Refining pulp for tensile strength

Determination of N

The number of impacts on pulp depends on several factors in addition to N B because only some of the fibres in grooves are captured and transported into gaps. The probability can be expressed as the ratio of the mass captured by a bar, m C ,to the mass in a groove from which capture takes place, m G

The maximum amount of fibre that can be captured, is bounded by fibre length, l, and groove width, G, as shown in Figure 4.

Figure 4

The maximum amount of fibre that can be captured by the gap is related to the groove width (G) and fibre length (l) which is a measure of floc size.

During bar passage through a groove, some fibre may be forced from the sweep zone by hydrodynamic forces. For example, dewatering pulp from the consistency in a groove (about 4 %) to that in a gap, estimated to be about 20 %, takes place in less than a millisecond, and therefore produces large hydrodynamic forces on pulp fibres (Eriksen et al. 2008). Steenberg (1980) described this compression process as “oozing and consolidation’, meaning that compression of a pulp suspension which is laterally unconstrained will either densify the suspension in the direction of compression (consolidate) or disperse it laterally (ooze). The outcome depends on the relative sizes of hydrodynamic force and network strength. The latter increases with fibre length and strongly with consistency. Given that flocs are stronger than surrounding pulp, it is likely that fibres are captured as flocs, which have a size of about a fibre length, l. We can estimate the captured pulp m C by Equation (A.1) where φ is an unknown fraction.

Fibre mass in a gap is given by

Therefore we may express N as

Determination of I

Energy expended per mass pulp is a key refining variable affecting tensile strength, and therefore we express I as the energy expended on the pulp mass within a gap. SEL has been shown to be energy per bar crossing per bar length (Kerekes and Senger 2006). This scalar-based derivation was obtained by dividing power to a refiner by the rate of bar crossings and refiner size. We assume that this energy can be expressed as the product of force and distance over which this force acts, implying mechanical friction imposed by normal force and sliding as the main action. The scalar-based derivation of the SEL energy does not preclude a hydrodynamic force in addition to mechanical force. However, the reasonable agreement between predicted and measure forces using the friction approach (Kerekes 2011, Kerekes and Meltzer 2018, Berg et al. 2015) suggests that mechanical friction is a good approximation.

The SEL energy is expended on mass in the gap, m T . This mass may not be the same as the captured mass because some fibre may be sheared off mechanically at gap entry. In addition, hydrodynamic forces may affect the amount of fibre in the gap, for example by a stronger holding action on bar edges that resists mechanical shear. Only limited attempts have been made to determine fibre mass in refiner gaps by theoretical estimates (Heymer 2009) or by measurement in a static device (Rantanen et al. 2011). The details of gap mechanics needs further study.

A range of compression and shear forces acting on pulp during a bar crossing produce internal and external fibrillation. The combined effect of these forces may be represented by the energy expended per mass of captured pulp. This action differs from fibre shortening which is caused by a single impact of high force. In this case force rather than energy governs the outcome (Kerekes and Meltzer 2018). Thus, for tensile increase, the appropriate gap fibre mass is represented by floc size l, giving:

φ can be estimated by a mass balance between equation (A.5), and the capacity of a gap to contain fibre for typical conditions of gap consistency C T and gap size, T

As an example, assuming C T = 0.2 and gap size T = 0.2 mm, for l = 2 mm and C S = 0.04, the mass balance gives φ ≈ 0.5. This approximation is a “best estimate” given our current state of knowledge, but its precise value remains to be determined. Thus, we express I generally as

In summary, we have defined N and I by simple expressions that take into account both machine and fibre variables. Parameter φ remains unknown, but for this study we will assume φ = 1. Parameters N and I may be used as independent parameters in place of E and SEL for correlating refining action to refining result, i. e. development of pulp properties. However, we focus in this paper on a causal link to tensile strength.

Specific refining energy, E

It is useful to relate the above equations to Specific Refining Energy, E, which has proven useful over the years for quantifying refining action:

And consequently

We note a similarity between (A.9) and a parameter E/SEL proposed by Batchelor et al. (2017) for use with SEL to characterize refining. Parameters SEL and E/SEL are independent and therefore meet one of the needs identified earlier. The present study has extended this approach by incorporating the additional key variables l, m G to make the link between SEL, E, and N and I. We further note that in cases where Q and CEL are unknown, but E, SEL, and m G are known, Equation (A.9) may be employed to estimate N B .

Western Canada – Northern Bleached Softwood Kraft (NBSK)

Figure 5

The fit of Equation 7 to western Canadian NBSK laboratory data using plates with a bar width of 1 mm for SEL of 1.0, 0.5 and 0.25 J/m. The other conditions for the experiments are given in Table 2.

These experiments on a western Canada NBSK pulp were performed on a 12″, single-disc laboratory refiner using the conditions in Table 2. T 0 is the unrefined tensile strength of the pulp and T max was considered to be the ultimate possible value which was determined by PFI refining to 12,000 revolutions.

Equation 7 was fit simultaneously to all the data using a non-linear least-squares program to give α = 1.6 ∗ 10 − 6  kg/J. As can be seen in Figure 1 in the main section of this paper for the 2.5 mm bar width, and in Figure 5 for the 1 mm bar width for several specific edge loads, the fit of Equation 7 to the data is excellent.

Eastern Canada – Northern Bleached Softwood Kraft (NBSK)

The refining for this Eastern Canada NBSK pulp was done on both 22″ Beloit double-disk and Escher-Wyss refiners using a variety of conditions (Table 3).

The fit gave α = 2.8 ∗ 10 − 6  kg/J which agreed well with the experimental data as shown in Figure 6.

Figure 6

Fitted lines of Equation 7 to refining data for an eastern Canadian NBSK using a 22″ double-disc refiner (G,H,I) and an Escher-Wyss refiner (J,K). The value of parameter “α” is 2.8 × 10 − 6  kg/J. The refining conditions are shown in Table 3.

Refining conditions for a Southern pine bleached kraft

The southern pine bleached kraft pulp was treated in an Escher-Wyss refiner using the conditions in Table 4. The data and fit to equation 7 are shown in Figure 7. The results for the eastern Canadian spruce pulp (test K) are included for comparison.

Figure 7

The relative change in tensile for eastern Canadian spruce and southern pine bleached kraft pulps as a function of number of impacts for the refining conditions shown in Tables 3 and 4. The lines are fits to Equation 7 with α = 2.8 × 10 − 6  kg/J for the spruce pulp and α = 3.0 × 10 − 6  kg/J for the pine pulp.

Refining conditions for several eucalyptus pulps

The experimental data for eucalyptus pulps from four different sources using different refiners and operating conditions is summarized in Table 5 and plotted in Figure 8. Although these pulps were made from different eucalyptus species and originated from different geographical regions, we have used a single value for T max in the calculations. Ideally, T max should have a unique value for each test but this was not measured for these pulps. Nevertheless, the calculated values of α are within a factor of 1.5 for the four pulps.

Figure 8

The relative change in tensile as a function of impacts for eucalyptus pulps from four different refining trials which are summarized in Table 5.

The value of the α parameter ranged from 2.1 to 3.3 × 10 − 6  kg/J giving fitted lines that closely followed the experimental data (Figure 8).