Original article

Capillary pressure–saturation curves ofthin hydrophilic fibrous layers: effects ofoverburden pressure, number of layers,
and multiple imbibition–drainage cycles

Textile Research Journal0(00) 1–10
! The Author(s) 2019

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DOI: 10.1177/0040517519844209
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Amir Hossein Tavangarrad1 , S. Majid Hassanizadeh1,
Rodrigo Rosati2, Luigi Digirolamo2 andMartinus Th van Genuchten1,3

Abstract
Unsaturated fluid flow in thin porous media depends on hydraulic properties, such as the capillary pressure, Pc, as afunction of saturation, S. We measured this relationship for two different types of compressible thin hydrophilic fibrouslayers under varying conditions. Among other factors, we changed the number of layers and the overburden pressure(i.e. the confined solid pressure applied on top of the sample) imposed on one layer or a stack of layers. Applying an
overburden pressure drastically affected the Pc ðSÞ curves. However, increasing the number of fibrous layers had little
impact on the capillary pressure–saturation curves. We also investigated the effect of multiple imbibition–drainage cycles
on the Pc ðSÞ data. Measured data points were used to find general expressions for the Pc ðSÞ relationships of compressible thin porous media. Existing quasi-empirical correlations used in vadose zone hydrology, notably expressions by
van Genuchten (Van Genuchten MTh. A closed-form equation for predicting the hydraulic conductivity of unsaturated
soils. Soil Sci Soc Am J 1980; 44: 892-898) and Durner (Durner W. Hydraulic conductivity estimation for soils withheterogeneous pore structure. Water Resour Res 1994; 32: 211–223) for single- and dual-porosity media, respectively,
were employed to fit the measured data points.

Keywords
thin porous media, nonwoven fabrics, capillary pressure–saturation curves, hysteresis, overburden pressureThin nonwoven fabrics have many applications, such as
for use in hygiene products, clothes, ﬁlters, and fuelcells.1–6 The hydraulic characteristics of a thin ﬁbrouslayer have great impact on the performance of ﬁbrousproducts. Knowledge of the hydraulic properties of thinfabrics is hence essential for optimizing the performance of these products. Unfortunately, there are several
challenges when measuring the unsaturated hydraulicproperties of such thin layers. A layer is consideredphysically thin when the number of pores along its
thickness is less than approximately 15 [see Qin and
Hassanizadeh,7,8 Ceballos et al.,9 and Tavangarrad
et al.10], with the thickness of a thin porous layer obviously being much smaller than its planar extent.
A number of studies focusing on measurement of thecapillary pressure–saturation relationships of thin

nonwoven fabrics are reported in the literature.
Several concern the Pc ðSÞ curves of water–air systems
in the gas diﬀusion layer (GDL) of polymer electrolyte
fuel cells (PEFCs) [see Sole,11 Gostick et al.,12,13

1
Department of Earth Sciences, Environmental Hydrogeology Group,
Utrecht University, The Netherlands
2
Procter & Gamble Service GmbH, Germany
3
Center for Environmental Studies, CEA, São Paulo State University,
BrazilCorresponding author:
Amir Hossein Tavangarrad, Department of Earth Sciences, Environmental
Hydrogeology Group, Utrecht University, Princetonplein 9, 3584CC
Utrecht, The Netherlands.
Email: A.H.Tavangarrad@uu.nl

2
Nguyen et al.,14,15 Kumbur et al.,16,17 Fairweather
et al.,18 Jena and Gupta19]. A comprehensive review
of available techniques employed for GDLs is reported
in a study by Sole.11 Some measurements have been
carried out also to determine the Pc ðSÞ relationshipsof thin hydrophilic fabrics used in medical and hygienic
absorbent products.10,20,21
Several modeling studies also exist to estimate thecapillary pressure–saturation curves of thin ﬁbrouslayers. For example, in a recent study, general expressions for the Pc ðSÞ relationship of thin fabrics weredeveloped for a family of ﬁbrous media using a poremorphology methodology.22 That work, however, wasbased on virtual nonwoven ﬁbrous materials. Poremorphology modeling has been used also to determine
the Pc ðSÞ relationship of uncoated thin paper.23
A few studies can be found in the literature onchanges in the Pc ðSÞ curves of thin fabrics due to theeﬀect of an overburden pressure. In an experimental
study by Kumbur et al.,17 the eﬀect of compression
on the drainage capillary pressure–saturation curve ofthin ﬁbrous layers with mixed wettability was investigated. Another study concerned the image analysis ofcompression-induced morphological changes of nonwoven ﬁbrous materials.24 Furthermore, Jena andGupta25 investigated the inﬂuence of overburden eﬀects
on the pore structure of battery separators made ofnonwoven ﬁbrous layers. These various studies, however, focused on changes in the pore-size distribution
rather than capillary-pressure–saturation curves.
To the best of our knowledge, the eﬀects of overburden pressure, the occurrence of multiple imbibition–
drainage cycles, and the number of layers on theimbibition–drainage Pc ðSÞ relationships of thin hydrophilic nonwoven fabrics have not been studied experimentally thus far. These diﬀerent eﬀects areencountered in many practical applications. Examples
are hygienic products such as diapers, in which theweight of a baby imposes compression on the stack ofthin ﬁbrous layers. The compression eﬀect is also a key
factor in the optimization of fuel cell stack assemblies.
Multiple imbibition–drainage cycles occur in many
products, such as diapers, adult incontinence products,
and absorption pads. The number of imbibition–
drainage cycles is then diﬀerent depending upon thevolume of liquid in each gush of ﬂuid, and the maximum available pore volume for ﬂuid storage.
For our study we used an autoporosimetry technique developed by Miller and Tomkin26 to characterize thin hydrophilic nonwoven fabrics. Our objective
was to evaluate the eﬀects of three main factors on
the capillary pressure–saturation relationship of thinhydrophilic nonwoven fabrics: the number of layers,
overburden pressure, and number of imbibition–
drainage cycles. Measurements were performed on

Textile Research Journal 0(00)thin layers made of two diﬀerent synthetic polymers.
A comprehensive study was carried out to determine
the Pc ðSÞ curves of compressed and uncompressedthin fabrics. The individual data points were ﬁtted
with the relationships proposed by van Genuchten(VG)27 and Durner28 for single- and dual-porosity
media, respectively. We also investigated the eﬀects ofoverburden pressure on porosity and permeabilitychanges of the thin layers.
The remainder of this paper is organized as follows.
In the second section, the experimental setup and procedure are brieﬂy described. The ﬁtting function are
also introduced in this section. In the third section,
inﬂuences of the overburden pressure, the number oflayers, multiple imbibition-drainage cycles, and thelayer material on the capillary pressure-saturation measurements are discussed. Finally, scaling Pc ðSÞ curves
using the Leverett J-function are described in the fourth
section, followed by conclusions in the ﬁfth section.

Methods and material
Materials
Two diﬀerent nonwoven fabrics were used in this study:polyoleﬁn fabric and polyethylene terephthalate (PET)
fabric. The layers were made of polyoleﬁn fabric thermally bonded in some regions during the production
process. They were also treated with a surfactant tomake them hydrophilic. Each layer was about 260 mm
thick with a porosity of approximately 90%. The PET
fabric was made of hollow ﬁbers. The PET layer was
about 1500 mm thick with a porosity of close to 97%.
The porosity value was calculated from the maximum
uptake of the layer based on the following equation
’¼

mlmax
l

mlmax þ  f ms

ð1Þ

where mlmax is the maximum mass of the liquid phase,
ms is the solid mass of the ﬁbrous layer, l is the liquiddensity, and  f the ﬁber density. The ﬁber content was
distributed symmetrically across both layer materials.
The ﬁber content variation of the polyoleﬁn-basedmaterial versus depth was found to have the form of
a bell-shaped function. Other properties of the materials, including ﬁber radius and density values, are given
in Table 1.
A saline solution, made of 0.9% NaCl (by weight)
and distilled water, was chosen as the working liquid.
The solution had a surface tension of 72.5 mN=m,a density of 1.005 g=cm3 , and a viscosity of
1.019 mPa:s. Both ﬁbrous materials exhibited negligible
swelling in such a solution.1

Tavangarrad et al.

3

Experimental setup

Experimental procedure

The setup used in this study to measure capillary pressure
and saturation is referred to as a PVD-Autoporosimeter(Pore Volume Distribution Autoporosimeter), as developed by Miller and Tyomkin.26 A schematic view and apicture of the setup is shown in Figure 1. The PVDAutoporosimeter consisted of two parts: a chamber containing the fabric sample and a solution reservoir. The
sample chamber consisted of a glass frit, a membrane, atube to connect the chamber to the reservoir, an electronicbalance, and an automatic system to control the pressure
and temperature of air in the headspace. The membrane
covered the glass frit, while the circular sample with adiameter of 50 mm was placed on the membrane. A
weight could be placed on the sample to provide compression loading. The solution reservoir was placed on a highprecision balance. The reservoir was covered by a lid tominimize evaporation, while still being connected toatmospheric air. The water level in the reservoir was set
equal to the same elevation as the top of the membrane.
Changes in the water level due to drainage or imbibitionof the sample could be considered negligible, since thelateral surface area was relatively large.

The PVD-Autoporosimeter was used to obtain capillarypressure–saturation curves based on quasi-static multistep inﬂow–outﬂow measurements. Capillary pressures
were varied by increasing or decreasing the air pressureduring drainage and imbibition, respectively. Water
pressures in the sample were assumed to remain equal
to atmospheric pressure at equilibrium since they were at
the same level as the level of the solution reservoir. Air
pressure steps were speciﬁed in the PVDAutoporosimeter software and fed into an automatic
controller, which could change the air pressure in thechamber. Fluid saturation values of the sample were
measured gravimetrically using the balance. At each
step, the air pressure was kept constant until equilibrium
was reached and capillary ﬂow had ceased. A few hours
were needed to perform a full imbibition–drainage cycle.
We note that a slight loss of weight of the solution reservoir was still recorded due to evaporation, which could
not be neglected completely despite the reservoir being
covered by a lid. The evaporation rate was determinedfrom the mass loss of the reservoir as measured for an
extended period of time. During measurement of the
Pc ðSÞ curves, we assumed that equilibrium was reachedwhen the reservoir mass loss rate became less than somesmall threshold value. The experimental results were corrected by taking the measured evaporation rate into an
account. More information about the equilibrium
threshold is given in Appendix B (Supplemental material
available online).
The glass frit and membrane were kept fully saturated at all times. Sometimes during imbibition a few
droplets of water formed on the membrane surface, butdisappeared during drainage. Also, a very small volume
of water ðﬃ200 mlÞ could accumulate around the edge ofthe membrane at the bottom due to capillary riseagainst the wall of the chamber in the form of acorner triangle. Such eﬀects are negligible for Pc ðSÞ
measurements of large porous samples (such as soil

Table 1. Properties of the two fibrous layers used in this study
Properties

Unit

Polyolefin

Fiber radius[mm]
10
Fiber density[g=cm3 ] 0.92
Porosity (compressed)½
0.84
Porosity (uncompressed) ½
0.902
Permeability (compressed) ½m 
8:29  10112
Permeability½m 
2:05  1010(uncompressed)
Thickness (compressed)[mm]
200
Thickness (uncompressed) [mm]260
PET: polyethylene terephthalate.

PET
16
1.35
0.93
0.97
1:46  109
5:10  109
900
1500

Figure 1. Schematic view and picture of the Pore Volume Distribution Autoporosimeter.

4

Textile Research Journal 0(00)samples). However, because of the very small pore volumes involved, they cannot be neglected in the case ofthin layers. In order to reduce this eﬀect, we modiﬁed
the setup. This reduced the capillary rise volume toabout 40 ml. Therefore, in order to reduce uncertainty
and measurement errors, the corresponding volume ofwater was quantiﬁed in blank measurements (without
any sample) at various air pressures. The mass loss orgain of the reservoir during Pc ðSÞ measurements of
the layers was corrected using this blank volume.
More details about this correction are provided inAppendix A (Supplemental material available online).

Fitting of data points
Equations commonly used for describing observed
capillary pressure–saturation data are those proposed
by VG,27 Brooks and Corey (BC),29 and Durner,28
among others. The VG formula is given by
Se ðhÞ ¼

1
ð1 þ jhjn Þmð2Þwhere h is the capillary pressure head,  and n are ﬁtting parameters, m ¼ 1  1=n, and Se is eﬀective saturation given by Se ¼ ðS  Sir Þ=ð1  Sir Þ, in which S is thedegree of ﬂuid saturation and Sir is irreducible saturation. Because of the very large porosity of our samples, no residual air saturation needed to be considered.
In physical terms,  corresponds approximately to theinverse of the non-wetting phase entry pressure, whilethe value of n reﬂects the pore-size distribution.
Another formula is the BC equation29 hSe ðhÞ ¼;heforh 4 heð3Þ

where he is the air entry pressure head, while  is often
referred to as the pore-size distribution index. For more
complex cases, the Durner bimodal function, which isconstructed by linear superposition of VG sub-curves,
may be neededSe ðhÞ ¼wfwm
  n mf þ
ð1 þ jm hjnm Þmm
ð1 þ f h f Þ

ð4Þ

where f , nf , , m , nm are ﬁtting parameters, wf andwm are weights of the overlapping regions(subject to wf þ wm ¼ 1Þ, mf ¼ 1  1=nf , and mm ¼
1  1=nm .
The above equations may be used for woven or
nonwoven fabrics under both compressed and uncompressed conditions. The VG and BC equations areappropriate for unimodal Pc ðSÞ curves, while Durner’s
equation (and extensions thereof) can be applied tobimodal (and multi-modal) curves. For instance,

Gostick et al.13 only used unimodal VG- and BCbased Pc ðSÞ curves for their thin ﬁbrous GDLs.
Bimodal models such as Durner’s equation should provide better descriptions of some of their Pc ðSÞ data sets.

Results
Influence of overburden pressure
To study the eﬀect of overburden pressure on the capillary pressure–saturation curves, the Pc ðSÞ curves of asingle polyoleﬁn layer were measured with and without
placing a metal weight on top of the sample. We alsostudied the eﬀect of compression on the porosity of thefabric. When putting a 0.3 psi metal weight on top of
the polyoleﬁn fabric, the porosity was reduced from 0.9
to 0.84. The measured imbibition and drainage curves
with and without compression were both found to besigniﬁcantly diﬀerent also, as shown in Figure 2. The
error bars in this ﬁgure are based on duplicate measurements. Higher capillarity was observed with theoverburden pressure as compared to the uncompressed
layer. This is because the mean pore size becomes smaller when the fabric carries a metal weight. Jaganathan
et al.24 observed similar eﬀects on the mean pore size ofa hydroentangled nonwoven fabric when exposed to an
overburden pressure, based on Digital Visual Interface(DVI) image analyses. We also observed that duringdrainage both curves showed a bimodal character,which was much more pronounced for the compressed
sample. This can be attributed to having pores near thesurface with a diﬀerent size distribution than the rest of
the layer. This eﬀect is far less important in the case ofcompressed layers.
The parameters of the ﬁtted imbibition and drainage
curves shown in Figure 2 are listed in Table 2. The VG
equation was found to ﬁt the imbibition data points satisfactorily. However, Durner’s formula could ﬁt thedrainage data of both the compressed and uncompressed
layers much better. The higher value of  for the imbibition curve of the uncompressed layer, compared to thecompressed layer, showed that the air entry pressure waslower for the uncompressed fabric. Similarly, corresponding f and m values of Durner’s equation ﬁtted
to the drainage data of the uncompressed layer werelarger than those of the compressed layer. A larger
value of nm in Durner’s formula was obtained for thecompressed layer, which indicates a sharper transition ofsaturation at larger capillary pressures compared to theuncompressed layer within the same range.
The bimodal porosity is indeed expected to aﬀect theshape of both drainage and imbibition curves. This eﬀect,
however, is not pronounced in the case of imbibition
because it occurs in a much narrower saturation range.
This is also the main reason why we could not get many

Tavangarrad et al.

5data points during the imbibition process. We could have
tried to ﬁt the imbibition data using the bimodal formula;
however, since only a few data points were available, oneof the weighting coeﬃcients became very close to zero.
This suggests that two ﬁtting parameters were suﬃcientfor ﬁtting the imbibition data points.

Influence of the number of layers
One ﬁbrous layer, or a stack of two or ﬁve layers, ofpolyoleﬁn was placed on top of the membrane in thesample chamber and exposed to an overburden pressure of 0.3 psi (about 2 kPa). Capillary pressure–saturation data for the compressed stack were collected forboth imbibition and drainage. The inﬂuence of increasing the number of polyoleﬁn layers on the Pc(S) curves
is shown in Figure 3. The error bars in this ﬁgure arebased on the standard deviation of two replicates of thesame experiment. Results indicate no signiﬁcant diﬀerence between the drainage data for diﬀerent stacks oflayers. VG ﬁtting parameters of the drainage curves,
shown in Table 3, conﬁrm the similarity of the various

curves. Diﬀerences are within the eﬀect of variability inthe sample material itself. Although small diﬀerences
exist in the imbibition data, this had only a marginal
eﬀect on the ﬁtted curves. The ﬁtted parameter valuesof the imbibition curves are given in Table 3.
A similar comparison was made between the Pc ðSÞ
curves of a single polyoleﬁn layer and stacks of multiple
layers without overburden pressure. The results areshown in Figure 4. Slightly higher saturation values
were obtained for a single layer as compared to multiple layers for saturations from zero up to about 50%
during drainage. Beyond this saturation, the trend
reversed and the stacks of multiple layers had higher
saturation values compared to a single layer.
Nevertheless, diﬀerences between the measured curves
are relatively minor. We conclude that the number oflayers has little impact on measured capillary pressure–saturation data points, especially for uncompressed
layers.

Influence of multiple imbibition–drainage cycles
We next investigated the eﬀect of multiple imbibition–
drainage cycles on the hydraulic properties of a single

Figure 2. Measured capillary pressure–saturation data for asingle polyolefin layer with and without overburden pressure.
Lines show curves fitted to the data using van Genuchten (VG)
and Durner formulas.

Figure 3. Capillary pressure–saturation data for different setsof polyolefin layers under 0.3 psi overburden pressure.

Table 2. Fitting parameters of imbibition and drainage curves of a compressed and an uncompressed single polyolefin layer

Uncompressed polyolefin
Compressed polyolefin
VG: van Genuchten.

Imbibition
VG formula [1/Pa]

Imbibition
VG formulan []Irreducible
saturation
Sir []Drainage
Durner formula
wf , wm []Drainage
Durner formulaf [1/Pa], m [1/Pa]

Drainage
Durner formulanf , nm []0:003780:00197

8:53
3:44

0:02
0:06

0:42, 0:58
0:35, 0:65

0:00260, 0:00056
0:00069, 0:00044

2:07, 6:64
2:63, 11:80

6

Textile Research Journal 0(00)Table 3. Van Genuchten fitting parameters of the imbibitionand drainage curves of compressed samples containing different
numbers of polyolefin layers
SampleImbibition Imbibition Drainage Drainage
 [1/Pa]n [] [1/Pa] n []Single layer
0:00197
Stack of two layers 0:00197
Stack of five layers 0:00143

3:44
5:04
7:24

0:000469 6:29
0:000475 7:16
0:000488 6:62

Figure 5. Effect of multiple imbibition–drainage cycles on
capillary pressure–saturation measurements of a single polyolefin
layer subject to overburden pressure.

Figure 4. Capillary pressure–saturation data points for different numbers of polyolefin layers without applying overburdenpressure.

polyoleﬁn layer, starting with a dry sample subject toan overburden pressure of 0.3 psi. Figure 5 shows
results for two consecutive imbibition–drainage cycles.
No signiﬁcant diﬀerence is apparent for the drainage
data, except for a clear shift in the imbibition data
points toward higher saturation and capillarypressures.
The main reason for this eﬀect is the fact that dry
polyoleﬁn ﬁbers have a low surface energy and are
receptive to being wetted by water. At the start of thesecond imbibition cycle, the ﬁbers already containedsome ﬂuid (because of an irreducible saturation ofaround 6%). Surface energies as a result increased,leading to higher capillary pressures at given saturationlevels.

Effect of layer material
The experiments thus far were carried out using polyoleﬁn fabric. A similar series of experiments was performed on layers made of PET. The PET layers are
thicker than those made of polyoleﬁn, but are muchcoarser by containing at most 10 pores along their

thickness (Table 1). Fiber diameters and mean poresizes of the PET layers, as well as their porosity, arelarger than those of the polyoleﬁn layer.
Measured capillary pressure–saturation data forvarious sets of PET layers are presented in Figure 6.
As expected, a lower capillarity for the PET layer wasobserved during both imbibition and drainage (compare Figures 2 and 6). Values of the VG parameters,
obtained by ﬁtting Equation (1) to the data points, arelisted in Table 4. Clearly, values of  for the imbibitionand drainage curves of the compressed PET layers weremuch larger than those of the polyoleﬁn layer, as isshown also by the entries in Tables 2 and 3. Similarly,
the measured permeability and porosity of PET fabric
are much higher.
Results of the capillary pressure–saturation measurements of the stacks with diﬀerent numbers of PET
layers are depicted in Figure 6. The variability in themeasurements can be attributed mainly to inherent differences in the fabrication of the fabric. The relatively
small diﬀerence in the data for diﬀerent numbers oflayers shows that the eﬀect of interlayer space is negligible. This is similar to the results we obtained for thepolyoleﬁn stacks, as shown in Figure 3.
Next, the eﬀect of multiple imbibition–drainage
cycles was studied on a single PET layer under compressed conditions. The results are shown in Figure 7.
The data again did not show any diﬀerences between
the second and third cycles for both imbibition anddrainage. However, similarly as for the polyoleﬁnexperiments, the imbibition curves of the second andthird cycles exhibited higher capillary pressurescompared to the ﬁrst cycle. Finally, we studied theeﬀect of overburden pressure on the Pc ðSÞ curves ofa single PET layer. Figure 8 shows the capillaryTavangarrad et al.

7

Figure 6. Capillary pressure–saturation of different numbers ofpolyethylene terephthalate layers under 0.3 psi overburdenpressure.

Figure 7. Effect of multiple imbibition/drainage cycles on
capillary pressure–saturation measurements of a single polyethylene terephthalate layer.

Table 4. Hydraulic parameters of the imbibition and drainage
curves of a single compressed polyethylene terephthalate layer
used in this study
Imbibition Imbibition Irreducible Drainage
Drainage
VG formula VG formula saturation VG formula VG formula [1/Pa]n []Sir [] [1/Pa]n []
0:0073

4:32

0:01

0:001698

7:71

VG: van Genuchten.

pressure–saturation drainage curves with and without
the overburden pressure (again 0.3 psi). Correspondingﬁtting parameters of the Pc ðSÞ drainage curves using
the unimodal VG and bimodal Durner models are
given in Tables 4 and 5, respectively. The PET results
are very much in line with those of the polyoleﬁnfabric, as shown in Figure 3. Higher capillary pressures were obtained with the overburden pressure,since the fabric then deforms and the pores become
smaller.

Scaling of Pc(S) curves using the Leverett
J-function
The purpose of employing the Leverett J-function30 is
to use measured Pc ðSÞ curves of a given nonwovenﬁbrous material in order to construct Pc ðSÞ curves for
similar materials and/or for diﬀerent conditions. The
Pc(S) equation as proposed by Leverett30 is of the form
Pc ðSÞ ¼  cosðÞ

 ’ 12
K

JðSÞ

ð5Þ

Figure 8. Observed (symbols) and fitted (lines) drainage capillary pressure–saturation curves of a single polyethylene terephthalate layer with and without overburden pressure. VG: van
Genuchten.

in which  is the static contact angle of a ﬂuid–solid
system, ’ is porosity, and  is the interfacial tension
between the wetting and non-wetting ﬂuids.
The function JðSÞ presumably is the same for similar
media. Udell31 did propose an equation for Pc ðSÞ forhighly hydrophilic geological porous media, which wasused later also for thin ﬁbrous layers32

82>< 1:417ð1  SÞ  2:12ð1  SÞ
3JðSÞ ¼
þ1:263ð1  SÞ>:
1:417S  2:12S2 þ 1:263S3for  90for 4 90
ð6Þ

8

Textile Research Journal 0(00)Table 5. Fitting parameters of the drainage curve of theuncompressed single polyethylene terephthalate layer used in thisstudy
Durnerformulawf , wm []Durner formulaf [1/Pa], m [1/Pa]

Durnerformulanf , nm []Irreducible
saturation
Sir []0:43, 0:57

0:012, 0:0023

1:94, 7:38

0:02

control drainage events while the larger pore regions
control imbibition,33 often referred to as the ink
bottle eﬀect.
As explained in previous studies [e.g. Nguyen et al.14
and Kumbur et al.16], the equations above are insuﬃcient for describing capillary ﬂow phenomena. One
should consider such additional variables as pore-size
distribution and stress–strain relationships to better
scale the Pc ðSÞ curves under diﬀerent compression
loads. However, as illustrated in Figure 9, similar
trends in Leveret’s -J function, and hence the Pc ðSÞ
curves, were obtained due to the overburden pressure
eﬀect. The predicted curves could not reproduce thebimodal behavior of the uncompressed layer under
the drainage condition. However, as shown by
Figure 9, changes in the Pc ðSÞ curves due to hysteresis
and the overburden pressure were well reproduced by
the Leverett scaling approach.

Conclusions

Figure 9. Observed and fitted imbibition–drainage curves of acompressed polyolefin layer using Leveret’s J-function. The fitted
curve was used to obtain the Pc ðSÞ curve for an uncompressed
layer based on Equation (5).

The generic Leveret approach given by the above
equations was used to ﬁt capillary pressure–saturation
curves of a compressed polyoleﬁn layer. Assuming theinterfacial tension between air and liquid remains
constant during the measurements, the only unknown
parameter is the static contact angle. The best ﬁt of thedrainage data was obtained with a contact angle of
25 degrees, while the imbibition data points werematched using a contact angle of 77 degrees. We thus
used Equation (5) to predict the Pc ðSÞ data of an
uncompressed nonwoven ﬁbrous material from a similar type of fabric based on equality of the J-function for
the two fabrics as follows33
 1  1
2 K1 2 ’2 2
Pc2 ðSÞ ¼ Pc1 ðSÞ
1 K2
’1

In this research we investigated the eﬀect of several
factors on the capillary pressure–saturation curves of
two diﬀerent thin nonwoven ﬁbrous materials. Results
for both materials demonstrated the important eﬀect ofoverburden pressure on the Pc(S) curves. However,increasing the number of layers did not seem to aﬀect
the curves drastically. In addition, the inﬂuence of multiple imbibition–drainage cycles showed that wetting ofa sample in the ﬁrst cycle would increase the capillarity
in the next cycles. We used both the unimodal VG andbimodal Durner models to ﬁt the experimental data.
The Durner model is recommended when the capillarypressure–saturation data show clear bimodal behavior.
One major question that remained unanswered is how
the capillary-pressure–saturation function of nonwoven
fabric (like that of many medical absorbent products)
may change during dynamic ﬂow conditions, as has
been noted for other porous media34 (see Appendix C(Supplemental material available online)). Work on the
dynamic capillary pressure–saturation curves is still inprogress.
Declaration of conflicting interests
The authors declared no potential conﬂicts of interest withrespect to the research, authorship, and/or publication of thisarticle.

ð7Þ

where the subscripts 1 and 2 denote uncompressed andcompressed layers, respectively. The contact angle
was assumed to be same for both layers. It should be
noted that a change in the contact angle is not the only
reason for hysteresis in the capillary pressure–saturation curve. Diﬀerences occur also since small pores

Funding
The authors disclosed receipt of the following ﬁnancial support for the research, authorship, and/or publication of thisarticle: The research leading to these results was supported by
the European Research Council under the European Union’s
Seventh Framework Program ((FP/2007-2013)/ERC Grant
Agreement no. 341225) and by Procter & Gamble.

Tavangarrad et al.

9

Supplemental material
Supplemental material is available online for this article.

ORCID iD
Amir Hossein Tavangarrad
3831-1555

http://orcid.org/0000-0002-

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