Chemical Engineering Science 160 (2017) 275–280

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Characterizing the hydraulic properties of paper coating layer using FIBSEM tomography and 3D pore-scale modeling

MARK

⁎

H. Aslannejada, , S.M. Hassanizadeha, A. Raoof a, D.A.M de Wintera, N. Tomozeiub,
M.Th. van Genuchtena,caMultiscale porous media lab., Department of Earth Sciences, Utrecht University, Utrecht, The Netherlands
R & D Department, Océ Technologies B.V., Venlo, The NetherlandscDepartment of Mechanical Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazilb

A R T I C L E I N F O

A BS T RAC T

Keywords:
Coated paper
3D pore structure
Focused ion beam scanning electron
microscopy
Pore scale modeling
Image analysis

Paper used in the printing industry generally contains a relatively thin porous coating covering a thicker ﬁbrousbase layer. The three-dimensional pore structure of coatings has a major eﬀect on ﬂuid ﬂow patterns inside thepaper medium. Understanding and quantifying the ﬂow properties of thin coating layers is hence crucial. Pore
spaces within the coating have an average size of about 180 nm. We used scanning electron microscopy
combined with focused ion beam (FIB-SEM) to visualize the nano-scale pore structure of the paper coating
layer. Post-processing of the FIB-SEM images allowed us to reconstruct the three-dimensional pore space of thecoating. The 3D FIB-SEM images were analyzed in detail to obtain pore size distribution and porosity value. The
permeability was estimated using the GeoDict software, based on solutions of the Stokes equation. By
determining the porosity and permeability of increasingly larger domain sizes, we estimated the size of arepresentative elementary volume (REV) for the coating layer to be 60 µm3, which is well within the volume
analyzed using FIB-SEM. The estimated porosity and permeability of the REV domain were 0.34 and 0.09
mDarcy, respectively. Using the pore morphology method, capillary pressure-saturation (Pc-S) and relative
permeability curves of the REV domain could be constructed next. The Pc-S curves showed that the coating had
a high air entry suction, which is very favorable for printing in that ink will invade the coating as soon as it isapplied to the coating. Our results are essential for macroscale modelling of ink penetration into a coating layer
during inkjet printing. Macroscopic models can be valuable tools for optimization of the penetration depth andthe spreading of ink on and within paper substrates.

1. Introduction
During inkjet printing, once an ink droplet reaches the paper
surface, spreading and evaporation processes determine overall ink
penetration. The dynamics of these processes aﬀect the ﬁnal print
quality. In order to optimize ink penetration during inkjet printing,paper is often coated with a layer of ultra-ﬁne mineral particles, usuallycomposed of kaolin or calcium carbonate and bound together with anadhesive. Surface-modiﬁed calcium carbonate and clays, colloidalprecipitated calcium carbonate, alumina silicate, and zeolite areconsidered to be among the most promising pigments (Malla andDevisetti, 2005; Vikman and Vuorinen, 2004). The extent of ink
penetration depends on the structure of this coating as well as on theﬂuid properties of the employed ink (Heard et al., 2004).
The porosity and pore size distribution of a coating layer determines the extent, speed, and ﬁnal distribution of the injected ink.
⁎

Fig. 1. shows an overview of the processes that occur during inkjet
printing (Kettle et al., 2010). The speciﬁed times indicate the approximate moment at which various phenomena are expected to start. The
forces that cause lateral spreading of a droplet on the paper surface
compete with the capillary suction of liquid into the paper (Girard
et al., 2006). Capillarity is the dominant force drawing ink into the pore
structure. Micro capillary penetration starts typically within 0.1 ms
after the droplet arrives (Ridgway and Gane, 2002; Desie et al., 2004).
Several studies have been conducted to explore the performance of
ink in diﬀerent papers. Dalton et al., (2002) used secondary ion mass
spectrometry and X-ray photoelectron spectroscopy (XPS) to determine the ﬁnal distribution of ink a cross section of paper samples. Alamet al. (2009) used computational ﬂuid dynamics simulations in order tocalculate the permeability of three packing structures representing thecoating layer of paper. Calculated permeability values were within one
order of magnitude of reported experimental equivalents. Matilainen

Correspondence to: Environmental Hydrogeology Group, Department of Earth Sciences, Universiteit Utrecht, Princetonplein 9, 3584 CC Utrecht, The Netherlands.
E-mail address: H.aslannejad@uu.nl (H. Aslannejad).

http://dx.doi.org/10.1016/j.ces.2016.11.021
Received 5 July 2016; Received in revised form 25 September 2016; Accepted 5 November 2016
Available online 11 November 2016
0009-2509/ © 2016 The Author(s). Published by Elsevier Ltd.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/).

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Ridgway and Gane (2002), who employed the Bosanquet equation(Bosanquet, 1923) to show the role of pore size and viscous drag(Ridgway et al., 2002).
The spreading and penetration of ink is generally very muchaﬀected by such paper bulk properties as porosity, permeability,
thickness, moisture content, temperature, and layer structure. Gane
et al. (2009) showed that standard ground calcium carbonate coatings,
because of their relatively broad particle size distributions and low
permeability, produce slower initial rates of adsorption of ink thanmore reﬁned coating having a narrower pore size distribution andhigher permeability. They found that coatings with a higher speciﬁc
surface area and permeability have a faster initial moisture uptake.
The aim of this work is to obtain the detailed pore structure of acoating layer at a very high resolution, and from this its hydraulicproperties using a pore-scale computational method. We ﬁrst introduce
a visualization method of extracting the 3D structure of the layer byusing FIB-SEM imaging. The approach allowed a resolution of up to
three nanometers. The method involved many cycles of removing avery thin cross-sectional layer by ion beam, and imaging by electron
microscopy. Image analysis was used to obtain pore morphologicalinformation about the coating layer. Finally, using the pore morphology method, pore-scale simulations were carried out to estimate theeﬀective hydraulic properties of the coating. Such estimates are
required for continuum scale-models of ink movement in the coating
layer.

Fig. 1. Overview of processes during inkjet printing (adopted from Kettle et al., 2010).

et al., (2012) studied the spreading and penetration of bio-based ink,
which contained laccase enzyme and its substrate ABTS, on three
diﬀerent coated printing papers. Optical and confocal microscopy
techniques were used, together with a tape laminating method(Matilainen et al., 2012). The pore size distribution of the printing
substrate was further explored using mercury porosimetry. Pore sizes
were found to be 1–5 µm for the base layer, and 0.05–0.5 µm for thecoating pores.
Lamminmäki et al., (2012) studied the coupled eﬀects of pore
structure and swelling of the binder of a coating layer on ink imbibitionin terms of its penetration and spreading. The coating structure wasstudied with respect to its absorption behavior for polar and non-polar
liquids. The measurements were performed on compressed tablets(having thicknesses of about 200 µm) containing polyvinyl alcohol(PVOH) or styrene acrylic latex (SA) as the binder. Results indicatedthat small pores play a dominant role in the ink imbibition processduring the ﬁrst two seconds. Simultaneously, water diﬀusion into thehydrophilic PVOH binder caused its swelling. This swelling reduced thediameters of the remaining pores, thus decreasing capillary ﬂow. In
contrast, the SA latex binder did not absorb water, which hence
indicates capillary absorption was the dominant process.
Short-time processes during the early stages of ink penetration
cannot be described using equilibrium ﬂuid ﬂow simulation methods.
The liquid advance in a porous structure is usually simulated using
some approximate method (e.g., (Lamminmäki et al., 2012). A wellknown method is based on the Lucas–Washburn equation, whichassumes that the coating consists of a collection of vertical capillarytubes. The method was improved later by Schoelkopf et al. (2002) and2. Material and methods
2.1. Paper sample
The paper samples used in this study (i.e., Sappi Magno Gloss
paper) were made of a ﬁbrous layer covered on both sides with coating
material. The total thickness of the samples was 83 µm, with a basis
weight of 115 g/m2 and a porosity of 0.34. The coatings, which had athickness of 12.8 µm on each side of the paper, consisted mostly of
CaCO3 along with a small amount of binder. All samples were kept
under room conditions (21 °C and relative humidity of 88%). A typicalimage of the surface and a vertical cross section of the coating areshown in Fig. 2.
2.2. FIB-SEM imaging
Samples for imaging were prepared by attaching a small piece(1 cm2) of coated paper to a standard aluminum SEM stub with a

Fig. 2. Surface (a) and cross-sectional (b) views of the paper coating.

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Fig. 4. Reconstructed FIB-SEM results showing (a) one layer of the scanned stack, (b)volume rendering of the entire scanned domain, (c) the segmented domain, and (d)labeled pores using the “Label analyzing” module.

Fig. 3. An image of the coating layer under FIB-SEM tomography, showing the pit and
two trenches made by the ion beam.

solid structures (Fig. 4c). The threshold values for the solid phase weremanually chosen by comparing real gray scale images with thesegmented images. With the above segmentations, the 3D structureof the coating layer could be reassembled and visualized (Fig. 4d).
The Avizo label analysis module was used to calculate the volume ofpores. This module performs a connectivity analysis of individual pores
within the entire 3D volume. The calculated volumes were needed forthe porosity calculations.

conductive carbon sticker. The paper was sputter coated with approximately 5 nm of platinum (HQ280; Cressington Scientiﬁc Instruments
Ltd, Watford, UK). The samples were placed in the vacuum chamber ofa Nova Nanolab 600 focused ion beam scanning electron microscope(FIB-SEM) (FEI Company, Eindhoven, Netherlands). SEM imaging
conditions were kept low to prevent potential damage of the layer by
the beam. Typical imaging conditions were 2 kV and 0.21 nA. The FIB
acceleration voltage was 30 kV for all processes (e.g., deposition, roughcutting, polishing); the current density was varied according to therequired process.
Standard FIB-SEM tomography preparation procedures were used
(Karwacki et al., 2011). An additional layer of Platinum (about 100 nm)
was deposited over the area of interest to prevent damage from the FIB
and to improve the ﬁnish (smoothness) of cross sections. Also, a verythin layer of platinum was deposited over a small square to the left of
the area of interest, to be used as a ﬁducial marker for aligning both the
FIB and the SEM during the FIB-SEM tomography process. Two
trenches were subsequently milled alongside the area of interest (seeFig. 3) to create suﬃcient space for redepositing material that wasremoved by the FIB during tomography. A large pit (10 µm in eachdirection) was milled in front of the region of interest, to allow the SEM
to view consecutive vertical cross sections (Fig. 3). In order tosmoothen the ﬁrst vertical cross section, the pit was polished with amoderate FIB current. After imaging the ﬁrst cross section, FIB with acurrent of 0.3 nA was used to remove a 25 nm thick vertical slice andthus to expose the next cross section for electron microscopy.
The tomography measurements were carried out with the SEM
recording images at 2 kV and 0.21 nA in BSE mode, with the immersion lens switched on. The scan resolution was 2048×1768 and the
pixel width 3.5 nm. The dwell time was 4 µs, and the line integration
two times, resulting in a frame time of approximately 35 s. A total of
678 cross sections were recorded.

2.4. Pore scale contact angle
The contact angle, ψ, is one of the key parameters aﬀecting ﬂuid
retention and movement. We note that the contact angle is diﬀerent
from the spreading angle, which is measured as the edge angle of adroplet lying on the paper surface. This angle decreases with time as
the liquid penetrates into the substrate. The contact angle, on the other
hand, is the angle that a ﬂuid-ﬂuid interface inside a capillary forms
with the pore wall. Under static isothermal conditions, this is aconstant property of the two ﬂuids involved (air, water) and the solid.
Practical limitations of the microscopy techniques make it diﬃcult tomeasure the real contact angle of liquids inside a single pore (in ourcase having an average diameter of only about 180 nm). Nevertheless,various approaches have been employed to estimate the contact angle.
Here we used an average value of 45° for the contact angle based onstudies by Järnström et al. (2010).
2.5. Determination of hydraulic properties
Upon arrival of an ink droplet, ﬂuid will start moving into the pore
network of dry paper (initially ﬁlled completely with air). Replacementof air by the invading liquid during ink setting constitutes an imbibition(wetting) process. Full characterization and simulations of the imbibition process requires information about several key parameters such as
the pore size distribution, the porosity, and the capillary pressure –saturation (Pc-S) curve (Song et al., 2016). The 3D pore structure of thecoating layer was used as input of the GeoDict software (Math2Market,
Kaiserslautern, Germany) to obtain estimates of the capillary pressure(Pc-S) and relative permeability (Kr-S) curves. GeoDict uses for thispurpose the pore morphology method (Schulz et al., 2015), whichcalculates the stationary distributions of the wetting and non-wetting
phases at a given capillary pressure (Fig. 5). This approach neglects

2.3. Three-dimension tomography data analysis
We used Avizo Fire software 9.0 (FEI, Oregon, US) for the 3D
tomography data analysis of the images. Fig. 4a shows the image of one
slice. The full stack of images (Fig. 4b) was ﬁrst smoothened using a
median ﬁlter, with a neighborhood of 6, using 5 iterations. Watershedsegmentation was used next to distinguish and separate pores from the277

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Fig. 5. Images of the sample at three diﬀerent air pressures during imbibition, with pressures P1 > P2 > P3. The red and blue colors represent air and water ﬁlled pores, respectively.
(For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

gravity eﬀects and requires a known value for the contact angle.
For any given capillary pressure, a critical pore size is calculated
based on the Young- Laplace equation:

r=

2σ
cos ψ
Pc

(1)

where σ is surface tension, ψ the contact angle, and Pc the capillarypressure. For imbibition, initially, all pores are ﬁlled by the non-wetting
phase. We then search for all pores whose size is equal to or smaller
than the critical pore size rc and are connected to the wetting phasereservoir. All those pores are assumed to become ﬁlled with the wetting
phase (Hilpert et al., 2001). For drainage, all pores are at ﬁrst ﬁlledwith the wetting phase and we search for all pores whose size is equal toor larger than the critical pore size rc and are connected to thenonwetting phase reservoir. All those pores are assumed to become
invaded by the non-wetting phase. At the end of drainage process, acertain part of the wetting phase may remain trapped in some pores,
which leads to irreducible wetting saturation. Similarly, at the end of an
imbibition process, the non-wetting phase may remain trapped in somepores, thus producing residual non-wetting saturation.
The relative permeability under imbibition was determined basedon the distribution of phases obtained with the pore morphology
method during imbibition. Thus, in order to calculate the relative
permeability at a given saturation, the distribution of the phases(wetting and non-wetting) were determined. A pressure gradient was
subsequently imposed on each phase and ﬂow was simulated by solving
Stokes equation. Flow of each phase was assumed to be independent of
ﬂow of the other phase (i.e., transfer of momentum along the phaseinterfaces was not considered). The permeability of each phase wasthen determined by substituting the pressure gradient and total ﬂow
rate in Darcy's law. We refer to several previous studies for details(Schulz et al., 2014); (Hilpert et al., 2001); (Cheng et al., 2013).

Fig. 6. The pore size distribution of the paper coating.

coating has a high capillary suction.
3.2. Hydraulic properties of the coating
3.2.1. Representative elementary volume (REV)An important issue to be considered before performing pore-scale
simulations is the minimum domain size that provides statisticallymeaningful parameter values. Calculated hydraulic properties for sucha domain are then relatively insensitive to the pore network size. Such a
representative network size will be considered as the REV of the porous
medium being modeled. The REV size in our study was determined by
calculating values of the porosity and permeability for diﬀerent domain
sizes, and plotting the results versus the domain dimension. Our resultsin Fig. 7 show that the porosity and permeability increased withdomain size up to a domain of about 60 µm3, above which theyremained essentially constant at values of 0.34 and 0.1 mDarcy,
respectively. For domains larger than 60 µm3, the porosity andpermeability changed less than 3%. Based on these results, we used a
domain size of 60 µm3 as the REV in our study.

3. Results
3.1. Pore size distribution
Properties of the pore structure of the coating layer are listed inTable 1. The total porosity of the sample was found to be 0.34 which isin good agreement with independent mercury porosity measurements
as well as previous literature (Gane et al., 1996). The pore size
distribution showing the probability of the various pore sizes is given
in Fig. 6. The average pore size was 180 nm, which means that the3.2.2. Capillary pressure- saturation (Pc-S) and relative permeability(Kr-S) curves
The capillary pressure curves associated with drainage and imbibi-

Table 1
Pore network parameters of the coating.
Total surface area (µm2)

Ave. pore eq. diameter (nm)

Total no. pores

1273

180

31587

Pore volume (nm3)

Porosity
Porosity
0.34

278Open porosity
0.339

Closed porosity
0.001

Min.
1213

Max.
113e6

Ave.
118e4

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Table 2
Values of the van Genuchten parameters of the Pc-S curves in Fig. 8.

Primary Imbibition
Primary Drainagenα (kPa−1)

3.96
5.00

0.712
0.731

Sr
0.476
0.00

Sir
0.000
0.082

capillary pressure- saturation relationship is then given by

Se (Pc ) = [1 + (αPc )n ]−m , Se =Sw (Pc )−Sir −Sr
1 − Sir − Sr(2)where Se, Sr, Sir, and Sw are eﬀective saturation, air residual
saturation, irreversible wetting phase saturation, and wetting phasesaturation, respectively, Pc is the capillary pressure, α and n areempirical shape parameters reﬂecting the average pore size and widthof the pore-size distribution, respectively, and m=1−1/n. The parameter α is closely related to the inverse of the air-entry capillarypressure of the medium (Luckner et al., 1989). The ﬁtting parameters
for the primary imbibition and drainage curves are shown in Table 2;
they are in good agreement with the hydraulic parameters reported forsimilar porous materials having relatively narrow pore-size distribution(Carsel and Parrish, 1988; Ghanbarian-Alavijeh et al., 2010).
As explained above, relative permeability at diﬀerent saturations
imbibition was calculated using phases distribution determined by poremorphology method. Results for the primary imbibition are shown in
Fig. 9 as symbols. Values are given up to a saturation of 0.534, which
was the largest saturation value reached with the Pc- S imbibition
curve.
The relative permeability can be also determined based on Eq. (2).
On the basis of the van Genuchten- Mualem model (van Genuchten,1980), the relative permeability of the wetting phase (krw) is given by

Fig. 7. Plots of calculated porosity and permeability values for diﬀerent domain sizes of
the coating.

krw = sel {1 − [1 − sem]1/ m }2(3)

where l is a pore connectivity parameter, generally set equal to 0.5
following the early work by Mualem (1976) and van Genuchten (1980).
Sometimes, however, its value is ﬁtted to experimental data in order tohave more ﬂexibility in describing observed relative permeability data((Luckner et al., 1989; Leij et al., 1997)). Here we kept the originalvalue of 0.5 for l .
The calculated relative permeability curve for primary imbibition isshown in Fig. 9 as a solid line. Good agreement was obtained between
the relative permeability values calculated using the pore morphology
method and the van Genuchten-Mualem equation as based on the
primary imbibitioncurve. Eq. (3) provided only slightly higher values ofFig. 8. Estimated Pc-S curves of the coating of a paper sample. Symbols represent
simulation results obtained with the pore morphology method, while solid lines are basedon the ﬁtted van Genuchten-Mualem equation.

tion obtained with the software GeoDict, are shown in Fig. 8. The plotsshow that the air entry suction during both drainage and imbibition
was very high (about 1 MPa or 10 bar). This feature of the coating isvery favorable for printing purposes. Having a high capillary suctionmeans that the ink (or droplet) will invade the coating as soon as thedroplet touches the surface of the coating layer. The macroscopic (bulk)
hydraulic parameters for ﬂuid movement in a variably-saturated coating layer can be determined by ﬁtting an empirical equation to thesimulated Pc-S data. While several equations for the Pc–S curve can beused for this purpose (e.g., Leij et al., 1997), in this study we use thevan Genuchten-Mualem model (van Genuchten, 1980), which is often
used in numerical studies of ﬂuid ﬂow in variably-saturated media. The
Fig. 9. Relative permeability curves for the wetting phase.

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the calculated data points. Moreover, diﬀerences between the calculated primary drainage and imbibition curves using Eq. (3) with theparameter values in Table 1 were found to be negligible, indicating thathysteresis between the primary drainage and imbibition curves can beignored when plotting results as a function of saturation. This is verymuch in agreement with many previous studies of ﬂow in variablysaturated porous media.
4. Conclusions
The standard focused ion beam scanning electron microscope (FIBSEM) used in our study was found to be a very eﬀective technique forvisualizing the three-dimensional morphology of coating layers of
paper. In combination with image analysis methods, the technique
was used to extract a 3D pore network of the coating layer. By analyzing
segmented images, the pore size distribution and porosity of thecoating could be determined. The minimum domain size for obtaining
statistically meaningful values for porosity and permeability (REV) was
found to be 60 µm3. Capillary pressure – saturation (Pc- S) and relative
permeability (Kr-S) values for the coating were obtained using the
GeoDict software, based on the pore morphology method. By ﬁtting thevan Genuchten-Mualem equation to the Pc- S data, required parameters for calculation of the relative permeability were determined.
The resulting hydraulic functions and its parameters provide a macroscopic characterization of the coating layer. These function can be usedin continuum models for simulating ink penetration and spreading
inside the coating layers of paper.
Acknowledgments
The ﬁrst two authors would like to thank European ResearchCouncil (ERC) for support provided under the ERC Grant Agreement
no. 341225. Wealso acknowledge partial support from theSustainability Program of Utrecht University.
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