Analyses of the effects of fiber diameter, fiber fibrillation, and fines content on the pore structure and capillary flow using laboratory sheets of regenerated fibers

2.1 Regenerated fibers

Natural fibers exhibit a very wide range of fiber properties (Alava and Niskanen 2006). The fiber length, geometry, and diameter can be precisely adjusted in the manufacture of regenerated fibers (Kühl 2015). Therefore, the cellulose of the natural fibers will be specifically modified by first dissolving the cellulose and then regenerating it in the desired way (Harms 2003).

One way to produce such regenerated fibers is to dissolve the cellulose in the solvent NMMO (N-methylmorpholine-N-oxide) (Firgo 1996). Afterwards, the solution is spun through an air gap and the solvent is washed out with water (Röder et al. 2013). The resulting regenerated fibers have been marketed by the Lenzing company since the 1990s under the brand names Tencel^® and Lenzing Lyocell^® (Slater 2005).

The range of applications for regenerated fibers is diverse. They can be used for clothing such as sportswear, for consumer goods such as bed linen or handkerchiefs, or for technical applications such as for papers of all kinds, as a carrier material for enzymes, or as a plastic reinforcement (Eichinger et al. 1996). The advantages of Lyocell fibers are, in addition to high dry and wet strength, suitable moisture absorption and their purity (Kühl 2015). Therefore, Lyocell fibers are usually applied when hygiene requirements are high. This is the case, for example, for insulating paper for electronic applications or for filters used in the cigarette or food industry (Kühl 2015; Slater 2005). In summary, Lyocell fibers can replace fully synthetic polymers in various products (Harms 2003).

Schuster et al. (2003) described the exact structure of the Lyocell fiber: A Lyocell fiber consists of macrofibrils, which have a diameter between 0.5 and 1 µm. The macrofibrils are crucial for the good fibrillation of the Lyocell fibers. A macrofibril consists of microfibrils with diameters in the range of 100 nm. The microfibrils consist of crystalline as well as amorphous regions. The amorphous areas contain small pores in which they can absorb water and thus enable the fiber to swell. Compared to other regenerated fibers, Lyocell fibers have a high orientation of the crystalline as well as amorphous areas. In addition, there are only a few bonds between the fibrils (Röder et al. 2013). Lyocell fibers have a smooth surface. Fibrils can be detached from the crystalline structure by mechanical wet abrasion. The fibrillated fibers can form a fiber network, which is suitable for filtration applications, for instance (Slater 2005).

Pulp fibers and regenerated fibers can be combined in applications, as shown by Kühl (2015) in the production of flushable moist toilet tissue from Tencel^® and pulp, as well as by Bernt (2011) in the production of Rapid-Köthen laboratory sheets from Danufil^® viscose (regenerated fiber from pure cellulose) and eucalyptus (refined, 26 SR). The pure viscose laboratory sheets do not show paper-like properties because the density of the viscose sheets is between 40 and 50 % lower than the density of the laboratory sheets made of cellulose. In addition, the tear strength is very low. Therefore, Bernt (2011) concluded that the bonding between the viscose fibers is much lower compared to the eucalyptus fibers. The tensile strength could hardly be increased even by refining for ten minutes.

2.2 Fiber modification by refining

The original fibers can be pretreated to influence the properties of the paper later on. One common method of fiber pretreatment in the paper industry is refining. During refining, external and internal fibrillation, fiber shortening, fines formation, and fiber straightening occur (Gharehkhani et al. 2015).

On the one hand, during external fibrillation, individual fibrils, and fibril bundles detach from the fiber wall, which increases the specific surface area and may lead to an increase in roughness (Gharehkhani et al. 2015). This leads to a higher bond strength (Östlund and Niskanen 2021). On the other hand, internal fibrillation occurs, which allows the fiber to gain flexibility and to come into closer contact with other fibers, also resulting in higher bond strength. The fiber shortening that occurs is often undesirable, but reduces flocculation and leads to a more uniform result. External fibrillation, as well as fiber shortening, produces fines which can also improve fiber-to-fiber bonds. Fines, which are not bonded to a fiber, can move freely and deposit in the pores during dewatering, resulting in poorer dewatering properties (Gharehkhani et al. 2015).

Fibrils and fines can build bridges during drying between the fibers, bringing the fibers into closer contact (Alava and Niskanen 2006). Besides, they fill the voids between the fibers, which decreases the Canadian Standard Freeness of the pulp as well as the porosity of the paper (Lee et al. 1993). Roberts and Sampson (2003) were able to show that fines have a great influence on the paper structure. The fines dominate the void space from a fraction of 20 % fines, whereby the density is, however, determined by the long-fiber fraction.

2.3 Capillary flow of water through paper

If a fluid imbibes spontaneously into the pores of a porous system, it is called capillary-driven flow. This is the case in water-paper systems, for example. The capillary flow of water through paper depends on the microstructure of the paper, the fluid properties such as surface tension, as well as the interaction between the fluid and the fiber (Cai et al. 2021). Further factors influencing this process are fiber properties such as fiber shape, surface characteristics, fibrillation, and fiber orientation (Keller 2020).

Roberts et al. (2003) have analyzed the flow of water through paper in more detail. They identified four ways in which a liquid can flow through paper: through the fiber interstices as bulk flow, along the channels formed by fiber overlap, along the fiber through cracks or depressions due to surface roughness, and through pores in the fiber. They considered film flow along channels formed by fiber overlap to be the main mechanism. These small channels form a dense, interconnected network. In the process, a meniscus will be formed in the open channel, which will become larger and larger. The increase in the fluid film allows it to get into full contact with the surrounding fibers. When the inter-fiber space is small, and/or the fluid film is sufficiently thick, this condition is unstable. As a result, the air film is displaced and collapses, causing the pore to fill completely with fluid. Roberts et al. (2003) observed no flow in the intra-fiber pores as well as very little flow along the fiber due to surface roughness. As a result, Roberts et al. (2003) identified film flow in the capillaries to be the primary flow mechanism.

First Bump et al. (2015) and later Mikolei et al. (2022) were able to observe the flow of water in the paper very precisely using a confocal microscope. The fluid flow takes place on the inner as well as on the outer fiber surface. Not all fibers and fibrils are wetted and the pores between the fibers are not filled. If only a small amount of fluid penetrates through the paper structure, the fluid flow takes place only on the outer fiber surface. In their experiments, fiber swelling seems to be the dominant imbibition mechanism. In contrast to Roberts et al. (2003), Mikolei et al. (2022) observe the main flow to be on the fiber surface and not along channels formed by fiber overlap.

Thus, filling the pores is not the primary flow mechanism (Roberts et al. 2003; Senden et al. 2007). Consequently, not all pores are directly filled with the first visible liquid front, instead there is a post-wetting flow (Bico and Quéré 2003; Walji and MacDonald 2016). Other authors support this theory: Chang et al. (2018) showed that the post-wetting flow is mainly dependent on the intra-fiber pores and less on the inter-fiber pores. Furthermore, it is showed that water first flows along the fibers (Aslannejad and Hassanizadeh 2017) or along the channels caused by fiber overlaps (Senden et al. 2007) and later fills up the pores.

The ascending velocity of water through the paper depends on the fiber type and length (Carstens 2015). In general, the larger the inter-fiber pores, the smaller the intra-fiber pore volume fraction and the swelling ratio, the faster the ascending velocity (Chang and Kim 2020). The grammage seems to have no effect on the ascending velocity as shown by Carstens (2015), Carstens et al. (2016) as there was no correlation between grammage and ascending velocity for isotropic as well as anisotropic paper.

Paper fibers absorb through-flowing water due to two effects: First, the hydrophilic fiber surface is wetted by water (Alava and Niskanen 2006; Christensen and Giertz 1965). The amount of retained water increases with refining due to fines and fibrils (Christensen and Giertz 1965). In particular, the fibrils are hydrophilic and can absorb water (Aslannejad and Hassanizadeh 2017). Second, the absorption of water by the fiber leads to the swelling of the fiber (Alava and Niskanen 2006). The swelling changes the pore structure and thus also the dynamics of the water flow (Chang and Kim 2020).

Lucas (1918) and Washburn (1921) have developed a model for the flow of a fluid through a porous medium. It is assumed that the flow is a one-dimensional capillary flow. Furthermore, the pores are described as parallel cylinders with the same radius, constant contact angle with the fluid, and no connection to each other (Cai et al. 2021). In addition, an infinite fluid reservoir is assumed (Song et al. 2021).

The Lucas–Washburn model in Equation (1) describes the relationship between the ascending height h (in m), the surface tension σ (in N/m), the viscosity μ of the liquid (in N/m²), the contact angle θ between the liquid and the porous medium, the characteristic length of the pores r (in m), as well as the ascending time t (in s).

The Lucas–Washburn model has often been applied to fluid transport through paper e.g., in (Chang et al. 2018; Hong and Kim 2015; Kvick et al. 2017) as well as through µPADs e.g., in (Fu et al. 2011). The model shows mostly good agreement with the experiments, although many physical effects such as fiber swelling, variation of pore size and geometry, filling of intra-fiber pores or liquid evaporation are not considered (MacDonald 2018). On a macroscopic level, a uniform flow can be observed, which is also modeled by the Washburn equation. Microscopically, however, the flow is heterogeneous (Bump et al. 2015), irregular, and discontinuous due to variations in the size and shape of the pores and different surface conditions (Hodgson and Berg 1988).

The contact angle between the liquid and the porous medium is required for modeling. The contact angle between a fiber and a liquid can be determined, for example, using the powder contact angle method. The procedure is described in more detail in Peršin et al. (2002). This method measures the absorbed water mass over time. The contact angle can be determined in the linear range using the modified Washburn equation. Stana-Kleinschek et al. (2003) measured the contact angle between regenerated fibers and water. They reported a contact angle of 81.06° (±2.87°) for the contact angle between water and a Lyocell fiber in the untreated state and 71.52° (±1.29°) for finished Lyocell fibers.

2.4 Determination of the pore size distribution by mercury porosimetry

One way to determine the pore size distribution of a porous material such as paper is mercury porosimetry. Mercury is non-wetting with respect to most solid materials and will only enter the capillaries of a porous material under pressure (Webb 2001). For the measurement, the relationship between the applied pressure and the pore diameter is used, which is described in the modified Young–Laplace equation, which is often referred as Washburn equation (see Equation (2), with pressure difference ∆ P , surface tension γ of mercury, contact angle θ between porous material and mercury, as well as pore size r ). The smaller the opening diameter of a pore, the greater the required pressure for the mercury to penetrate into the pore. The pressure is slowly increased during the measurement and at the same time, the amount of mercury pressed into the sample per pressure point is measured. This results in a distribution of the required amount of mercury over the pressure or the pore diameter. This measurement method can be used to determine not only the pore size distribution but also the porosity, total pore volume, specific surface area, etc. (Webb 2001; Giesche 2006).

Pores in the range from approximately 3.5 nm to 500 µm can be detected by mercury porosimetry. The limits are determined by the highest possible pressure of the measuring device as well as the starting pressure, which is caused by the weight of the mercury column (Giesche 2006). Therefore, the first pressure point is usually 0.5 psi (Anovitz and Cole 2015; Giesche 2006).

The method has been used several times to measure paper e.g., in (Carstens et al. 2016; Charfeddine et al. 2019; Moura et al. 2005). Pores in the range of 10–100 µm are usually assigned to the paper surface porosity and pores in the range of 0.1–10 µm to the internal porosity (Moura et al. 2005). It should be noted that the pore structure of compressible paper can be damaged by the pressure applied during the measurement, which affects the accuracy (Carstens et al. 2016; Huang and Duan 2017). It has to be taken into account that the diameter of the largest opening and not the “true” pore diameter is determined during the measurement (Giesche 2006). Furthermore, the evaluation of the measurement results is based on the modified Young–Laplace Equation (2), which assumes a cylindrical pore model (Giesche 2006). Also, it should be noted that the method determines pore sizes with a liquid that does not swell fibers. Hence, differences to the situation when water imbibes into paper must be expected. A recent development allows the determination of mean pore sizes with water as the fluid (Postulka et al. 2021).

The mean pore radius of paper depends on the fiber type, length, and grammage (Carstens 2015). For example, Habibi et al. (2017) showed for papers made from flax fibers that the pore size increases with increasing fiber length. Carstens et al. (2016) showed a correlation between freeness and specific surface area for three different fractionated pulps. Moreover, Eichhorn and Sampson (2005), Sampson (2003) assumed that the mean pore radius increases with fiber width if mean areal density and porosity remain constant.

3.1 Sheet production

For sheet production, 6 mm long Lyocell fibers from Lenzing Group (Lenzing, Austria) with a titer of 1.7 as well as 6.7 dtex are used. The titer or fineness provides an indication of the fiber diameter. The fibers are refined in the Jokro mill according to DIN 54360 for 5, 15, and 30 min. The Jokro mill fibrillates the fibers and has barely any fiber shortening effect.

Next, the refined fibers are fractionated by a Bauer and McNett fractionator. Before fractionation, no Haindl fractionator was used to avoid holding back of the long fibers. After fractionation, the R14 fraction (corresponding to a wire with a mesh size of 1.410 mm) contains the long fibers, but no fines and short fiber fragments from the refining process. Afterwards, Rapid Köthen laboratory sheets are produced in accordance with DIN EN ISO 5269-2 with the R14 fraction. A cover sheet is normally used during the drying of the laboratory sheets. However, silicone paper is used instead since the fibers stick to the cover sheet during drying. Sheets with unrefined, unfractionated fibers are also produced for comparison.

Moreover, laboratory sheets with a defined fines content are produced. For the production of fines, 3 mm long Lyocell fibers with 1.7 dtex are refined in a “Voith LR 40” laboratory refiner (SEL 0.5 J/m, set 2/3-1.42-60, 800 kWh/t). Consequently, the fines are secondary and fibrillated consisting of pure cellulose. The length-weighted average fiber length (measured with a Valmet Fiber Image Analyzer FS5) is 0.432(±0.000) mm. It should be noted that the fines used here and designated by this name do not fulfill the definition of fines according to ISO 16065-2, as a non-negligible portion are longer than 0.2 mm. Consequently, the fines are longer than regular fines from pulp made from conventional chemical pulp fibers. Sheets are produced from unrefined as well as 5 min refined and fractionated Lyocell fibers with an addition of 5, 20, and 35 % fines on the Rapid-Köthen sheet former.

The thickness and grammage of the sheets are determined. Both values have some uncertainties due to the strong inhomogeneity caused by flocculation. Furthermore, a fiber analysis of the fibers of the final sheet is carried out with the Valmet Fiber Image Analyzer FS5. According to Laitinen et al. (2014), the fibrillation rate is defined as the ratio between the fibrils area, which are connected to the fiber surface, to the total fiber area, including the main fiber and fibrils, scaled in percent.

3.2 Ascending test with a Flow Pyramid

The flow rate of water through the sheets is determined with an ascending test. Three 15 × 40 mm strips are prepared for each specimen. Fine lines are drawn with a pencil at a distance of 5 mm. The strips are placed in the Flow Pyramid (see Figure 1). Afterwards, the reservoir is filled with approximately 150 µl of distilled water and the camera recording is started (USB digital microscope, Andonstar A1, 30 frames/sec, resolution 640 × 480). From the recorded video, the times at which the visible water front reaches the pencil lines are noted. The setup is based on the measurement of capillary flow time (Wong and Tse 2005; Wong and Tse 2009) and has already been further described by the authors (Helbrecht et al. 2021). The measurement is carried out in standard atmosphere (DIN EN 20 187) with conditioned samples.

Figure 1:

Three measuring strips are placed next to each other in the Flow Pyramid for the ascending test.

The ascending height is approximately a root function of time, so that the curve in the diagram of the ascending height to the root of the ascending time can be approximated by a regression line (see Figure 2). The gradient of the curve describes the ascending rate in mm/√s. The measurement does not start at 0 mm, but has an offset and starts at about 5 mm, as th e s trip is submerged in the water reservoir of the Flow Pyramid. Consequently, the capillary flow starts at the top level of the filled reservoir at about 5 mm. For this reason, the regression of the curves is started at 15 mm so that these conditions do not influence the calculation of the ascending rate.

Figure 2:

Example of an analysis of an ascending test. The ascending height is plotted over the root of the ascending time. It can be seen that the measurement points can be approximated by a regression line. The measurement has an offset due to the setup.

3.3 Microscope images

The fiber structure of the sheet is visually observed using a Keyence VHX-600 microscope and a Keyence VH-Z100UR objective with a 200× magnification.

Fluorescent confocal images were made using a Leica TCS SP8 (Leica Microsystems, Mannheim, Germany) confocal laser scanning microscope (CLSM). Fibers were stained with 10 µM Calcofluor White. Fluorescence was excited using a 405 nm laser and the emission was detected between 470 and 520 nm.

Also the flow of water through the sheet was observed under the confocal microscope. For this purpose, the resonant scanner of the above mentioned CLSM was used. The procedure was first shown by Bump et al. (2015) and then elaborated as described in Mikolei et al. (2022). In brief, a hydrophilic channel is created on the sample by means of wax printing. The strip is then placed horizontally in a custom made chamber that prevents the hydrophilic channel to touch any side walls or the microscope slide on the bottom, in order to prevent any capillary fluid transport between the fibers and a chamber wall. A 30 µl aqueous FITC-Dextran 70 solution is added to one end of the strip, which flows through the sheet. Fast CLSM video sequences are then taken from the x–y plane, to observe the dynamics of the fluid transport within the sheet at high spatial and temporal resolution.

3.4 Determination of the pore size distribution with mercury porosimetry

The pore size distribution of the laboratory sheets is measured using a mercury porosimeter (Autopore V, Micromeritics Instrument Corporation). For the measurement, 20 mm wide strips with an average weight of 0.100(±0.014) g were prepared. A double determination is performed in each case. A contact angle with the mercury of 130° is assumed. The evaluation is carried out on the basis of DIN ISO 15901-1 where the pore diameter is calculated from the equivalent pressure by the Washburn equation. In this work, the average pore size is defined as the measured pore size when half of the pore volume is filled (0.5 Cumulative Intrusion).

3.5 Modeling of the ascending test using the Lucas–Washburn equation

Furthermore, the ascending test is modeled with the Lucas–Washburn equation. Literature values (Haynes et al. 2016) are used for the surface tension (0.07228 N/m) as well as for the viscosity (0.966 mN/m²) of water. The Eötvös rule (Eötvös 1886)/Andrade equation (Da Andrade 1934) was used to calculate the value for 23 °C and 1 bar ambient pressure.

For the mean pore diameter, the pore diameter from mercury porosimetry is taken, in which half of the pore volume is filled with mercury. The contact angle between fiber and water was used as a fitting parameter and calculated by least squares regression from the ascending rate differences between the model and experiment.

4.1 Influence of refining on fiber properties

The regenerated fibers change due to the refining process in the Jokro mill. Firstly, the average length weighted fiber length decreases. According to the manufacturer, the original fiber length is 6 mm. However, an average fiber length of 4.8 mm is measured for the unrefined (0 min refining time) but disintegrated fibers. The fibers are shortened by the refining process, so that after a refining time of 30 min the fibers have an average length around 2 mm.

Furthermore, the fibrillation increases. The unrefined fibers are only slightly fibrillated, which is due to slight damage caused by disintegration. The fibrillation rate is 2 % after 5 min and 4.3 % after 30 min. The increase in fibrillation due to refining is illustrated in Figure 3. Consequently, the effect of fibrillation can be separated from that of fines, but not from the effect of fiber length. It should be kept in mind that the increase in fibrillation is also accompanied by a shortening of the fibers. The results of the fiber analysis can be found in Table 1.

Figure 3:

Confocal microscope images of Lyocell sheet made from 1.7 dtex fibers, (A) unrefined, (B) refined for 15 min in the Jokro mill. It can be seen that the fibrillation of the unrefined fibers is very little and of the refined fibers high.

4.2 Influence of fibrillation on the pore structure and capillary flow

Figure 4 shows the ascending rate in mm/√s for laboratory sheets with different refining times. The coefficient of determination (R²) is between 0.98 and 1.00. The standard error of regression (SER) is between 0.11 and 1.06. Two findings can initially be noted from these results. First, the ascending rate continuously decreases with refining time up until 15 min. Second, the ascending rates of the sheets from 1.7 dtex fibers do not differ significantly from the sheets from 6.7 dtex fibers (single factor analysis of variance with ANOVA, α = 5 %). As already described in Section 3.1, the grammage of the laboratory sheets differs, but this should not have a major influence on the water flow (cf. Section 2.3).

Figure 4:

The ascending rate in mm/√s for laboratory sheets with different refining times. Error bars indicate the distance between the minimum and maximum.

The refining process changes the fiber properties, which in turn affects the properties of the sheet. In particular, the fibers are fibrillated during refining. The influence of fiber fibrillation on the flow of water through the sheet becomes clear considering the ascending rate over the fibrillation rate (see Figure 5). The ascending rate decreases with increasing fibrillation rate (i.e. also refining time). With increasing refining time, the difference in fibrillation rate between a titer value of 1.7 and 6.7 dtex becomes obvious. For fibers with 6.7 dtex, the fibrillation rate changes only slightly after 5 min of refining, whereas for 1.7 dtex, the fibrillation rate differs greatly between 5 and 15 min of refining. Only the difference between 15 and 30 min refining is small.

Figure 5:

Ascending rate in mm/√s of laboratory sheets made of refined fibers, over fibrillation rate. The error bars of the x-axis indicate the standard deviation of four fiber analyses measurements. The error bars of the y-axis indicate the deviation from the maximum/minimum value of the ascending tests.

Figure 6 shows microscope images of the laboratory sheets of refined 1.7 dtex fibers. It can be seen how the unrefined fibers have a very low curl and are almost rod-like in structure. In addition, no fibrils are visible. Additionally, the figure illustrates how the fibrils increase with increasing refining time and form an interwoven network. The visible fibrils on the fiber surface are numerous and very long. In a Lyocell fiber, the microfibrils lie parallel to each other and there are no different fiber walls or a lumen as in pulp fibers. This makes it very easy to detach fibrils and fibril bundles from the structure during refining. This explains the unusually large number of very long fibrils and fibril bundles projecting into the pore structure. The fibrils in sheet made from pulp fibers are usually shorter and fewer in number.

Figure 6:

Laboratory sheets made from refined 1.7 dtex fibers. The refining times (0, 5, 15, 30 min) are indicated above the figure respectively.

Comparing the microscope images of laboratory sheets made from 1.7 dtex fibers (see Figure 6) and 6.7 dtex fibers (see Figure 7) refined at different refining degrees, it is clear that the fiber network is similar. Although the pores are considerably larger in sheets from 6.7 dtex fibers, where the fiber diameter and fiber stiffness are considerably larger. The pore diameter increases accordingly with increasing fiber diameter as shown in (Eichhorn and Sampson 2005) and (Sampson 2003). Moreover, it highlights the fact that the pores become smaller due to the refining or rather the increase in fibrillation, as the fibrils reach into in the large pores. It can also be seen that a large number of long fibrils and fibril bundles stick out into the pore structure. As a result, the interwoven network of fibrils in the pores becomes clearer as the refining times increases.

Figure 7:

Laboratory sheets made from refined 6.7 dtex fibers. The refining times (0, 5, 15, 30 min) are indicated above the figure respectively.

These two findings can be confirmed by mercury porosimetry measurements of the pore size distribution (see Figure 8). Due to refining, the pore size distribution becomes broader and flatter. In addition, the maximum shifts towards smaller pores. While the overall shape of the pore size distributions of the 1.7 dtex sheets and 6.7 dtex sheets are similar, the values for the 6.7 dtex sheets are shifted towards larger pore sizes.

Figure 8:

Pore size distribution from mercury porosimetry for sheets made from refined fibers. Displayed is the log differential intrusion over the pore diameter. A double determination was carried out for each sample.

In summary, the pore size distributions of sheets made from 1.7 and 6.7 dtex fibers differ. Consequently, the average pore size at which half of the pore volume is filled also differs as illustrated in Figure 9. However, the difference between the ascending rates is not significant (see Figure 4).

Figure 9:

The pore size at 0.5 cumulative intrusion in µm for laboratory sheets with different refining times. The error bars indicate the distance between the minimum and maximum.

According to Mikolei et al. (2022) (cf. Section 2.3), the main flow of water is a film flow along the fiber surface. This theory explains the presented results. The pore space between the fibers has no influence on the film flow, since the initial film flow only occurs at the fiber surface. Consequently, the surface fibrillation has a strong influence on the flow rate, since a considerably larger surface area has to be wetted and more material can swell due to the fibrils. It is conceivable that the second liquid front, which fills the inter-fiber pores, differs for the sheets made from 1.7 dtex and 6.7 dtex fibers.

4.3 Influence of fines on the pore structure and capillary flow

Figure 10 shows the ascending rate in mm/√s for laboratory sheets with different fine contents which are added during sheet production. Interestingly, the water flows faster through the sheet made of unrefined fibers with a fines content of 5 % than without any fines. It should be noted that the phenomenon is not clear, since the range of error bars overlaps. The ascending rate decreases with further increasing fines content. In contrast, the ascending rate of paper samples made from fibrillated fibers (refined for 5 min) decreases with increasing fines content. No increase in ascending rate can be observed at a fines content of 5 % for refined fibers.

Figure 10:

Ascending rate in mm/√s of laboratory sheets with different fines contents. The fines content indicates the content that was added during sheet production. The error bars indicate the distance between the minimum and maximum.

Bump et al. (2015) and Mikolei et al. (2022) have shown that liquid transport initially takes place at the fiber surface. It is conceivable that the smooth surface of unrefined Lyocell fibers is too smooth for a good initial wetting. On the one hand, fines on the fiber surface might help to improve wetting, accelerating the flow of water, but on the other hand, more swellable material is present which inhibits the flow. Consequently, a low fines content can lead to a faster liquid transport, while higher fines contents lead to a deceleration. Again, there is no significant difference of the ascending rate between the respective samples of 1.7 and 6.7 dtex fibers in the comparison of ascending rates by varying the fines content (single factor analysis of variance with ANOVA, α = 5 %).

Figure 11 illustrates microscope images of laboratory sheets made of unrefined fibers with different fines content. It is visible how the fibrillated fines are deposited between and around the fibers, which also form an interwoven network.

Figure 11:

Laboratory sheets made from unrefined 1.7 dtex fibers. The fines content (0, 5, 20, 35 %) is indicated above the figure respectively.

Mercury porosimetry measurements confirm the conclusions of the microscope images. The average pore size decreases due to the addition of fines. The average pore size is smaller for sheet made from 1.7 dtex fibers than for 6.7 dtex fibers (cf. Figure 12).

Figure 12:

The pore size at 0.5 cumulative intrusion in µm for laboratory sheets with different fines content. The error bars indicate the distance between the minimum and maximum.

The pore size distribution shown in Figure 13 also demonstrates the correlation. The pore size distribution becomes flatter due to the addition of fines and shifts towards smaller pores on the x-axis. The same observation obtained when the fiber fibrillation was analyzed.

Figure 13:

Pore size distribution from mercury porosimetry for sheets made from unrefined fibers with added fines. Displayed is the log differential intrusion over the pore diameter. A double determination was carried out for each sample.

The two considered effects overlap in the case of sheets made from fibrillated fibers as well as added fines, so that both the ascending rate and the mean pore size are smaller than the similar sheets made from unfibrillated fibers or without fines as you can see in Figures 12 and 14.

Figure 14:

The ascending rate in mm/√s for laboratory sheets with different fines content. The error bars indicate the distance between the minimum and maximum.

In conclusion, the absolute pore size seems to have no or a subordinate influence on the ascending rate which was determined using the visible water front. This observation supports among others the theory of Roberts et al. (2003) and Mikolei et al. (2022) (see Section 2.3). The pore size would have a large influence on the ascending rate if water would flow through the sheet as bulk flow. When water flows through the sheet as a film flow, the pore size has very little effect on the ascending rate. It is conceivable that the pore size has an influence on the velocity with which the pores are filled later on.

In a film flow, the fiber surface, the channels on the fiber surface, and between fiber overlaps have an influence on the ascending rate. Furthermore, it is conceivable that the specific surface area and the fiber orientation play a role. The more fibers are oriented in the flow direction and the more undisturbed the fluid can flow in this direction, the faster it is. If there are only a few fibers, the water flows precisely along these fibers and wets them. In the case of fibrils and fines, the water is divided so that one part continues to follow the fiber and the other part initially flows along the fibril/fine, thus reducing the velocity.

According to this theory, sheet made of unfibrillated fibers and without fines should have had the highest ascending rate. However, the water flowed, however not significant, faster through the sheet made of unfibrillated fibers and 5 % fines. The fines and fibrils consist of cellulose, which is hydrophilic and swells with water. Thus, the hydrophilic attraction and/or swelling capability of these could initially accelerate the water transport by pulling the water forward. When a critical point is reached, the effect of surface wetting, swelling, and cross flow prevails, preventing the water from flowing. Accordingly, there are two opposite effects which overlap.

It should be clearly pointed out that fiber shortening also takes place with fibrillation, so that the effect of fibrillation cannot be clearly distinguished from the influence of fiber length. In addition, the results refer to a small sample size.

4.4 Observation of the capillary water flow with a confocal microscope

The flow through a laboratory sheet (1.7 dtex, 5 min refined) captured over time by a confocal microscope is shown in Figure 15. Note that the colored fluid (green) flows along the fibers as a film flow and wets the fiber surface confirming Bump et al. (2015) and Mikolei et al. (2022). The inter-fiber pores fill up later, whereby some pores are not completely filled.

Figure 15:

Flow over time of a fluid (containing a fluorescent dye, which is shown in green) through a laboratory sheet (1.7 dtex, 5 min refined). This shows how the fluid flows through the sheet as a film flow. Not all inter-fiber pores are filled with the fluid. The time is indicated in seconds on the images. The scale is the same for all images, but only given for one.

The confocal microscope images further demonstrate that fibrils are also wetted and lead to cross-flow. Figure 16 depicts a close-up image from the confocal microscope, showing that the fluid has wetted mainly one fiber as well as its fibrils. Only a little fluorescent fluid can be seen on the other fibers.

Figure 16:

Cutout from a fluid wetted Lyocell fiber (1.7 dtex, 5 min refined), (A) microscope image, (B) the same microscope image overlaid with the image from the confocal microscope, where the dye in the fluid is visible. A film flow along one fiber can be seen and no bulk flow using the channel between the two parallel fibers.

4.5 Ascending rate modeling

The Lucas–Washburn equation (see Equation (1) in Section 2.3) describes the linear relationship between the ascending height and the root of the ascending time. The mean pore diameter, fluid properties, as well as the contact angle between the water and the fiber are required for modeling the ascending height as a function of the ascending time. In the following, the Lucas–Washburn equation is used to model the water transport in the Lyocell sheets. For modeling, the mean pore diameter is determined by mercury porosimetry. In each case, the pore diameter is taken at which half of the pore volume is filled. The fluid properties were taken from literature (cf. Section 3.5). The contact angle between the fiber surface and water is calculated in such a way that the sum of the least squares of the ascending rates of the model as well as the experiment becomes minimal.

The mean pore diameters of the sheets made from 1.7 and 6.7 dtex fibers differ considerably, so they are considered separately in the contact angle calculation. The modeled contact angle is 83.0° for 1.7 dtex sheets (least square error: 11.92) and 87.0° for 6.7 dtex sheets (least square error: 4.81). The results agree well with the value of 81.06° (±2.87°) determined by Stana-Kleinschek et al. (2003) (cf. Section 2.3). In the modeling, the calculated contact angle of the fibers of the two different titers differ, although the contact angle should be independent of the titer. This is due to the consideration of the mean pore diameter in the modeling which differs greatly.

The comparison between the modeled ascending rate (R² = 0.86, adjusted R² = 0.85) and the experimentally determined ascending rate is shown in Figure 17A. The two samples of unfibrillated fibers and 5 % fines are marked in red. These two samples cannot be modeled well due to their unusual behavior.

Figure 17:

Correlation between the modeled ascending rate and the experimentally determined ascending rate (A) with the Lucas–Washburn model and (B) with a statistical model. The samples from unfibrillated fibers and 5 % added fines are marked in red. The error bars indicate the distance between the minimum and maximum measured ascending rate.

The Lucas–Washburn equation has often successfully been used for modeling fluid flow through paper (see Section 2.3). However, it can be shown, that the pore diameter is not a sufficient parameter for modeling, as it has only a small influence on the water transport, as described in Section 4.2. Other parameters such as the fibrillation rate or the fines content have also an influence on the water transport.

Using the statistics program Design-Expert v12, models were created to calculate the ascending rate in the linear range with the fibrillation rate (R² = 0.834, adjusted R² = 0.819), fines content (R² = 0.131, adjusted R² = 0.092), as well as pore diameter (R² = 0.429, adjusted R² = 0.403). The model with the fibrillation rate clearly describes the ascending rate best. The model can be improved a little if the fines content is added as a second parameter (R² = 0.834, adjusted R² = 0.819) and the pore diameter as a third parameter (R² = 0.839, adjusted R² = 0.815). The models are based only on the few experiments carried out here and not on a physical model. Therefore they cannot be used for other purposes. For other observed parameter ranges, the model could look considerably different. The models merely intend to show that in this example, the ascending rate correlates very well with the fibrillation and a bit with the fines content.

As an example, Figure 17B illustrates the modeling of the ascending rate with two parameters in comparison to the Lucas–Washburn equation. The underlying model is given in Equation (3). As previously described, the ascending rate in sheets made from unfibrillated 1.7 dtex fibers and 5 % added fines is surprisingly high and therefore cannot be well represented by the model. The simple statistical model with only two fiber parameters models the ascending rate for water a little less precise than the Lucas–Washburn equation.

4.6 Comparison of pulp and regenerated fibers

In this work, the influence of fibrillation, fines content, and fiber diameter on the pore structure and the flow of water through the fiber network was investigated. The separation or control of these parameters independently of other properties is not possible with conventional chemical pulp fibers, since such fibers exhibit a very wide range of distributed fiber properties. For this reason, regenerated fibers were used.

There are differences as well as similarities between regenerated fibers and pulp fibers. On the one hand, regenerated fibers consist of microfibrils lying next to each other, from which very long and numerous fibrils and fibril bundles are detached by refining. Conventional pulp fibers consist of different cell walls. In addition, the fibrils are less numerous and smaller (cf. chapter 4.2) and the fines of regenerated fibers produced by refining are larger than by refining pulp (see Section 3.1). Furthermore, the fiber analysis is designed for pulp fibers and not for regenerated fibers. On the other hand, both sheets made from regenerated fibers as well as papers made from chemical pulp fibers have an open-pore fiber network of cellulose-based fibers built up from microfibrils and are manufactured with the same processes. It has not yet been investigated whether the results can be transferred to paper made from conventional pulp fibers.

Consequently, the presented results are valid for fiber networks from Lyocell fibers and most likely transferable to fiber networks from regenerated fibers with similar properties, e.g. size scale and mass fraction of the fibrils and fines. It is not the aim of this study to draw conclusions on the transferability of results for Lyocell fiber based sheets to conventional pulp papers.