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Permeability of pulp fiber mats with filler particles
Colloids and Surfaces A: Physicochem. Eng. Aspects 333 (2009) 96–107
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Permeability of pulp fiber mats with filler particles R. Singh, Sergiy Lavrykov, Bandaru V. Ramarao ∗ Department of Paper and Bioprocess Engineering, Empire State Paper Research Institute, College of Environmental Science and Forestry, State University of New York, 1 Forestry Drive, Syracuse, NY 13210, USA
a r t i c l e
i n f o
Article history: Received 17 April 2008 Received in revised form 14 August 2008 Accepted 11 September 2008 Available online 26 September 2008 Keywords: Permeability Fibrous media Wood pulp Fillers Specific surface area Precipitated calcium carbonate
a b s t r a c t We studied the permeability of fibrous media composed of filler particles in addition to fibers which are often encountered in industrial practice. Bleached Kraft pulp wood fibers and different kinds of fillers used in papermaking were the focus of this study. The fillers consisted of (i) scalenohedral precipitated calcium carbonate (PCC-Albacar), (ii) prismatic PCC (Albafil), and (iii) kaolin clay particles. The composite permeability increased with the addition of smaller quantities of PCC but higher loadings lowered the permeability significantly. The kaolin particles decreased the permeability of the pulp mats at all loading levels. The initial permeability increase observed with PCC was also accompanied by a simultaneous increase in the drainage rates of the pulps. The higher permeability is due to flocculation caused by heterocoagulation of PCC particles and the pulp fibers. At higher filler loadings, the PCC particles clog the pore spaces and reduce the permeability. Kaolin particles do not cause flocculation and hence decreased the permeability at all loadings. A model for the permeability of such composites was developed based on the Kozeny–Carman equation, considering the specific surface area as composed of two contributions. The first, due to fibers alone can result in lower specific surface areas caused by flocculation. The second contribution was an increase in surface area due to clogging of the fiber mats. The specific volume of the composite pulp mats was modeled as a simple weighted mixture of the specific volumes of the individual components. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Paper is manufactured by draining a suspension of wood pulp fibers on a wire screen and subsequently dewatering the pulp mat by vacuum and applied pressure. The removal of water in these operations depends upon the flow resistance of the wet pulp mat. There have been many investigations of the permeability of water-saturated pulp mats (see e.g. Han [1]). An excellent and comprehensive summary of the permeability of paper has been given by Lindsay [2]. Pulp mats consolidate to higher solid concentrations when pressure is increased, primarily due to fiber bending and compression of the cell walls. Therefore their permeability decreases with increasing applied pressure. This dependence can be used to determine the hydrodynamic specific surface area and the specific volume of the pulp fibers by applying the Kozeny–Carman model. Robertson and Mason [3] developed a permeability based measurement technique that has formed the basis of the Pulmac Permeability Tester. Cowan characterized wet pulps using specific surface area and compressibility [4]. Kumar and
∗ Corresponding author. Tel.: +1 315 470 6513; fax: +1 315 470 6945. E-mail address: [email protected] (B.V. Ramarao). 0927-7757/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2008.09.035
Ramarao [5] and later, Wei and Ramarao [6] described the application of the specific filtration resistance to determine the pulp specific surface area and specific volume. Maunier and Ramarao [7] used this technique to study the impact of retention aid polymers on pulp mat permeability whereas Das and Ramarao [8] and Das et al. [9] discussed methods of determining the specific surface area and specific volume from permeability data obtained by simple gravity drainage experiments. The Kozeny–Carman equation can be given as follows for pulp fibers (Ingmanson et al. [10])
K=
1
ε3
2 kS0,f
(1 − ε)2
.
(1)
The parameter k is treated as an empirical constant that lumps together all the uncertainties related to the fluid flow and structure of the porous media. It depends upon the shape of the channels, the orientation and size distribution functions and the manner in which the channels are interconnected. At porosities less than 0.8, the constant k has a fixed value (see e.g. Han [1]). For pulp fiber mats, the specific surface area (denoted Sw,f ) is usually based on oven dry fiber mass of the pulp instead of the volume. This specific
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Nomenclature
The total solid concentration of the composite fiber–filler mat is given below
c
c=
k K K0,f mf mm mp rf
S0 S0,m S0,f S0,f S0,p Sw Sw,m
vf vf,f vf,p vf,m Vf Vp Vv Vm ˛
mass concentration, defined as mass of solid material/volume, kg m−3 Kozeny–Carman constant [Eq. (1)], assumed to be 5.5 for fibrous media permeability, m2 parameter representing specific surface area of fibers [Eq. (10)] mass of fibers (oven dry) mass of mixture (fiber + filler) mass of filler parameter representing mean pore radius in fibrous mat (without filler), taken to be equal to fiber radius, m specific surface area based on volume, m−1 specific surface area of mixture (fiber + filler), m−1 specific surface area of fibers (flocculated state), m−1 specific surface area of fibers (unflocculated state), m−1 specific surface area of filler particles, m−1 specific surface area based on mass, m2 kg−1 specific surface area of mixture (fiber + filler), m2 kg−1 specific volume of mat, m3 kg−1 specific volume of fibers, m3 kg−1 specific volume of filler particles, m3 kg−1 specific volume of mixture (fiber + filler), m3 kg−1 volume of fibers in mat, m3 volume of filler in mat, m3 volume of void space in mat, m3 volume of mat, m3 parameter representing permeability increase to flocculation [Eq. (11)] parameter representing permeability increase to flocculation [Eq. (11)] parameter representing permeability decrease to fillers [Eq. (12)] parameter representing permeability decrease to fillers [Eq. (12)] porosity of mat mass fraction, fibers mass fraction, filler
ˇ ε ωf ωp
due due
2. Materials and methods
due
Bleached Kraft softwood and hardwood pulps were obtained from pulp manufacturers. The pulps were disintegrated according to TAPPI standard methods [T-205 sp-95] and were stored for further use. The fiber length distributions of these pulps were determined using the Kajaani FS-100 fiber length analyzer. Two types of PCC fillers [Albacar (AC) and Albafil (AF)] were obtained from Specialty Minerals Inc. (SMI) in slurry form. Small samples of both PCC-Albacar and -Albafil were dried and SEM pictures were taken. Albacar is scalenohedral in shape with an average particle size of 2 m and specific surface area of 7.4 m2 g−1 . Albafil is prismatic in shape with 0.8 m average size and specific surface area of 9.77 m2 g−1 . Albacar is a PCC containing scalenohedral shaped particles (Fig. 1a) whereas Albafil has prismatic shaped (Fig. 1b) particles. The zeta potential of the PCC fillers was measured using a Brookhaven BIC Zetaplus & Nanoplus (Brookhaven Instruments Corp., Brookhaven, NY). The properties of the fillers are summarized in Table 1. In order to characterize the action of the PCC fillers on the pulps, we determined the drainage rates in a gravity drainage tester (see Kumar and Ramarao [5], Das et al. [9] for more details). The tester consists of a transparent vertical column of diameter 0.06 m and height of 1 m connected to a vacuum pump at the bottom. A screen is provided at the bottom of the column. Pulp suspension is allowed to drain under gravity or the combined action of vacuum and
due
(2)
The specific volume of the fibers vf,f is defined as the ratio of the volume of the (water swollen) pulp fibers to their dry mass. The fiber mat concentration c defined as the total (oven dry) fiber mass/mat volume. The relation between the porosity and fiber concentration is given below ε = 1 − vf,f c.
(3)
The Kozeny–Carman equation takes the following form: K=
1
(1 − vf,f c)3
2 k Sw,f
c2
.
(5)
Wang et al. [11] investigated the permeability of pulp mats under higher pressures (representative of those in the wet-pressing of paper) and identified a limiting value of 1/vf,f for the mat concentration beyond which Eq. (3) is not valid. Our experimentation was conducted under lower pressure conditions and any potential changes of the specific volume with pressure were neglected. Particles of mineral fillers such as precipitated calcium carbonate (PCC) and kaolin clay are included along with pulp fibers in fine paper furnishes. Fillers serve two important purposes: to replace the more expensive wood pulp fibers in the product and to improve the optical and printing characteristics of fine papers. As lowering manufacturing costs for paper is an important objective, a current trend in papermaking is to use higher filler levels in the range of 20–30% of the fiber mass. Inclusion of fillers at such high levels can significantly reduce water drainage due to increased flow resistance increasing manufacturing costs or reducing production. Therefore, knowledge of the effect of fillers on the drainability of pulp suspensions is necessary. Most papermaking experience indicates that fillers hinder drainage. Springer and Kuchibhotla [12] found that clay, calcium carbonate and titanium dioxide fillers increased the specific filtration resistance. In an earlier investigation of dewatering, we measured the drainage properties of softwood and hardwood Kraft pulps with different types of fillers. When PCC fillers were added to these pulps, drainage measured by the freeness and drainage time increased [18]. Liimatainen et al. [13] reported that the addition of calcium carbonate fillers to pine, eucalyptus and birch Kraft pulps increased the drainage rates and decreased the specific filtration resistance. They conjectured that the specific surface area is reduced upon addition of the fillers. The present paper presents new experimental data on the variation of the permeability of pulp fiber mats with PCC and kaolin fillers. We also present a new semi-empirical model to predict these permeability characteristics of filler loaded pulp mats.
surface area is given by: Sw,f = S0,f vf,f .
mf + mp Vf + Vp + Vv
(4)
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Fig. 1. (a) SEM picture of precipitated calcium carbonate (PCC-AC) Albacar (picture by Specialty Minerals Inc.) and (b) SEM picture of precipitated calcium carbonate, Albafil (PCC-AF) (picture by Specialty Minerals Inc.) .
gravity, through the screen while a mat builds on it. An ultrasonic range sensor measures the suspension-air interface as a function of time. All water used in these experiments was at neutral conditions and was de-ionized and distilled. No additional additives
or salts were added to the suspensions except where noted in the results. Pulp mats were formed by steady sedimentation in a Pulmac permeability tester [Pulmac Instruments Ltd., Montreal, Canada]
Table 1 Filler and fiber properties.
PCC-AC PCC-AF SW pulp fiber length, mm HW pulp fiber length, mm a b c
Particle size (m)
Zeta potential (mV)
Specific surface area (×103 m2 kg−1 )
3.03b 0.8a 2.6c 0.9c
27.9b 24.3b CSF: 650 ml CSF: 510 ml
7.4a 9.77a Bleached Kraft Northern SW Bleached Kraft Eucalyptus
From SMI. Measured using BIC—Zetaplus & 90 Plus. Kajaani FS 100 Fiber length Analyzer.
Fig. 2. (a) Drainage of a pulp suspension in a column as a function of time (PCC-AC). 1—Hardwood control (no-filler), 2—hardwood pulp loaded with 10% PCC-AC (based on OD pulp mass). (b) Drainage of a pulp suspension in a column as a function of time (PCC-AF). 1—Hardwood control (no-filler), 2—hardwood pulp loaded with 10% PCC-AF (based on OD pulp mass).
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Fig. 3. (a) Effect of filler loading on the permeability of composite fiber–filler mats (HW − PCC-AC). 1—0% filler; 2—1.8%; 3—9.42%; 4—14.00%; 5—21.22%; 6—29.00%. (b) Effect of filler loading on the composite fiber–filler mats (HW + PCC-AF). 1—0%; 2—1.5%; 3—10.65%; 4—16.00%; 5—20.00%; 6—30.00%. (c) Effect of filler loading on the composite fiber–filler mats (SW + PCC-AC). 1—0%; 2—2%; 3—9%; 4—14.15%; 5—20.50%; 6—27.00%; 7—38.00%. (d) Effect of filler loading on the composite fiber–filler mats (SW + PCC-AF). 1—0%; 2—1.3%; 3—10.65%; 4—20.50%; 5—35.00%. (e) Effect of filler loading on the composite fiber–filler mats (HW + Kaolin). 1—0%; 2—3%; 3—10%.
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Fig. 4. (a). Permeability of pulp-filler mat with filler mass fraction in mat. (Hardwood pulp with PCC-AC filler). Fiber concentration is at 120 kg m−3 . (b) Permeability of pulp-filler mat with filler mass fraction in mat. (Hardwood pulp with PCC-AF filler). Fiber concentration is at 120 kg m−3 . (c) Permeability of pulp-filler mat with filler mass fraction in mat (hardwood pulp with Kaolin filler). Fiber concentration is at 140 kg m−3 .
after the pulps were deaerated under vacuum for at least 24 h. The same procedure was used to form pulp fiber–filler mats also. After the mats were formed, they were pressed to different levels by placing weights and allowing compression to predefined thicknesses using spacers. The pulp mat thicknesses varied from 8 to 18 mm. The loads applied on the mat ranged from 1.0 to 7 kg translating into applied pressures of 3–22 kPa. The compressibility of the pulp mats was determined and will be reported in a separate investigation. The permeability of the formed mats was determined by flowing distilled and deaerated water through them and measuring the flow rate and pressure drop under steady conditions. A plot of the mat flow resistance against the solid concentration yields the specific surface area and the specific volume of the composite, assuming the validity of the Kozeny–Carman equation for pulp fibers. For more details on this procedure, one may refer to the publication by Mason [20]. There are some concerns about permeability measurements in a constant pressure apparatus such as this instrument. In particular, the concentration within the pulp mats may vary along their thickness. Since the permeability is generally a non-
linear function local variations in porosity can introduce significant errors in its measurement. Long-time dynamic effects of compression such as mat creep, mat rearrangement or pore-blocking due to fine particle deposition can also cause systematic deviation in permeability. Care was taken in our measurements to ensure that the mats reached a state of equilibrium and no time-dependent effects were observable on the flow or pressure measurements. The effects of local variation of porosity and permeability are neglected in the analysis but will be the subject of a future report. 3. Results 3.1. Experimental results The drainage of a suspension containing BKPHW and PCC is shown in Fig. 2a (for PCC-AC) and Fig. 2b (for PCC-AF). When PCC is added to the pulp at low concentrations, the drainage is increased as shown by curves labeled 2 in both of these figures. Liimatainen et al. [13] found that the specific filtration resistance of the pulps
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decreased upon addition of PCC, but they did not investigate in terms of the permeability parameters. The permeability of pulp-filler mats was determined at different solid concentrations defined as in Eq. (5). Fig. 3a–e show these permeabilities for softwood and hardwood pulp mats over different mat concentrations. Each curve in these figures corresponds to a different fiber mat containing different filler fraction (ωp ). The permeability decreases with increasing mat concentration due to a decrease in the porosity. However, the addition of PCC as filler results in a large increase in permeability at different filler levels for both PCC-AC and PCC-AF as shown in Fig. 3a–d. This behavior is obtained for both the hardwood and softwood pulps. Fig. 3e shows the permeability of pulp mats loaded with kaolin fillers. The experimental permeabilities indicate that kaolin decreases the mat permeability at a given mat concentration. The reduction in permeability can be understood as a consequence of the blocking action of the added filler clogging the pores within the fiber mats. This decrease contrasts with the increase in permeability with PCC filler addition. Fig. 4a–c shows the mat permeabilities with increased filler concentrations for the two PCC samples (AC and AF) and kaolin. The mats were prepared such that the fiber concentration
101
was kept constant in these cases. We observe a spike in permeability, due to flocculation in the case of the PCC fillers whereas the permeability of the kaolin-filled mats decreases monotonically. Fig. 5a–d show scanning electron micrographs of the pulp-filler mats obtained after drying and sectioning. Views of the lateral (i.e. frontal) and cross sections in the thickness (ZD) are presented for fiber mats loaded with PCC-AC and PCC-AF. We observe that the filler particles tend to agglomerate around the pulp fibers as well as filling up the inter-fiber pore spaces. Aggregates of fillers tend to plug the pore space causing large increases in flow resistance, i.e. large drop in permeability of the composite mats, whereas filler adsorbed on the fibers may not have such a dramatic effect on the permeability decrease. By applying the Kozeny–Carman equation [Eq. (4)] to the permeability-concentration data, it is possible to fit for the specific surface area (Sw,m ) and specific volume, vf,m , respectively. We followed Robertson and Mason’s procedure of using a linearized version of the flow resistance-mat concentration relationship for this purpose. A critical assumption we made here was that the Kozeny–Carman equation, including the Kozeny constant was directly applicable to the pulp-filler mixtures under all our exper-
Fig. 5. (a) SEM picture of hardwood pulp + PCC-AC filler 20% (lateral/in-plane view). (b) SEM picture of hardwood pulp + PCC-AC filler 20% (ZD view). (c) SEM picture of hardwood pulp + PCC-AF 7.44% (lateral/in-plane view). (d) SEM picture of hardwood pulp + PCC-AF 7.44% (transverse/ZD view).
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Fig. 5. (Continued ).
imental conditions. This assumption may not be valid for pulp fiber–filler mixtures. Figs. 6–9(a–c) show the specific surface area (Sw,m ) and the specific volume (vf,m ) of pulps loaded with PCC. Results for hardwood and softwood pulps filled with AC and AF types of PCC are shown. The specific volume always decreases with filler addition since fillers have much higher densities than the fibers and their incorporation into the mats gives more compact solids and lower specific volume. The results for the specific surface area based on volume are shown for each of these cases also. S0 decreases to a minimum value after which it begins to increase resulting in decreased permeability. 3.2. Permeability model Permeability models are important because they can be used to predict the performance characteristics of fibrous filters and drainage resistances of pulp mats. Models to predict the permeability of pulp-filler composite mats can also be useful in determining the effect of different types of fillers on drainage and other physical
processes such as dewatering during papermaking. The experimental results discussed in the previous section indicate that flocculation and pore blockage could be the main factors impacting the permeability of the pulp-filler composite mats. Tentatively, the differences in the action of different fillers may be explained as due to differences in their charge interactions and sizes. PCC particles are cationic and also larger in size compared to the other particles. The filler particles were aggregated and no retention aids were necessary to achieve high levels of loading of these fillers in the pulp mats. The PCC filler can initially flocculate the pulp suspensions. When these fillers were added to the pulp suspension, the formation of flocs could be also be observed visually. The resulting pulp mats must be heterogeneous with denser floc regions and lighter ‘inter-floc’ void regions. These are similar to formation inhomogeneities in paper sheets caused by flocculation of the papermaking suspension. As increasing levels of fillers are added, flocculation increases to a maximum level after which, fillers serve only to block the pores in the pulp mat and can no longer increase pore diameter. Blocking reduces the pore diameter as well as increasing the tortuosity. In the case of kaolin particles, pulp flocculation is not
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Fig. 6. (a) Specific volume of pulp-filler mat with filler mass fraction in mat (hardwood pulp with PCC-AC filler). (b) Specific surface area (based on composite mat mass) of pulp-filler mat with filler mass fraction (hardwood pulp with PCC-AC filler). (c) Specific surface area (based on composite mat volume, m−1 ) of pulp-filler mat with filler mass fraction (hardwood pulp with PCC-AC filler).
observed and the fillers only serve to plug the pores and reduce the permeability as shown in the experiments. The specific volume of the fiber–filler mixture can be obtained as a linear function of the mass fraction of each of the components. The specific volume of the mixture is given by the following equation:
vf,m =
Vm . mm
(6)
If the fibers and filler particles are incompressible, the total volume of the solid phase is equal to the sum of the fibers and filler volumes and vf,m is given below
vf,m = vf,f ωf + vf,p ωp .
(7)
If the specific volume of fiber and filler are known, we can calculate the specific volume of the mixture at any mass fraction. The surface area of the fiber–filler mixture can be modeled as follows. We assume that the Kozeny–Carman constant k is equal to 5.55 for the combined fiber–filler mat. Since typical filler loading is rarely greater than 30% based the fiber mass, the change in the value of this constant due to the presence of the filler is expected to be secondary and would probably be absorbed by the other fitting constants in the equation developed below. The surface area is first defined in terms of a composite surface area per unit volume and
the mat specific volume Sw,m = S0,m vf,m .
(8)
The composite specific surface area based on volume, S0,m is now assumed to be composed of the contributions of the fibers and the fillers. The fiber contribution can change depending on the flocculation state of the pulp suspension S0,m = S0,f + S0,p .
(9)
The specific surface area of the fibers is S0,f as and S0,p as the surface area contributed by the fillers acting independent of the fibers. The increased permeability with fiber flocculation can be modeled as a reduction in the specific surface area since its contribution to the flow resistance is reduced upon flocculation. The fiber specific surface area in the unflocculated state is given by the equation below: S0,f =
K0,f . rf
(10)
The parameter K0,f will be equal to 2 for fibers that are perfectly cylindrical whereas it is treated as an empirical parameter obtained by fitting the permeability of the fiber mat without any fillers present. Wood pulp fibers tend to assume elliptical cross-sectional
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Fig. 7. (a) Specific volume of pulp-filler mat with filler mass fraction (hardwood pulp with PCC-AF filler). (b) Specific surface area (based on composite mat mass) of pulp-filler mat with filler mass fraction (hardwood pulp with PCC-AF filler). (c) Specific surface area (based on composite mat volume, m−1 ) of pulp-filler mat with filler mass fraction (hardwood pulp with PCC-AF filler).
shapes depending on the compression level (see e.g. [14–16]). Furthermore roughness of the fiber surfaces adds to the flow resistance leading to increased values of K0,f . The effect of pulp flocculation, is modeled by decreasing the surface area according to a decay law given below. Note that the decrease is proportional to filler loading S0,f =
S0,f ˇ
1 + ˛ωp
,
(11)
S0,p = S0,p ωp .
(12)
The specific surface area for the pulp mat with filler is given by the sum of Eqs. (11) and (12) with a factor of (1 − ωp ) allowing for the effect of the fiber surface to decrease with increased filler loading K0,f (1 − ωp ) ˇ rf (1 + ˛ωp )
Limωp →0 [S0,m ] = S0,f =
K0,f rf
+ S0,p ωp .
(13)
(14)
and Limωp →1 [S0,m ] = S0,p = S0,p .
˛ and ˇ are empirical parameters. The surface area of fibers in the flocculated mat is given by S0,f whereas S0,f is that for the unflocculated case. The increase in surface area due to blocking of the pores is given by the expression below
S0,m =
The specific surface area of filler particles is S0,p . K0,f , ˛, ˇ, and are treated as empirical parameters. This equation fulfills the conditions below
(15)
The equations for specific volume and specific surface for the fiber–filler mixtures [Eqs. (7) and (13) along with Eqs. (2) and (4) represent the complete permeability model for these fiber–filler mats. The parameter K0,f is obtained from the specific surface measurement on the pulp fiber whereas S0,p represents the specific surface area (volume basis) for the filler particles. The other parameters namely, ˛, ˇ, and are treated as fitting parameters obtained through non-linear fitting of the experimental data on specific surface area vs. filler loading shown in Figs. 6–9(a–c). Table 2 presents the best fitting parameters for this set of data. Figs. 6–9 show curves through experimental data corresponding to the correlation given by Eq. (13). A good fit of all the experimental data is obtained indicating that Eq. (13) presents a satisfactory
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Fig. 8. (a) Specific volume of pulp-filler mat with filler mass fraction in mat (softwood pulp with PCC-AC filler). (b) Specific surface area (based on composite mat mass) of pulp-filler mat with filler mass fraction (softwood pulp with PCC-AC filler). (c) Specific surface area (based on composite mat volume, m−1 ) of pulp-filler mat with filler mass fraction (softwood pulp with PCC-AC filler).
albeit empirical description. Figs. 6–9(a–c) also show the corresponding specific volumes of the pulp-filler mixtures along with estimates obtained through Eq. (7). Additivity of the filler and fiber volumes seems to provide a good description of the experimental data. The parameter K0,f obtained was higher than 2 showing that the fiber cross sections do deviate from cylindrical shapes. This parameter is expected to be independent of the filler content as shown by the data for softwood. The differences in the value for hardwood for AF and AC are probably not significant. The parameter ˛ denotes the rate at which the permeability of the pulp increases due to flocculation. The large value for AC with hardwood indicates that this PCC types causes the strongest flocculation of hardwood pulp.
This parameter is smaller for softwood, perhaps because the softwood pulp is liable to flocculate easily and increases in flocculation brought about by addition of filler are smaller. In fact, for the case of AF, this parameter is almost negligible, showing that Albacar acts better to cause flocculation or aggregation than Albafil, perhaps on account of its larger particle size. The parameters and represent the growth of filler deposits blocking the pulp pores. These are also seen to be higher for the PCC-AC filler than the PCC-AF. This can again be explained by the larger particle size of AC as compared to AF. Since is greater than 1 in both cases, we conclude that the rate at which blocking decreases the permeability is strongly dependent on the amount of deposited particles. This non-linear decrease in permeability is also observed in the clogging of granular filters (see
Table 2 Parameters for specific surface area change with filler loading (S0,m given by Eq. [13]). The range of filler fractions and total solid concentration, expressed as ×103 kg m−3 for the validity of these parameters (mass OD filler/total OD mass of mat) is shown in the bottom rows. Parameter
HW + PCC-AC
HW + PCC-AF
SW + PCC-AC
SW + PCC-AF
K0,f ˛ ˇ Filler fraction Total solid concentration
2.56 4.25 1.33 0.10 1.32 0–0.29 0.09–0.22
3.00 1.80 1.02 0.40 2.16 0–0.30 0.09–0.21
2.32 1.34 1.31 0.05 1.22 0–0.38 0.11–0.21
2.38 0.02 0.46 0.30 2.03 0–0.35 0.11–0.20
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Fig. 9. (a) Specific volume of pulp-filler mat with filler mass fraction in mat (softwood pulp with PCC-AF filler). (b) Specific surface area (based on composite mat mass) of pulp-filler mat with filler mass fraction (softwood pulp with PCC-AF filler). (c) Specific surface area (based on composite mat volume, m−1 ) of pulp-filler mat with filler mass fraction (softwood pulp with PCC-AF filler).
e.g. Tien and Ramarao [19]). The growth parameters seem to be larger for the PCC-AF than the PCC-AC filler, a result which is contradictory with their particle sizes. More investigation is necessary to resolve this issue. 4. Conclusion Permeability of pulp mats decreases with loading on account of their inherent compressibility. However, the addition of filler particles can cause interesting and complex changes in the permeability [17]. Lavrykov et al. [18] found that the compressibility of the pulp mats decreases with added filler, perhaps due to the interference to bonding and bending or flexing of fibers within the mat interstices. Therefore filled pulp mats require larger loads to obtain the same consistency as unfilled pulp mats. However, even when the mats have been compressed to the same concentration, differences in permeability between filled and unfilled pulp mats persist. Filled mats which may have been flocculated due to the action of the filler can have larger permeability than the corresponding unfilled mats as was found in this work. The increase in the permeability value is much greater at low solid concentrations (100–200 kg m−3 ). As the concentration range increases, the influence of the PCC filler on pulp permeability begins to reduce because, at high consistency,
mat is more compact and the pore sizes are relatively small. When the loading of PCC is increased beyond the level needed to cause flocculation, permeability decreases are observed. The decrease is due to the combined effect of pore-blocking and replacement of low density fibers by higher density particles. In contrast with PCC, increased kaolin content in the mats leads to lower the permeability as kaolin particles clog the pores within the fiber mat. Our model for permeability is based on the Kozeny–Carman equation and the additivity of the specific volumes and specific surface areas of the fibers and filler particles. Parameters to describe the non-linear growth of the specific surface area due to poreblocking and flocculation were obtained by fitting to experimental data. More elaborate models to establish the applicability of the Kozeny–Carman model to composite mats are necessary. Predictive models of the clogging behavior of particles in fibrous mats are also necessary. Acknowledgements The financial support of the member companies of the Empire State Paper Research Associates Inc., funding the Empire State Paper Research Institute is gratefully acknowledged. The support of Dr. D. Bruce Evans & Specialty Minerals Inc. for supplying the fillers used
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in this study and for application of the results in this study is also gratefully acknowledged. References [1] S.T. Han, Compressibility and permeability of fibre mats, Pulp Pap. Mag. Can. (1969) 65–77. [2] J.D. Lindsay, The anisotropic permeability of paper: theory, measurement and analytical tools, in: IPC Technical Paper Ser., 298, Institute of Paper Science and Technology, Georgia Institute of Technology, Atlanta, 1988. [3] A.A. Robertson, S.G. Mason, Specific surface of cellulose fiber by the liquid permeability method, Pulp Pap. Mag. Can. 50 (1947) 110–117. [4] W.F. Cowan, Wet pulp characterization by means of specific surface, specific volume and compressibility, J. Pulp Pap. Sci. (1970) 63–66. [5] P. Kumar, B.V. Ramarao, Characterization of specific surface area, specific volume, compressibility and specific filtration resistance of papermaking pulps, Proc. TAPPI Papermakers’ Conf. (1995) 465–488. [6] H.L. Wei, B.V. Ramarao, Characterization of pulp slurries using a novel drainage tester, Proc. TAPPI Eng. Conf. 2 (1996) 517–523. [7] C.O. Maunier, B.V. Ramarao, Effect of flocculation on pulp drainage characteristics, Proc. TAPPI Eng. Conf. 2 (1996) 221–238. [8] S. Das, B.V. Ramarao, Inversion of lime mud and papermaking pulp filtration data to determine compressibility and permeability relationships, Sep. Purif. Technol. 28 (2002) 149–160. [9] S. Das, T. Cresson, B.V. Ramarao, Pulp characterization using permeability measures: effect of refining, 6th Intl. Conf. Pulp Refining, Toronto, ON, Canada, PIRA Intl., Leatherhead, Surrey, England, 2001.
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[10] W.L. Ingmanson, B.D. Andrews, R.C. Johnson, Internal pressure distribution in compressible mats under fluid stress, TAPPI J. 42 (1959) 840–849. [11] J. Wang, A.N. Hrymak, R.H. Pelton, Specific surface and effective volume of water-swollen pulp fibers by a permeability method, J. Pulp Pap. Sci. 28 (1) (2002) 3–16. [12] A.M. Springer, S. Kuchibhotla, The influence of filler components on specific filtration resistance, TAPPI J. 75 (1992) 187–194. [13] H. Liimatainen, S. Kokko, P. Rousu, J. Niinimaki, Effect of PCC filler on dewatering of fiber suspension, TAPPI J. 5 (11) (2006) 11–17. [14] A.C. Jain, Moisture transport in paper and coatings, Ph.D. Thesis, Drexel University, Philadelphia, PA, 2004. [15] F.J. Chen, The permeability of compressed fiber mats and the effects of surface area reduction and fiber geometry, Ph.D. Dissertation, Institute of Paper Science and Technology, Atlanta, Georgia, 1982. [16] R.P. Labrecque, The effects of fiber cross-sectional shape on the resistance to the flow of fluids through fiber mats, TAPPI J. 51 (1968) 8–15. [17] R. Singh, S. Lavrykov, B.V. Ramarao, Saturated permeability of filler loaded pulp mats, Empire State Paper Research Institute Report No., ESPRI, SUNY ESF, Syracuse, NY, 126, 2007, pp. 96–112. [18] S. Lavrykov, B.V. Ramarao, D.B. Evans, Permeability of pulps and fillers and their relationship to wet pressing, in: Proceedings of the 6th PIRA Intl. Conf. Wet End Chemistry, Boston, MA, October, 2005. [19] C. Tien, B.V. Ramarao, Granular Filtration of Aerosols and Hydrosols, 2nd Ed., Elsevier Publ., 2007. [20] S.G. Mason, The specific surface of fibers—its measurement and applications, TAPPI J. 33 (1950) 403–409.
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Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa
Permeability of pulp fiber mats with filler particles R. Singh, Sergiy Lavrykov, Bandaru V. Ramarao ∗ Department of Paper and Bioprocess Engineering, Empire State Paper Research Institute, College of Environmental Science and Forestry, State University of New York, 1 Forestry Drive, Syracuse, NY 13210, USA
a r t i c l e
i n f o
Article history: Received 17 April 2008 Received in revised form 14 August 2008 Accepted 11 September 2008 Available online 26 September 2008 Keywords: Permeability Fibrous media Wood pulp Fillers Specific surface area Precipitated calcium carbonate
a b s t r a c t We studied the permeability of fibrous media composed of filler particles in addition to fibers which are often encountered in industrial practice. Bleached Kraft pulp wood fibers and different kinds of fillers used in papermaking were the focus of this study. The fillers consisted of (i) scalenohedral precipitated calcium carbonate (PCC-Albacar), (ii) prismatic PCC (Albafil), and (iii) kaolin clay particles. The composite permeability increased with the addition of smaller quantities of PCC but higher loadings lowered the permeability significantly. The kaolin particles decreased the permeability of the pulp mats at all loading levels. The initial permeability increase observed with PCC was also accompanied by a simultaneous increase in the drainage rates of the pulps. The higher permeability is due to flocculation caused by heterocoagulation of PCC particles and the pulp fibers. At higher filler loadings, the PCC particles clog the pore spaces and reduce the permeability. Kaolin particles do not cause flocculation and hence decreased the permeability at all loadings. A model for the permeability of such composites was developed based on the Kozeny–Carman equation, considering the specific surface area as composed of two contributions. The first, due to fibers alone can result in lower specific surface areas caused by flocculation. The second contribution was an increase in surface area due to clogging of the fiber mats. The specific volume of the composite pulp mats was modeled as a simple weighted mixture of the specific volumes of the individual components. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Paper is manufactured by draining a suspension of wood pulp fibers on a wire screen and subsequently dewatering the pulp mat by vacuum and applied pressure. The removal of water in these operations depends upon the flow resistance of the wet pulp mat. There have been many investigations of the permeability of water-saturated pulp mats (see e.g. Han [1]). An excellent and comprehensive summary of the permeability of paper has been given by Lindsay [2]. Pulp mats consolidate to higher solid concentrations when pressure is increased, primarily due to fiber bending and compression of the cell walls. Therefore their permeability decreases with increasing applied pressure. This dependence can be used to determine the hydrodynamic specific surface area and the specific volume of the pulp fibers by applying the Kozeny–Carman model. Robertson and Mason [3] developed a permeability based measurement technique that has formed the basis of the Pulmac Permeability Tester. Cowan characterized wet pulps using specific surface area and compressibility [4]. Kumar and
∗ Corresponding author. Tel.: +1 315 470 6513; fax: +1 315 470 6945. E-mail address: [email protected] (B.V. Ramarao). 0927-7757/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2008.09.035
Ramarao [5] and later, Wei and Ramarao [6] described the application of the specific filtration resistance to determine the pulp specific surface area and specific volume. Maunier and Ramarao [7] used this technique to study the impact of retention aid polymers on pulp mat permeability whereas Das and Ramarao [8] and Das et al. [9] discussed methods of determining the specific surface area and specific volume from permeability data obtained by simple gravity drainage experiments. The Kozeny–Carman equation can be given as follows for pulp fibers (Ingmanson et al. [10])
K=
1
ε3
2 kS0,f
(1 − ε)2
.
(1)
The parameter k is treated as an empirical constant that lumps together all the uncertainties related to the fluid flow and structure of the porous media. It depends upon the shape of the channels, the orientation and size distribution functions and the manner in which the channels are interconnected. At porosities less than 0.8, the constant k has a fixed value (see e.g. Han [1]). For pulp fiber mats, the specific surface area (denoted Sw,f ) is usually based on oven dry fiber mass of the pulp instead of the volume. This specific
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Nomenclature
The total solid concentration of the composite fiber–filler mat is given below
c
c=
k K K0,f mf mm mp rf
S0 S0,m S0,f S0,f S0,p Sw Sw,m
vf vf,f vf,p vf,m Vf Vp Vv Vm ˛
mass concentration, defined as mass of solid material/volume, kg m−3 Kozeny–Carman constant [Eq. (1)], assumed to be 5.5 for fibrous media permeability, m2 parameter representing specific surface area of fibers [Eq. (10)] mass of fibers (oven dry) mass of mixture (fiber + filler) mass of filler parameter representing mean pore radius in fibrous mat (without filler), taken to be equal to fiber radius, m specific surface area based on volume, m−1 specific surface area of mixture (fiber + filler), m−1 specific surface area of fibers (flocculated state), m−1 specific surface area of fibers (unflocculated state), m−1 specific surface area of filler particles, m−1 specific surface area based on mass, m2 kg−1 specific surface area of mixture (fiber + filler), m2 kg−1 specific volume of mat, m3 kg−1 specific volume of fibers, m3 kg−1 specific volume of filler particles, m3 kg−1 specific volume of mixture (fiber + filler), m3 kg−1 volume of fibers in mat, m3 volume of filler in mat, m3 volume of void space in mat, m3 volume of mat, m3 parameter representing permeability increase to flocculation [Eq. (11)] parameter representing permeability increase to flocculation [Eq. (11)] parameter representing permeability decrease to fillers [Eq. (12)] parameter representing permeability decrease to fillers [Eq. (12)] porosity of mat mass fraction, fibers mass fraction, filler
ˇ ε ωf ωp
due due
2. Materials and methods
due
Bleached Kraft softwood and hardwood pulps were obtained from pulp manufacturers. The pulps were disintegrated according to TAPPI standard methods [T-205 sp-95] and were stored for further use. The fiber length distributions of these pulps were determined using the Kajaani FS-100 fiber length analyzer. Two types of PCC fillers [Albacar (AC) and Albafil (AF)] were obtained from Specialty Minerals Inc. (SMI) in slurry form. Small samples of both PCC-Albacar and -Albafil were dried and SEM pictures were taken. Albacar is scalenohedral in shape with an average particle size of 2 m and specific surface area of 7.4 m2 g−1 . Albafil is prismatic in shape with 0.8 m average size and specific surface area of 9.77 m2 g−1 . Albacar is a PCC containing scalenohedral shaped particles (Fig. 1a) whereas Albafil has prismatic shaped (Fig. 1b) particles. The zeta potential of the PCC fillers was measured using a Brookhaven BIC Zetaplus & Nanoplus (Brookhaven Instruments Corp., Brookhaven, NY). The properties of the fillers are summarized in Table 1. In order to characterize the action of the PCC fillers on the pulps, we determined the drainage rates in a gravity drainage tester (see Kumar and Ramarao [5], Das et al. [9] for more details). The tester consists of a transparent vertical column of diameter 0.06 m and height of 1 m connected to a vacuum pump at the bottom. A screen is provided at the bottom of the column. Pulp suspension is allowed to drain under gravity or the combined action of vacuum and
due
(2)
The specific volume of the fibers vf,f is defined as the ratio of the volume of the (water swollen) pulp fibers to their dry mass. The fiber mat concentration c defined as the total (oven dry) fiber mass/mat volume. The relation between the porosity and fiber concentration is given below ε = 1 − vf,f c.
(3)
The Kozeny–Carman equation takes the following form: K=
1
(1 − vf,f c)3
2 k Sw,f
c2
.
(5)
Wang et al. [11] investigated the permeability of pulp mats under higher pressures (representative of those in the wet-pressing of paper) and identified a limiting value of 1/vf,f for the mat concentration beyond which Eq. (3) is not valid. Our experimentation was conducted under lower pressure conditions and any potential changes of the specific volume with pressure were neglected. Particles of mineral fillers such as precipitated calcium carbonate (PCC) and kaolin clay are included along with pulp fibers in fine paper furnishes. Fillers serve two important purposes: to replace the more expensive wood pulp fibers in the product and to improve the optical and printing characteristics of fine papers. As lowering manufacturing costs for paper is an important objective, a current trend in papermaking is to use higher filler levels in the range of 20–30% of the fiber mass. Inclusion of fillers at such high levels can significantly reduce water drainage due to increased flow resistance increasing manufacturing costs or reducing production. Therefore, knowledge of the effect of fillers on the drainability of pulp suspensions is necessary. Most papermaking experience indicates that fillers hinder drainage. Springer and Kuchibhotla [12] found that clay, calcium carbonate and titanium dioxide fillers increased the specific filtration resistance. In an earlier investigation of dewatering, we measured the drainage properties of softwood and hardwood Kraft pulps with different types of fillers. When PCC fillers were added to these pulps, drainage measured by the freeness and drainage time increased [18]. Liimatainen et al. [13] reported that the addition of calcium carbonate fillers to pine, eucalyptus and birch Kraft pulps increased the drainage rates and decreased the specific filtration resistance. They conjectured that the specific surface area is reduced upon addition of the fillers. The present paper presents new experimental data on the variation of the permeability of pulp fiber mats with PCC and kaolin fillers. We also present a new semi-empirical model to predict these permeability characteristics of filler loaded pulp mats.
surface area is given by: Sw,f = S0,f vf,f .
mf + mp Vf + Vp + Vv
(4)
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Fig. 1. (a) SEM picture of precipitated calcium carbonate (PCC-AC) Albacar (picture by Specialty Minerals Inc.) and (b) SEM picture of precipitated calcium carbonate, Albafil (PCC-AF) (picture by Specialty Minerals Inc.) .
gravity, through the screen while a mat builds on it. An ultrasonic range sensor measures the suspension-air interface as a function of time. All water used in these experiments was at neutral conditions and was de-ionized and distilled. No additional additives
or salts were added to the suspensions except where noted in the results. Pulp mats were formed by steady sedimentation in a Pulmac permeability tester [Pulmac Instruments Ltd., Montreal, Canada]
Table 1 Filler and fiber properties.
PCC-AC PCC-AF SW pulp fiber length, mm HW pulp fiber length, mm a b c
Particle size (m)
Zeta potential (mV)
Specific surface area (×103 m2 kg−1 )
3.03b 0.8a 2.6c 0.9c
27.9b 24.3b CSF: 650 ml CSF: 510 ml
7.4a 9.77a Bleached Kraft Northern SW Bleached Kraft Eucalyptus
From SMI. Measured using BIC—Zetaplus & 90 Plus. Kajaani FS 100 Fiber length Analyzer.
Fig. 2. (a) Drainage of a pulp suspension in a column as a function of time (PCC-AC). 1—Hardwood control (no-filler), 2—hardwood pulp loaded with 10% PCC-AC (based on OD pulp mass). (b) Drainage of a pulp suspension in a column as a function of time (PCC-AF). 1—Hardwood control (no-filler), 2—hardwood pulp loaded with 10% PCC-AF (based on OD pulp mass).
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Fig. 3. (a) Effect of filler loading on the permeability of composite fiber–filler mats (HW − PCC-AC). 1—0% filler; 2—1.8%; 3—9.42%; 4—14.00%; 5—21.22%; 6—29.00%. (b) Effect of filler loading on the composite fiber–filler mats (HW + PCC-AF). 1—0%; 2—1.5%; 3—10.65%; 4—16.00%; 5—20.00%; 6—30.00%. (c) Effect of filler loading on the composite fiber–filler mats (SW + PCC-AC). 1—0%; 2—2%; 3—9%; 4—14.15%; 5—20.50%; 6—27.00%; 7—38.00%. (d) Effect of filler loading on the composite fiber–filler mats (SW + PCC-AF). 1—0%; 2—1.3%; 3—10.65%; 4—20.50%; 5—35.00%. (e) Effect of filler loading on the composite fiber–filler mats (HW + Kaolin). 1—0%; 2—3%; 3—10%.
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Fig. 4. (a). Permeability of pulp-filler mat with filler mass fraction in mat. (Hardwood pulp with PCC-AC filler). Fiber concentration is at 120 kg m−3 . (b) Permeability of pulp-filler mat with filler mass fraction in mat. (Hardwood pulp with PCC-AF filler). Fiber concentration is at 120 kg m−3 . (c) Permeability of pulp-filler mat with filler mass fraction in mat (hardwood pulp with Kaolin filler). Fiber concentration is at 140 kg m−3 .
after the pulps were deaerated under vacuum for at least 24 h. The same procedure was used to form pulp fiber–filler mats also. After the mats were formed, they were pressed to different levels by placing weights and allowing compression to predefined thicknesses using spacers. The pulp mat thicknesses varied from 8 to 18 mm. The loads applied on the mat ranged from 1.0 to 7 kg translating into applied pressures of 3–22 kPa. The compressibility of the pulp mats was determined and will be reported in a separate investigation. The permeability of the formed mats was determined by flowing distilled and deaerated water through them and measuring the flow rate and pressure drop under steady conditions. A plot of the mat flow resistance against the solid concentration yields the specific surface area and the specific volume of the composite, assuming the validity of the Kozeny–Carman equation for pulp fibers. For more details on this procedure, one may refer to the publication by Mason [20]. There are some concerns about permeability measurements in a constant pressure apparatus such as this instrument. In particular, the concentration within the pulp mats may vary along their thickness. Since the permeability is generally a non-
linear function local variations in porosity can introduce significant errors in its measurement. Long-time dynamic effects of compression such as mat creep, mat rearrangement or pore-blocking due to fine particle deposition can also cause systematic deviation in permeability. Care was taken in our measurements to ensure that the mats reached a state of equilibrium and no time-dependent effects were observable on the flow or pressure measurements. The effects of local variation of porosity and permeability are neglected in the analysis but will be the subject of a future report. 3. Results 3.1. Experimental results The drainage of a suspension containing BKPHW and PCC is shown in Fig. 2a (for PCC-AC) and Fig. 2b (for PCC-AF). When PCC is added to the pulp at low concentrations, the drainage is increased as shown by curves labeled 2 in both of these figures. Liimatainen et al. [13] found that the specific filtration resistance of the pulps
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decreased upon addition of PCC, but they did not investigate in terms of the permeability parameters. The permeability of pulp-filler mats was determined at different solid concentrations defined as in Eq. (5). Fig. 3a–e show these permeabilities for softwood and hardwood pulp mats over different mat concentrations. Each curve in these figures corresponds to a different fiber mat containing different filler fraction (ωp ). The permeability decreases with increasing mat concentration due to a decrease in the porosity. However, the addition of PCC as filler results in a large increase in permeability at different filler levels for both PCC-AC and PCC-AF as shown in Fig. 3a–d. This behavior is obtained for both the hardwood and softwood pulps. Fig. 3e shows the permeability of pulp mats loaded with kaolin fillers. The experimental permeabilities indicate that kaolin decreases the mat permeability at a given mat concentration. The reduction in permeability can be understood as a consequence of the blocking action of the added filler clogging the pores within the fiber mats. This decrease contrasts with the increase in permeability with PCC filler addition. Fig. 4a–c shows the mat permeabilities with increased filler concentrations for the two PCC samples (AC and AF) and kaolin. The mats were prepared such that the fiber concentration
101
was kept constant in these cases. We observe a spike in permeability, due to flocculation in the case of the PCC fillers whereas the permeability of the kaolin-filled mats decreases monotonically. Fig. 5a–d show scanning electron micrographs of the pulp-filler mats obtained after drying and sectioning. Views of the lateral (i.e. frontal) and cross sections in the thickness (ZD) are presented for fiber mats loaded with PCC-AC and PCC-AF. We observe that the filler particles tend to agglomerate around the pulp fibers as well as filling up the inter-fiber pore spaces. Aggregates of fillers tend to plug the pore space causing large increases in flow resistance, i.e. large drop in permeability of the composite mats, whereas filler adsorbed on the fibers may not have such a dramatic effect on the permeability decrease. By applying the Kozeny–Carman equation [Eq. (4)] to the permeability-concentration data, it is possible to fit for the specific surface area (Sw,m ) and specific volume, vf,m , respectively. We followed Robertson and Mason’s procedure of using a linearized version of the flow resistance-mat concentration relationship for this purpose. A critical assumption we made here was that the Kozeny–Carman equation, including the Kozeny constant was directly applicable to the pulp-filler mixtures under all our exper-
Fig. 5. (a) SEM picture of hardwood pulp + PCC-AC filler 20% (lateral/in-plane view). (b) SEM picture of hardwood pulp + PCC-AC filler 20% (ZD view). (c) SEM picture of hardwood pulp + PCC-AF 7.44% (lateral/in-plane view). (d) SEM picture of hardwood pulp + PCC-AF 7.44% (transverse/ZD view).
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Fig. 5. (Continued ).
imental conditions. This assumption may not be valid for pulp fiber–filler mixtures. Figs. 6–9(a–c) show the specific surface area (Sw,m ) and the specific volume (vf,m ) of pulps loaded with PCC. Results for hardwood and softwood pulps filled with AC and AF types of PCC are shown. The specific volume always decreases with filler addition since fillers have much higher densities than the fibers and their incorporation into the mats gives more compact solids and lower specific volume. The results for the specific surface area based on volume are shown for each of these cases also. S0 decreases to a minimum value after which it begins to increase resulting in decreased permeability. 3.2. Permeability model Permeability models are important because they can be used to predict the performance characteristics of fibrous filters and drainage resistances of pulp mats. Models to predict the permeability of pulp-filler composite mats can also be useful in determining the effect of different types of fillers on drainage and other physical
processes such as dewatering during papermaking. The experimental results discussed in the previous section indicate that flocculation and pore blockage could be the main factors impacting the permeability of the pulp-filler composite mats. Tentatively, the differences in the action of different fillers may be explained as due to differences in their charge interactions and sizes. PCC particles are cationic and also larger in size compared to the other particles. The filler particles were aggregated and no retention aids were necessary to achieve high levels of loading of these fillers in the pulp mats. The PCC filler can initially flocculate the pulp suspensions. When these fillers were added to the pulp suspension, the formation of flocs could be also be observed visually. The resulting pulp mats must be heterogeneous with denser floc regions and lighter ‘inter-floc’ void regions. These are similar to formation inhomogeneities in paper sheets caused by flocculation of the papermaking suspension. As increasing levels of fillers are added, flocculation increases to a maximum level after which, fillers serve only to block the pores in the pulp mat and can no longer increase pore diameter. Blocking reduces the pore diameter as well as increasing the tortuosity. In the case of kaolin particles, pulp flocculation is not
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Fig. 6. (a) Specific volume of pulp-filler mat with filler mass fraction in mat (hardwood pulp with PCC-AC filler). (b) Specific surface area (based on composite mat mass) of pulp-filler mat with filler mass fraction (hardwood pulp with PCC-AC filler). (c) Specific surface area (based on composite mat volume, m−1 ) of pulp-filler mat with filler mass fraction (hardwood pulp with PCC-AC filler).
observed and the fillers only serve to plug the pores and reduce the permeability as shown in the experiments. The specific volume of the fiber–filler mixture can be obtained as a linear function of the mass fraction of each of the components. The specific volume of the mixture is given by the following equation:
vf,m =
Vm . mm
(6)
If the fibers and filler particles are incompressible, the total volume of the solid phase is equal to the sum of the fibers and filler volumes and vf,m is given below
vf,m = vf,f ωf + vf,p ωp .
(7)
If the specific volume of fiber and filler are known, we can calculate the specific volume of the mixture at any mass fraction. The surface area of the fiber–filler mixture can be modeled as follows. We assume that the Kozeny–Carman constant k is equal to 5.55 for the combined fiber–filler mat. Since typical filler loading is rarely greater than 30% based the fiber mass, the change in the value of this constant due to the presence of the filler is expected to be secondary and would probably be absorbed by the other fitting constants in the equation developed below. The surface area is first defined in terms of a composite surface area per unit volume and
the mat specific volume Sw,m = S0,m vf,m .
(8)
The composite specific surface area based on volume, S0,m is now assumed to be composed of the contributions of the fibers and the fillers. The fiber contribution can change depending on the flocculation state of the pulp suspension S0,m = S0,f + S0,p .
(9)
The specific surface area of the fibers is S0,f as and S0,p as the surface area contributed by the fillers acting independent of the fibers. The increased permeability with fiber flocculation can be modeled as a reduction in the specific surface area since its contribution to the flow resistance is reduced upon flocculation. The fiber specific surface area in the unflocculated state is given by the equation below: S0,f =
K0,f . rf
(10)
The parameter K0,f will be equal to 2 for fibers that are perfectly cylindrical whereas it is treated as an empirical parameter obtained by fitting the permeability of the fiber mat without any fillers present. Wood pulp fibers tend to assume elliptical cross-sectional
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Fig. 7. (a) Specific volume of pulp-filler mat with filler mass fraction (hardwood pulp with PCC-AF filler). (b) Specific surface area (based on composite mat mass) of pulp-filler mat with filler mass fraction (hardwood pulp with PCC-AF filler). (c) Specific surface area (based on composite mat volume, m−1 ) of pulp-filler mat with filler mass fraction (hardwood pulp with PCC-AF filler).
shapes depending on the compression level (see e.g. [14–16]). Furthermore roughness of the fiber surfaces adds to the flow resistance leading to increased values of K0,f . The effect of pulp flocculation, is modeled by decreasing the surface area according to a decay law given below. Note that the decrease is proportional to filler loading S0,f =
S0,f ˇ
1 + ˛ωp
,
(11)
S0,p = S0,p ωp .
(12)
The specific surface area for the pulp mat with filler is given by the sum of Eqs. (11) and (12) with a factor of (1 − ωp ) allowing for the effect of the fiber surface to decrease with increased filler loading K0,f (1 − ωp ) ˇ rf (1 + ˛ωp )
Limωp →0 [S0,m ] = S0,f =
K0,f rf
+ S0,p ωp .
(13)
(14)
and Limωp →1 [S0,m ] = S0,p = S0,p .
˛ and ˇ are empirical parameters. The surface area of fibers in the flocculated mat is given by S0,f whereas S0,f is that for the unflocculated case. The increase in surface area due to blocking of the pores is given by the expression below
S0,m =
The specific surface area of filler particles is S0,p . K0,f , ˛, ˇ, and are treated as empirical parameters. This equation fulfills the conditions below
(15)
The equations for specific volume and specific surface for the fiber–filler mixtures [Eqs. (7) and (13) along with Eqs. (2) and (4) represent the complete permeability model for these fiber–filler mats. The parameter K0,f is obtained from the specific surface measurement on the pulp fiber whereas S0,p represents the specific surface area (volume basis) for the filler particles. The other parameters namely, ˛, ˇ, and are treated as fitting parameters obtained through non-linear fitting of the experimental data on specific surface area vs. filler loading shown in Figs. 6–9(a–c). Table 2 presents the best fitting parameters for this set of data. Figs. 6–9 show curves through experimental data corresponding to the correlation given by Eq. (13). A good fit of all the experimental data is obtained indicating that Eq. (13) presents a satisfactory
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Fig. 8. (a) Specific volume of pulp-filler mat with filler mass fraction in mat (softwood pulp with PCC-AC filler). (b) Specific surface area (based on composite mat mass) of pulp-filler mat with filler mass fraction (softwood pulp with PCC-AC filler). (c) Specific surface area (based on composite mat volume, m−1 ) of pulp-filler mat with filler mass fraction (softwood pulp with PCC-AC filler).
albeit empirical description. Figs. 6–9(a–c) also show the corresponding specific volumes of the pulp-filler mixtures along with estimates obtained through Eq. (7). Additivity of the filler and fiber volumes seems to provide a good description of the experimental data. The parameter K0,f obtained was higher than 2 showing that the fiber cross sections do deviate from cylindrical shapes. This parameter is expected to be independent of the filler content as shown by the data for softwood. The differences in the value for hardwood for AF and AC are probably not significant. The parameter ˛ denotes the rate at which the permeability of the pulp increases due to flocculation. The large value for AC with hardwood indicates that this PCC types causes the strongest flocculation of hardwood pulp.
This parameter is smaller for softwood, perhaps because the softwood pulp is liable to flocculate easily and increases in flocculation brought about by addition of filler are smaller. In fact, for the case of AF, this parameter is almost negligible, showing that Albacar acts better to cause flocculation or aggregation than Albafil, perhaps on account of its larger particle size. The parameters and represent the growth of filler deposits blocking the pulp pores. These are also seen to be higher for the PCC-AC filler than the PCC-AF. This can again be explained by the larger particle size of AC as compared to AF. Since is greater than 1 in both cases, we conclude that the rate at which blocking decreases the permeability is strongly dependent on the amount of deposited particles. This non-linear decrease in permeability is also observed in the clogging of granular filters (see
Table 2 Parameters for specific surface area change with filler loading (S0,m given by Eq. [13]). The range of filler fractions and total solid concentration, expressed as ×103 kg m−3 for the validity of these parameters (mass OD filler/total OD mass of mat) is shown in the bottom rows. Parameter
HW + PCC-AC
HW + PCC-AF
SW + PCC-AC
SW + PCC-AF
K0,f ˛ ˇ Filler fraction Total solid concentration
2.56 4.25 1.33 0.10 1.32 0–0.29 0.09–0.22
3.00 1.80 1.02 0.40 2.16 0–0.30 0.09–0.21
2.32 1.34 1.31 0.05 1.22 0–0.38 0.11–0.21
2.38 0.02 0.46 0.30 2.03 0–0.35 0.11–0.20
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Fig. 9. (a) Specific volume of pulp-filler mat with filler mass fraction in mat (softwood pulp with PCC-AF filler). (b) Specific surface area (based on composite mat mass) of pulp-filler mat with filler mass fraction (softwood pulp with PCC-AF filler). (c) Specific surface area (based on composite mat volume, m−1 ) of pulp-filler mat with filler mass fraction (softwood pulp with PCC-AF filler).
e.g. Tien and Ramarao [19]). The growth parameters seem to be larger for the PCC-AF than the PCC-AC filler, a result which is contradictory with their particle sizes. More investigation is necessary to resolve this issue. 4. Conclusion Permeability of pulp mats decreases with loading on account of their inherent compressibility. However, the addition of filler particles can cause interesting and complex changes in the permeability [17]. Lavrykov et al. [18] found that the compressibility of the pulp mats decreases with added filler, perhaps due to the interference to bonding and bending or flexing of fibers within the mat interstices. Therefore filled pulp mats require larger loads to obtain the same consistency as unfilled pulp mats. However, even when the mats have been compressed to the same concentration, differences in permeability between filled and unfilled pulp mats persist. Filled mats which may have been flocculated due to the action of the filler can have larger permeability than the corresponding unfilled mats as was found in this work. The increase in the permeability value is much greater at low solid concentrations (100–200 kg m−3 ). As the concentration range increases, the influence of the PCC filler on pulp permeability begins to reduce because, at high consistency,
mat is more compact and the pore sizes are relatively small. When the loading of PCC is increased beyond the level needed to cause flocculation, permeability decreases are observed. The decrease is due to the combined effect of pore-blocking and replacement of low density fibers by higher density particles. In contrast with PCC, increased kaolin content in the mats leads to lower the permeability as kaolin particles clog the pores within the fiber mat. Our model for permeability is based on the Kozeny–Carman equation and the additivity of the specific volumes and specific surface areas of the fibers and filler particles. Parameters to describe the non-linear growth of the specific surface area due to poreblocking and flocculation were obtained by fitting to experimental data. More elaborate models to establish the applicability of the Kozeny–Carman model to composite mats are necessary. Predictive models of the clogging behavior of particles in fibrous mats are also necessary. Acknowledgements The financial support of the member companies of the Empire State Paper Research Associates Inc., funding the Empire State Paper Research Institute is gratefully acknowledged. The support of Dr. D. Bruce Evans & Specialty Minerals Inc. for supplying the fillers used
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