragraph), although this in turn causes some problems at the headbox

edges. To avoid jet flow misalignment, corrective mix additions sometimes are made at theheadbox edges.

6.2.4 Headbox nozzle

In the headbox nozzle, consisting of top and bottom lips, the mix is accelerated and leaves thenozzle outlet in the form of a plane jet. The lip opening determines the initial thickness of the jet.The ideal jet is perfectly flat, which requires that it contains no turbulence. When such a jet landsin the wire section, the wire contact will take place along a straight line, perpendicular to the MD.In reality, however, the jet surfaces are never planar, but deteriorate gradually with the distancefrom the nozzle end. The irregular jet contact with a wire will then cause flow disturbances andcan influence web formation and local fiber orientation.

To generate a jet with the smallest possible velocity variations, feeding the nozzle from alarge relative open area is important, as discussed above. The acceleration of the suspension in



14/85

the nozzle generates a pressure drop, and this will reduce local velocity defects and reduce thedegree of relative turbulence. Thus a high degree of acceleration using a large nozzle contractionratio (inlet divided by outlet cross sectional areas) will be positive.

Figure 15 shows results from studies of one channel in a Beloit headbox (see Fig. 13), fedwith relatively widely spaced pipes. At the largest slice opening, a velocity streak from each feed

pipe is evident. When the slice opening is reduced by a factor of three, i.e., the nozzle contractionratio is increased by a factor of three, the velocity peaks nearly disappear.

Figure 15. Velocity profiles at nozzle outlet for different slice openings d030.

During the 1990s, Beloit replaced the widely spaced feed holes by step diffusers with finalgentle transition from circular to rectangular sections. These are tightly packed sideways to give ahigh relative open area at the nozzle inlet.

The mix height in the main chamber of an air-cushion headbox is normally 500−1 000 mm,and the mix is fed directly from this chamber to the headbox nozzle. This means that thecontraction ratio of the headbox nozzle is large. This large contraction is needed to counteractthe high turbulence level downstream of a perforated roll.

A large stock height at the entrance to the headbox nozzle permits the use of a large jetthickness with acceptable jet quality. On, e.g., sack paper machines, a jet thickness of 50 mmmay be applied.

Hydraulic headboxes, on the contrary, were originally designed for much smaller jetthickness. It then seldom exceeded 15−20 mm for printing paper forming in twin-wire machines.Recently, however, hydraulic headboxes have been developed also for sack paper production,and the number of pipe layers in the package feeding the headbox nozzle has then beenincreased to give an acceptable jet quality.

The lower mix heights in hydraulic headboxes than in air-cushion headboxes often results in

a lower degree of large-scale turbulence in the jet, and this in turn reduces large-scale basisweight variations in the paper product.

Turbulence of all scales is harmful to the planeness of the free jet and then also to paper formation. Turbulence in the mix during dewatering in the wire section is also likely to bedetrimental to paper formation. Turbulence should therefore be avoided at these stages of forming, while at earlier stages it might be positive for deflocculation purposes and for decreasingfiber orientation anisotropy.

The level of relative turbulence generated by the mixing between the individual jets enteringthe headbox nozzle will be reduced by the acceleration of the nozzle flow. During theacceleration phase, however, some increase in the absolute turbulence level will take place in all

three directions. This is partly a result of "vortex stretching." The thickness of the boundary layersinside the headbox will decrease along the nozzle, due to the strong negative pressure gradientin the flow direction. Recent wind tunnel experiments indicate that, depending on the magnitudeof the nozzle contraction ratio, a boundary layer transition from turbulent to laminar state can takeplace before the nozzle outlet31.

Figure 16. Polar fiber orientation distribution. Left: Isotropic laboratory sheet. Right: Anisotropic,machine made sheet.

Besides producing a stable jet, a high degree of acceleration leads to increased fiber orientation anisotropy32,33, which is undesirable for many paper grades. Fiber orientation

anisotropy is also discussed by Niskanen in Volume 16: Paper Physics, and will be further discussed in a later section.

the nozzle generates a pressure drop, and this will reduce local velocity defects and reduce thedegree of relative turbulence. Thus a high degree of acceleration using a large nozzle contractionratio (inlet divided by outlet cross sectional areas) will be positive.

Figure 15 shows results from studies of one channel in a Beloit headbox (see Fig. 13), fedwith relatively widely spaced pipes. At the largest slice opening, a velocity streak from each feed

pipe is evident. When the slice opening is reduced by a factor of three, i.e., the nozzle contractionratio is increased by a factor of three, the velocity peaks nearly disappear.

Figure 15. Velocity profiles at nozzle outlet for different slice openings d030.

During the 1990s, Beloit replaced the widely spaced feed holes by step diffusers with finalgentle transition from circular to rectangular sections. These are tightly packed sideways to give ahigh relative open area at the nozzle inlet.

The mix height in the main chamber of an air-cushion headbox is normally 500−1 000 mm,and the mix is fed directly from this chamber to the headbox nozzle. This means that thecontraction ratio of the headbox nozzle is large. This large contraction is needed to counteractthe high turbulence level downstream of a perforated roll.

A large stock height at the entrance to the headbox nozzle permits the use of a large jetthickness with acceptable jet quality. On, e.g., sack paper machines, a jet thickness of 50 mmmay be applied.

Hydraulic headboxes, on the contrary, were originally designed for much smaller jetthickness. It then seldom exceeded 15−20 mm for printing paper forming in twin-wire machines.Recently, however, hydraulic headboxes have been developed also for sack paper production,and the number of pipe layers in the package feeding the headbox nozzle has then beenincreased to give an acceptable jet quality.

The lower mix heights in hydraulic headboxes than in air-cushion headboxes often results in

a lower degree of large-scale turbulence in the jet, and this in turn reduces large-scale basisweight variations in the paper product.

Turbulence of all scales is harmful to the planeness of the free jet and then also to paper formation. Turbulence in the mix during dewatering in the wire section is also likely to bedetrimental to paper formation. Turbulence should therefore be avoided at these stages of forming, while at earlier stages it might be positive for deflocculation purposes and for decreasingfiber orientation anisotropy.

The level of relative turbulence generated by the mixing between the individual jets enteringthe headbox nozzle will be reduced by the acceleration of the nozzle flow. During theacceleration phase, however, some increase in the absolute turbulence level will take place in all

three directions. This is partly a result of "vortex stretching." The thickness of the boundary layersinside the headbox will decrease along the nozzle, due to the strong negative pressure gradientin the flow direction. Recent wind tunnel experiments indicate that, depending on the magnitudeof the nozzle contraction ratio, a boundary layer transition from turbulent to laminar state can takeplace before the nozzle outlet31.

Figure 16. Polar fiber orientation distribution. Left: Isotropic laboratory sheet. Right: Anisotropic,machine made sheet.

Besides producing a stable jet, a high degree of acceleration leads to increased fiber orientation anisotropy32,33, which is undesirable for many paper grades. Fiber orientation

anisotropy is also discussed by Niskanen in Volume 16: Paper Physics, and will be further discussed in a later section.



15/85

Fiber orientation distribution can be described in a polar diagram and often shows an ellipticshape (see Fig. 16).

The orientation anisotropy ratio can be expressed as a/b, and α is the misalignment angle.A method to analyze fiber orienta-tion at different levels in the z-direction of a paper sample

has been developed34. The paper samples are delaminated using adhesive tape, and fiber

orientation anisotropy in each layer is evaluated using image analysis techniques.

Figure 17. Fiber orientation anisotropy at different levels in a paper sample, using low (8.5:1,squares) and high (30:1, triangles) headbox nozzle contraction ratio respectively. FEX twin-wireroll forming experiments, 60 g/m2, hardwood/softwood-mixture, 700 m/min. Minimum velocitydifference between mix and wires 35.

Figure 17 demonstrates the anisotropy effects using a low and a high nozzle contraction ratiorespectively.

Since a velocity difference between mix and wires increases orientation anisotropy (seefurther below), this difference was kept to a minimum in Fig. 17. The results then indicate to whatdegree fiber orientation anisotropy existed already in the headbox jet. There can be two reasonsfor the lower orientation anisotropy toward the paper surfaces using the high nozzle contractionratio:

- The boundary layers along the top and bottom lips in the headbox nozzle might haveprevented the MD orientation of the fibers.

- The disturbances at the interaction between jet surfaces and wires might have rearrangedan original MD fiber orientation in the jet.

The accelerating flow in the headbox nozzle also has a deflocculating effect. The flocs arestretched in the flow direction and can be broken down into smaller units, especially for

mechanical pulps. The influence of headbox nozzle contraction on fiber orientation anisotropyand on web formation is further demonstrated in a later section.It should be remembered that there is also some flow contraction in the initial part of the free

et. The total contraction ratio is the product of nozzle and jet contraction ratios.Söderberg showed theoretically and experimentally that deviations from a flat velocity profile

will generate surface instabilities in a plane jet36. This occurs when low velocity boundary layersare accelerated in the emerging free jet. The jet surfaces will become more uneven further awayfrom the lip opening, and it is therefore vital to keep the free jet length to a minimum.

Headbox instabilities generated by the side walls and the tube bank have been analyzed byAidun37.

6.2.5 Jet angle and veloci ty

As mentioned previously, the mix jet flow requirements are that the speed and flow direction areconstant across the whole width of the machine and that also the jet has a constant thickness inthe CD. Figure 18 shows the discharge from a headbox lip opening and the free jet. The top lipoften ends with a slice. This has two functions: firstly, to facilitate a local change in the lip opening(see later in this section) and, secondly, to reduce the thickness of the boundary layers formedalong the lips through local mix acceleration.

Figure 18. Outflow from a headbox with a sloping top lip and a vertical slice.

Because of the jet contraction, the thickness h at "vena contracta" is always less than the

geometrical slice opening ho. The ratio is called the contraction coefficient μ of the jet, where

Fiber orientation distribution can be described in a polar diagram and often shows an ellipticshape (see Fig. 16).

The orientation anisotropy ratio can be expressed as a/b, and α is the misalignment angle.A method to analyze fiber orienta-tion at different levels in the z-direction of a paper sample

has been developed34. The paper samples are delaminated using adhesive tape, and fiber

orientation anisotropy in each layer is evaluated using image analysis techniques.

Figure 17. Fiber orientation anisotropy at different levels in a paper sample, using low (8.5:1,squares) and high (30:1, triangles) headbox nozzle contraction ratio respectively. FEX twin-wireroll forming experiments, 60 g/m2, hardwood/softwood-mixture, 700 m/min. Minimum velocitydifference between mix and wires 35.

Figure 17 demonstrates the anisotropy effects using a low and a high nozzle contraction ratiorespectively.

Since a velocity difference between mix and wires increases orientation anisotropy (seefurther below), this difference was kept to a minimum in Fig. 17. The results then indicate to whatdegree fiber orientation anisotropy existed already in the headbox jet. There can be two reasonsfor the lower orientation anisotropy toward the paper surfaces using the high nozzle contractionratio:

- The boundary layers along the top and bottom lips in the headbox nozzle might haveprevented the MD orientation of the fibers.

- The disturbances at the interaction between jet surfaces and wires might have rearrangedan original MD fiber orien

web forming

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