Introduction
Internal fibrillation
External fibrillation
Formation of fines
Shortening of fibers through cutting
Straightening or curling of fibers
Combined effects on the sheet level
-
the higher swelling/deswelling rate of chemical pulp fibers due to differences in acidic groups.
-
the greater negative surface charge on the TMP fibers, which explains a limiting response to the addition of cationic strength additives.
-
a greater degree of fibrillation of the TMP fibers, which makes the interlocking mechanism more influential and yet limits the effect of added fines, since the effect from the fibrillar content is already saturated.
Experiments and measurements
Material | Strength additive (kg/t) | Refining (PFI revolutions) |
---|---|---|
R0 | 0 | 0 |
R1000 | 0 | 1000 |
R2000 | 0 | 2000 |
SR0 | 25 | 0 |
SR1000 | 25 | 1000 |
SR2000 | 25 | 2000 |
Pulp characterization
Device name | Length measurement | Width measurement | ||
---|---|---|---|---|
Minimum (\(\upmu \hbox {m}\)) | Resolution (\(\upmu \hbox {m}\)) | Minimum (\(\upmu \hbox {m}\)) | Resolution (\(\upmu \hbox {m}\)) | |
Kajaani | 10 | 10 | 1 (2.5*) | 1.5 |
L&W Pulp Tester | 4 (7*) | 0.1 | 4 (7*) | 0.1 |
Averaging method | Arithmetic | Length-weighted | ||||
---|---|---|---|---|---|---|
Pulp | R0 | R1000 | R2000 | R0 | R1000 | R2000 |
Fiber length (mm) | 0.966 | 0.925 | 0.917 | 1.694 | 1.614 | 1.591 |
Fiber width (\(\upmu \hbox {m}\)) | 30.2 | 29.4 | 29.7 | 36.1 | 35.3 | 34.8 |
Fiber wall-thickness (\(\upmu \hbox {m}\)) | 8.9 | 8.5 | 8.1 | 11.1 | 10.4 | 9.9 |
Fiber shape factor (−) | 0.91 | 0.91 | 0.91 | 0.91 | 0.91 | 0.92 |
External fibrillation (%) | 4.33 | 4.92 | 4.46 | 3.83 | 4.43 | 4.36 |
Fine length (\(\upmu \hbox {m}\)) | 117.9 | 119.8 | 117.6 | 140.8 | 142.1 | 142.0 |
Averaging method | Arithmetic | Length-weighted | ||||
---|---|---|---|---|---|---|
Pulp | R0 | R1000 | R2000 | R0 | R1000 | R2000 |
Fiber length (mm) | 0.744 | 0.698 | 0.659 | 1.555 | 1.370 | 1.297 |
Fiber width (\(\upmu \hbox {m}\)) | 30.2 | 30.7 | 30.2 | 36.9 | 36.8 | 36.3 |
Fiber shape factor (–) | 0.86 | 0.87 | 0.87 | 0.85 | 0.86 | 0.86 |
Fine length (\(\upmu \hbox {m}\)) | 25.7 | 25.5 | 25.5 | 51.4 | 50.8 | 50.1 |
Fine width (\(\upmu \hbox {m}\)) | 16.5 | 16.4 | 16.5 | 20.0 | 19.8 | 19.9 |
Fine aspect ratio (–) | 1.5 | 1.5 | 1.5 | 2.8 | 2.8 | 2.8 |
Pulp | All fines | Fines with aspect ratio > 4 | ||
---|---|---|---|---|
Arithmetic | Volumetric | Arithmetic | Volumetric | |
R0 | 97.6 | 22.6 | 2.4 | 0.9 |
R1000 | 97.7 | 24.2 | 2.4 | 1.0 |
R2000 | 97.8 | 27.0 | 2.4 | 1.1 |
Dewatering tests
Pulp | SR (mL) | CSF (mL) |
---|---|---|
R0 | 20.8 | 590 |
R1000 | 25.6 | 500 |
R2000 | 30.8 | 410 |
Micro-tomography
Pulp | Mean | Standard deviation | ||||
---|---|---|---|---|---|---|
R0 | R1000 | R2000 | R0 | R1000 | R2000 | |
Fiber width (\(\upmu \hbox {m}\)) | 25.54 | 25.95 | 25.69 | 5.6 | 5.7 | 5.1 |
Fiber height (\(\upmu \hbox {m}\)) | 14.85 | 15.05 | 15.25 | 3.4 | 3.0 | 3.2 |
Wall-thickness (\(\upmu \hbox {m}\)) | 3.09 | 4.00 | 3.23 | 0.75 | 0.85 | 0.63 |
Width-to-height ratio | 1.85 | 1.78 | 1.78 | 0.85 | 0.44 | 0.62 |
Mechanical properties of the handsheets
Pulp | Thickness (\(\upmu \hbox {m}\)) | Grammage (g/m\(^2\)) | Density (\({\hbox {kg/m}}^3\)) |
---|---|---|---|
R0 | 521.3 | 151.2 | 290.1 |
R1000 | 443.7 | 153.2 | 345.2 |
R2000 | 377.0 | 148.4 | 393.7 |
SR0 | 547.4 | 156.1 | 285.1 |
SR1000 | 423.3 | 153.6 | 362.7 |
SR2000 | 349.1 | 144.5 | 414.0 |
Retention of strength additives
Pulp | Starch retention (%) |
---|---|
SR0 | 1.1 |
SR1000 | 1.12 |
SR2000 | 1.21 |
Summary of the experimental results
Numerical simulations
Simulation method
-
We choose a random set of fiber geometry information from the corrected pulp characterization data and create a single fiber. This information includes the fiber length, width, width-to-height ratio, shape factor, and wall-thickness.
-
This fiber is then placed at a random location and with a random orientation on an imaginary 2D plane (for isotropic handsheets).
-
The intersections of this newly place fiber with the previously deposited fibers (from top view) are found.
-
The intersection points are raised vertically with appropriate values to avoid penetration of fibers. However, the fibers can undergo larger pressing at the bond sites and consequently, the distance between their centerlines becomes smaller. The normalized variation of the distance of cross-sectional centers before and after being pressed is demonstrated schematically in Fig. 4 as the press ratio.
-
The deposited fiber is then smoothed along its length. The smoothing procedure uses a given value for the maximum interface angle and it only permits the fiber segments to move upwards during the smoothing procedure to avoid penetration. The interface angle is schematically shown in Fig. 5.
-
This procedure is repeated until the desired network grammage is reached.
Analysis | Type | Nonlinear, implicit |
Convergence criteria | L2 norm of residual force \(< \, 10^{-3}\) | |
Network | Size |
\(\hbox {5 mm} \times \hbox {3 mm}\)
|
Thickness | \(374 \, \upmu \hbox {m}\) to \(526\, \upmu \hbox {m}\) | |
Number of fibers | 5300 to 6300 | |
Number of bonds | 60,000 to 90,000 | |
Fibers | Element type | Timoshenko/Reissner with geometric nonlinearity |
Number of nodes per element | 3 | |
DoF per node | 6 | |
Element size |
\(50 \,\upmu \hbox {m}\)
| |
Element cross-section | Solid or hollow rectangular | |
Element cross-section dimensions | Width: \(4.4\,\upmu \text {m}\) to \(95\,\upmu \text {m}\) | |
Height: \(2.5\,\upmu \text {m}\) to \(53\,\upmu \text {m}\) | ||
Total number of elements | 75,000 to 95,000 | |
Material type | Linear elastic | |
Stiffness | 15 GPa to 45 GPa | |
Strength | 70 MPa | |
Density |
\(1430 \, {\hbox {kg/m}}^3\)
| |
Fines | Element type | Link |
Number of nodes per element | 2 | |
DoF per node | 3 | |
Element size | One element per fine | |
Element cross-section | Circular | |
Element cross-section dimensions | Diameter: \(1\,\upmu \hbox {m}\) (varied between \(0.5\) to \(16\,\upmu \hbox {m}\) in parameter study) | |
Total number of elements | 600,000 if fines are included (varied between zero to 3,000,000 in parameter study) | |
Matrial type | Linear elastic | |
Stiffness | (Varied between 50 and 120 GPa in parameter study) | |
Strain to failure | 3% (varied between 0.5 and 8% in parameter study) | |
Density |
\(1430 \, {\hbox {kg/m}}^3\)
| |
Bonds | Element type | Inconsistent beam-to-beam inseparable point contact element based on closest point projection |
DoF per element | 24 | |
Penalty stiffness | 3000 N/m | |
Failure criteria | Maximum separation distance of \(2\, \upmu \hbox {m}\) Borodulina et al. (2016) |
The effect of captured pulp variations
The effect of density
The effect of inter-fiber bond strength
The effect of fines
Parameter | Initial value | Variation range |
---|---|---|
Fine diameter (\(\upmu \hbox {m}\)) | 1 | 0.5–16 |
Fine length (\(\upmu \hbox {m}\)) | 100 | 20–200 |
Fine stiffness (GPa) | 70 | 50–120 |
Fine strain to failure (%) | 3 | 0.5–8 |
Fine mass percentage (%) | 3 | 0–10 |
The effect of fine diameter
The effect of fine fraction
The effect of maximum length of fines
The effect of fine strength and stiffness
Conclusion
-
Fines with diameters below the resolution of the characterization devices have a greater influence at a given volume fraction. The main mechanism of improvement is the collective reinforcement and stiffening of the bonds.
-
Increasing the length of the fines up to a certain value with a given volume fraction improves the stiffness and strength of fiber networks because these fines can bridge more distant fibers. However, further increasing the length has an opposite effect since longer fines (resulting in their lower amount with the given volume fraction) cannot significantly change the properties as the collective action is required.
-
Even low volume fractions of fines affect the stiffness of the network, however, unless the fines are sufficiently well-bonded, the strength of the sheet is not affected.