Evaluation of absorption of micro-droplets on paper for
creation of paper-based microstructures*
Toshiharu Enomae, Kazutomo Dougome, and Akira Isogai
Graduate School of Agricultural and Life Sciences, The University of Tokyo, Bunkyo-ku, Tokyo 1138657, JAPAN
Tel.: +81-3-5841-8199, Fax: +81-3-5841-5271, E-mail: t@enomae.com, http://www.enomae.com/

Abstract
This work clarifies the absorption behavior of micro-droplets of water on treated paper in order to support the design offunctional microstructures, such as electronics and micro-fluid channels, on paper. The period of time between when a microdroplet of water ejected from an ink-jet head lands on the paper’s surface and its complete disappearance by absorption was
defined as the micro-sizing degree (MSD), and an MSD measurement method was established. The MSD was evaluatedusing microscopic high-speed video images of the side view recorded every millisecond. Several grades of commerciallyavailable ink-jet paper media and laboratory sheets having different levels of water repellency prepared from a pulp and asizing agent were examined. The MSD of commercial ink-jet papers, which are known to absorb water very quickly, was 3–6
ms. Weakly sized laboratory sheets exhibited a lower MSD of 2–3 ms. The absorption behavior was analyzed in terms of thecapillary pressure with and without the Laplace pressure; the theoretical and experimental results agreed moderately well.
The results indicated that the Laplace pressure cannot be neglected in the analysis. The MSD of a wet surface where apreceding micro-droplet had already landed was higher than that on a dry or partially wet surface, presumably because waterremains inside pores for an unexpectedly long time.

Keywords
Alkyl ketene dimer, ink-jet printing, micro-sizing degree, paper

Introduction
Ink-jet printing systems are currently applied not only for personal use but also for advanced commercial printing
capable of outputting variable information from sheet to sheet. Commercial high-grade ink-jet papers with silica or alumina
coatings provide the highest image quality. In addition, package printing on curved surfaces by use of a non-contact systemand textile printing on nonwoven fabrics were recently reported [1]. Ink-jet technologies such as liquid division into microdroplets and precise positioning have been applied widely in industries other than conventional printing, for example,
production of color filters for liquid crystal TVs and nano-patterning of semiconductors.

* Part of this research was presented at NIP22, Denver, CO, Imaging Science and Technology (2006) and the
TAPPI Advanced Coating Fundamentals Symposium, Munich, Germany, TAPPI (2010).
2

Ink-jet paper that reproduces photo-like quality has been developed and is widely used. Crucial problems with the print
quality of plain paper, such as feathering and bleeding, have been alleviated using microscopic ink droplets and nonfeathering types of ink. Printing paper compatible with both offset and ink-jet printing is being developed for efficientvariable-data printing. In short, ink-jet technology is oriented toward generic printing compatible with all types of paper aswell as particularly high image quality when specialized paper is used.
In addition, microelectromechanical systems (MEMS) and other micro-scale electronics can now be fabricated using
printing technologies [2]. Fabrication of such functional microstructures on paper would provide portability, eco-friendly
disposability, and recyclability at low cost. To achieve this, the lateral spreading, penetration, and solidification of liquidmaterials must be controlled for conformity with the desired design. As an initial step to realizing this technology, thefundamental interactions between liquid and paper are being investigated at the micrometer level.
Liquid penetration into paper is generally closely related to the paper’s water affinity or water repellency, the level ofwhich is described by the sizing degree. This property has been measured by several methods. One of the simplest is the
Stöckigt method [3]. A squared paper sheet is given a boat-like shape by folding up the four sides and then floated on asurface of aqueous ammonium thiocyanate. An aqueous ferric chloride solution is dropped onto the boat from above, and thetime until three red spots are visually detected is measured. The Stöckigt sizing degree does not represent the surface layer
properties involved in ink-jet penetration, and visual judgment can be applied only for moderately to strongly sized paper.
The Cobb sizing degree (Cobb value) [4] is defined as the mass of water absorbed in a specific time, which is called thewater absorptiveness. For accurate values, long periods of time must be specified. Thus, it is difficult to apply to rapid ink
absorption.
For methods more oriented to printability, the Hercules sizing degree [5] is used. An aqueous dye solution is allowed topenetrate a paper sample. The change in light reflectance is monitored from the other side of the paper, and the time required
for the reflectance to decrease to a specified value is defined as the sizing degree. More recently, original and modified
Bristow-type testers have become popular as a tool for direct measurement of the liquid absorption volume as a function of
the duration of liquid–paper contact [6]. Liquid is absorbed into the paper from a slit at the bottom of a liquid supply head.
The absorption volume per unit area is determined and plotted against the contact time, which is calculated from the velocity
at which the paper crosses the slit width. The shortest available contact time is about 10 ms.
The contact angle is not a direct measure of the absorption volume but is often used to indicate the wettability of media
surfaces as well as its change with time. Absorption tests measure the time required for a drop on a paperboard surface to beabsorbed, which is determined by a sudden decrease in the gloss [7]. Assuming that the three-dimensional shape of a liquid
drop on a paper surface is isotropic, the side view projection, which can be recorded simultaneously with contact angle
measurements, yields the volume of the drop. The contact angle is measured using a droplet having a volume ranging from 1
to 30 μL, which is about 106 times larger than common ink-jet droplets. A 1 μL sphere has a diameter of about 1.24 mm,
which is more than 10 times thicker than common copy paper. Considering the water drop’s dimensions, a large volume ofwater remains on the surface even after the leading edge of the water reaches the opposite side by penetration. Thus, a droplet
this large cannot be used to simulate the absorption of a droplet ejected by ink jet.
Questions have arisen about sizing effects. For example, are the sizing degrees or water absorption rates measured using
bulk water or macroscopic water drops by conventional methods applicable to the microscopic water droplets used in ink-jet
printing? Sizing agents distributed via small particles are reportedly scattered discretely [8]. Although two particles may bedeposited at locations several or several tens of micrometers apart, the sizing agent produces an adequate sizing effect owing
to the surface tension of the water bridging the two particles. Are water droplets with a diameter smaller than the distance
between two size particles absorbed quickly? The drop absorption time has been measured [9], but it was on the order ofseveral decades of milliseconds. Water micro-droplets of about 10 to 30 pL (about 20 to 40 μm in diameter, which isequivalent to the width of a pulp fiber) were ejected from a test ink-jet head and used to determine these properties, which are
expected to be on the order of milliseconds, using a high-speed video camera system [10].
In response to these questions, the authors previously reported the absorption rate of water micro-droplets on ink-jet
papers having a homogeneous ink-receptive layer [11]. The current report presents the absorption time or micro-sizing
degree (MSD), of plain paper with pulp fibers exposed on the surface and compares it to that of commercially available
silica-coated ink-jet papers. The water absorption rate is generally measured by Bristow’s apparatus and interpreted on thebasis of the Lucas–Washburn equation. In this case, the supplied liquid is assumed to be sufficiently abundant, and the
reduction in surface area of the bulk liquid during absorption is neglected. This paper also analyzes the absorption
mechanism in terms of the driving forces. The intermolecular attraction and surface tension have a much greater effect in a
micro-liquid droplet than in a bulk liquid. The surface tension of a micro-droplet’s spherical cap on a paper surface isconsidered to produce high pressure comparable to the capillary pressure. Thus, the absorption mechanisms of liquid microdroplets could differ from those of a bulk liquid. Because the surface tension and capillary pressure of liquids are both
involved in stable patterning of microstructures, it will be useful to understand liquid absorption into a substrate with a microporous structure.

3

Experimental
Samples
The following commercially available ink-jet papers were used. Sample PM is a photo-grade gloss-type PM paper from
Epson. Sample QP is Konica-Minolta’s gloss-type Photo-like QP paper. Sample HG is a Hi-Grade paper from Mitsubishi
Chemical. The liquid ejected as a micro-droplet was de-ionized water unless otherwise noted. Laboratory sheets of different
sizing (water repellency) degrees were prepared by adding different amounts of a sizing agent consisting mainly of alkyl
ketene dimer (AKD). Two types of AKD (Harima Chemicals, Inc., AK-720H) with different sizing performances wereapplied. Size L, which exhibits lower performance, was added to dry pulp mass at 0.05, 0.10, and 0.20%, whereas the higherperformance size H was added at 0.10, 0.15, and 0.20%. Polyamide amine epichlorohydrin (PAE) (Seiko PMC Corp., WS4002) was added as a retention aid at half the amount of AKD. PAE was added first, and the mixture was stirred for 5 min;
AKD was then added. Laboratory sheets with no AKD and no PAE were prepared as blank samples. The preparation
processes followed ISO 5269-1:2005 except that a pressure of 310 kPa was applied for 5 min with no repetition in the wetpress process.

Methods
The landing action and the absorption into paper of water micro-droplets ejected from an ink-jet head were recorded by
the microscopic high-speed video recording system shown in Fig. 1. The system consists of a high-speed video camera (ForA, Japan, VFC-1000, black-and-white model) and an optical microscope (Olympus, CX41) with a 10× objective lens. Two
ink-jet heads were used: a multi-nozzle type (KIE-2, Konica Minolta, Japan; Fig. 1, top) and a single-nozzle type (PIJ25NSET, Cluster Technology, Japan; Fig. 1, middle) driven by a controller (WaveBuilder PIJD-1) adjusted to Wave B mode
at a discharge voltage of 7.00 kV to stabilize the droplet volume to about 15 pL. The multi-nozzle and single-nozzle heads
were used for sizes L and H, respectively.
The sample stage has a smooth vertical surface to which a paper specimen is attached with double-sided tape (Fig. 1,
bottom). Backlighting is supplied by diffuse illumination produced by covering the opening for a cold light source with atranslucent film. The landing and absorption of micro-droplets ejected from the ink-jet heads were recorded at a speed of1000 frames/s and a shutter speed of 1/2000 or 1/5000 s. The projected hemisphere of each micro-droplet was recorded as adark object. The recording period was 4 s per ejection, and the resolution of the recorded images was 256 × 212 pixels. The
distance between the ink-jet head and the paper surface was set to 2 to 3 mm so that the landing velocity would be low
enough to ensure capture of the moment of landing. The first stage of micro-droplet deformation immediately after landing,which depends on the surface energies of both the ink and the substrate [12], was deliberately avoided.
To evaluate the absorption rate of a micro-droplet of water, the volume of the hemisphere was calculated from the shapeof the projected hemisphere. A prepared slide with an embedded scale was recorded, and the hemisphere volume wascalibrated to true values on the basis of a scale of 0.746 μm per pixel. To measure the shape parameters of the projected
hemisphere of a water droplet in video images, the coordinates of two ends of the chord and the zenith were determinedvisually. The volume, height, and radius of the circular area and the contact angle were then calculated from them, assumingthat the hemisphere is part of a circle and that the micro-droplet is isotropic in three dimensions.

Results and discussion
Size of water micro-droplets
The volumes of the water micro-droplets ejected from the ink-jet head varied widely. They can be grouped roughly into
tiny, intermediate, and large droplets. The diameters and estimated volumes of each type ejected from the single-nozzle head
were 8.0, 20.5, and 36.9 μm and 0.3, 4.5, and 26.4 pL, respectively. It appears that, on ejection, some micro-droplets mergedwith others, increasing their volume. Thus, the volume of the recorded micro-droplets ranged between 0.3 and 29.2 pL. The
volumes were distributed more broadly for the multi-nozzle head because not every micro-droplet was ejected from the same
nozzle.

4

Landing of water micro-dropletsFig. 2 shows the changes in the shape of the micro-droplets over time after landing on the laboratory sheet prepared with
0.05% and 0.20% added AKD. The horizontal white line that appears in the frames before landing is the top surface of a fiberat the paper’s surface. The landing locations were selected prior to ejection so that the fiber axis was as horizontal as possible.
Out-of-focus micro-droplets sometimes appeared to pass the front or back of the fiber and fall into the adjacent pore.
Therefore, they never spread over the fiber’s surface. In some cases, a micro-droplet hung on the tip of a fiber’s fibril forseveral ms and then suddenly disappeared by absorption. This phenomenon is explained in terms of the lotus effect, in whicha water droplet rolls off a hydrophobic surface having a porous microstructure containing trapped air. The preparedlaboratory sheets, even those with no AKD, pulled in micro-droplets less easily than commercial silica-coated ink-jet papers,
and many micro-droplets were seen to float away above the paper surfaces. Repulsive electrostatic forces might havedeveloped between the surfaces of the micro-droplets and the fibers.
For laboratory sheets sized with 0.05% AKD L, as shown in Fig. 2a, wetting and absorption occurred very quickly. Thisimplies that the absorption rate of a water micro-droplet is higher for unsized or weakly sized paper than for ink-jet paperwith an ink-receptive layer. When 0.20% of AKD was added, however, as shown in Fig. 2b, the absorption rate was very low.
The radius of the circular contact area also remained constant during the absorption process in this case.

Change in shape of water micro-droplet hemisphere
Fig. 3 shows an example of the projected hemisphere of a water micro-droplet on sample QP. The image in which thewater micro-droplet first appeared was designated as time 0. This rule of time setting was applied to every water microdroplet analysis. At 0 ms, the image faintly indicates the micro-droplet’s trajectory, suggesting that this frame is very close to
the true time 0, which is ideal for determining the landing time. The droplet’s height and contact angle decreased with time.
In contrast, the radius of the circular contact area initially decreased very little but then started to decrease at 6 ms. Fig. 4
plots these changes in the shape parameters numerically along with the decrease in volume of this water micro-droplet. Whenthe droplet height is low, as in the image at 8 ms, the contact angle data are no longer accurate. This difficulty becomesremarkable as the angle approaches 20º. Although the contact angle decreased, the radius of the circular contact area
remained almost constant in the earlier stages of absorption. This phenomenon is believed to be explained as follows. When awater micro-droplet collides with a paper surface, it spreads very quickly over the surface owing to its inertia, forming theadvancing contact angle. The shape of the circular contact area is maintained even during penetration of the water until thecontact angle matches the receding one. The receding contact angle is subsequently maintained as the contact line recedes
toward the inside.

Volume change of water micro-droplet
Fig. 5a shows the volume changes of water micro-droplets on sample QP. The volume decreased nonlinearly with theelapsed time. In Fig. 5b, the same data are re-plotted as a function of the square root of the time; a region of linearity appears
at the mid-point in the penetration time in several of the curves. This linearity implies penetration based on the Lucas–
Washburn equation,
Rσ cos θ ,
(1)
l=
t
2η
where l is the penetration depth, R is the capillary radius, σ is the surface tension of the liquid, θ is the contact angle, η is theviscosity of the liquid, and t is the time. This equation shows that the surface wetting force σcosθ of a liquid is the driving
force of penetration and applies well to liquid penetration of such micro-porous media. The initial gentle slope is probably
explained in terms of the time required to wet the surface. A gentle slope also appears at the other end of the curves.
Considering that the radius of the circular contact area decreased while the receding contact angle was maintained, as shownin Fig. 4, the droplet contracts toward the inside while maintaining its shape. Fig. 6 schematically illustrates the mechanismof water droplet penetration.
Fig. 7 shows the changes in the volume of water micro-droplets on sample PM. As with sample QP, the volume
decreased linearly as a function of the square root of the time. The water absorption rate should be reflected in the slope ofthe volume change. The two photo-grade ink-jet papers, QP and PM, did not show a significant difference in water
absorption rate.
Fig. 8 shows video frames of the water micro-droplets and their changes in volume on sample HG, a general grade ofcoated ink-jet paper. Scanning electron micrographs revealed aggregated silica particles 5 to 20 μm in diameter, and pulp
fibers were visible between the particles (not presented here). Therefore, the surface consisted of large, rough silica

5aggregates and pulp fibers. The base paper used for ink-jet coating is typically sized to some extent; thus, the water
absorbency is expected to be lower than that of the silica particles. However, the initial contact angle was lower for sample
HG, as shown in the image at 0 ms, and the water absorption rate was higher than that of photo-grade samples QP and PM.
Bristow’s test revealed a higher water absorption rate for QP and PM, presumably because the coat weight of sample HG wasmuch less, and any initial quick absorption that might occur was not detected.
Fig. 9 shows the changes in the volume of individual micro-droplets on the laboratory sheets with the square root of thetime. The volume of micro-droplets ejected from the head varied widely. However, large droplets did not always show higher
MSD values. As noted above, micro-droplets sometimes hung on the tip of fibrils for several ms before being absorbed on
sheets with 0.20% added AKD L. This also occurred, but less frequently, for sheets with 0.05% added AKD.
Fig. 10 shows the changes in the volume of water micro-droplets upon landing on laboratory sheets treated with size Hwith 95% confidence intervals attached to every data point of a mean value. The data points were plotted down to certain
volumes and not to volume zeros because some micro-droplets were completely absorbed early and the reasonable mean
volumes could not be calculated only from the remaining micro-droplets, that is, those chosen nonrandomly. The threeabsorption curves for the AKD-added sheets have fairly wide 95% confidence intervals. This result suggests that the three
curves can be regarded as equal in absorption rate and compared with theoretical curves as a whole in the following section.
The mean MSD was 380–450 ms for the three types of sheets irrespective of the amount of size H added. Sizing effects tend
to saturate at high levels of added sizing; therefore, the 0.1% addition level provided sufficient water repellency. However,
the wider 95% confidence intervals suggest that more sites lacked AKD when less sizing agent was added as summarized inTable 1.

Theoretical analysis of absorption
The velocity of liquid absorption into porous media has been investigated theoretically using the Lucas–Washburnequation (1) historically [13] and more recently using the Davis–Hocking model, which describes a porous medium saturated
by a liquid [14] and a dry porous medium [15]. For non-porous media with a water-absorbent polymer, the diffusion model
was shown to be appropriate, and the case of a porous medium was compared to it [8]. The ink absorption velocity ofpigment-based inks has also been determined [16]. The driving forces for liquid sorption into porous media are the capillarypressure, Laplace pressure, and hydrostatic (gravitational) pressure,ΔP =2σ cosθ 2σ++ ρgh ,
Rr

(2)

where ΔP is the total absorption pressure, r is the radius of the spherical cap of a micro-droplet remaining on the medium’s
surface, ρ is the density of the liquid, g is the gravitational acceleration, and h is the height of the spherical cap. The
gravitational pressure in the third term is far less than the other two pressures, especially for a micro-droplet. The Laplacepressure is usually neglected for bulk liquids such as film-shaped ink deposits above a medium in conventional printing
systems. It is also often neglected for ink-jet printing because the radius of curvature of a micro-droplet is larger than thecapillary radius for pigmented microporous layers with small pore sizes [13, 17, 18]. On the fiber-exposed surfaces of
uncoated paper such as the laboratory sheets, however, the pore radius is 1 μm or greater at the medium’s surface, which iscomparable to a micro-droplet’s radius of curvature. Therefore, the Laplace pressure cannot always be neglected.
The volume V and radius r of the spherical cap are functions of time t. It was assumed that the radius of the circular
contact area has a constant value a and the contact angle at the edge of the spherical cap continues to decrease during
absorption, as shown in Fig. 6, although θ, the advancing contact angle in the capillaries, is constant. If the liquid flow in
capillaries is assumed to follow Poiseuille’s law, and the gravitational pressure is neglected,
dl R 2 ΔP .
=
dt
8ηl

(3)

Equations (2) and (3) givedl R 2 ⎛ 2σ cosθ 2σ⎞=++ ρgh ⎟ .
⎜dt 8ηl ⎝
R
r
⎠

(4)

Substituting ρgh = 0 , V = V0 − φπa 2 l , and − dV = φπa 2 dl into equation (4) yields
dt

−

dt

dV R 2 (φπa 2 ) 2 ⎛ 2σ cos θ 2σ ⎞ ,=+⎜⎟dt 8η V0 − V ⎝
R
r ⎠

(5)

6

where φ is the porosity of the medium, and V0 is the initial volume of the spherical cap at t = 0. In equation (5), every value isconstant except V and r. Thus, it is difficult to determine V as a function of t. However, if some values are substituted for r,
the right-hand side value is determined by using the relationship
V =

π
3

{2r − (2r + a ) r − a }.
3

2

2

2

2

(6)

If dv and dt are observed starting at V = V0 and t = 0, respectively, the relationship between V and t can be illustrated
graphically.
Fig. 11 shows the absorption curves predicted by equation (5); the Laplace pressure 2σ/r is considered and neglected forboth sized and unsized papers. To draw these curves, the known physical constants of σ = 72.8 mN/m and η = 1.00 mPaxs
were applied, and φ was calculated from the paper and cellulose densities. R has not been measured, but 2.1 μm, which is themeasured value for generic uncoated paper, was used [19]. The values of θ, a, and r t=0 were those calculated from the initialdimensions of the micro-droplets recorded essentially as specified in the caption of Fig. 11 so that V0 would agree
approximately with the measured values in Fig. 10. The curves predicted with and without the Laplace pressure arereasonably different from each other. The difference becomes remarkable when the capillary pressure is reduced by thepresence of larger pore sizes or higher contact angles, that is, for low-density or sized paper, respectively. Both of thepredicted curves for the sized laboratory sheets match the experimental ones shown in Fig. 10. It was difficult to judge theimportance of considering the Laplace pressure. For unsized laboratory sheets, the predicted curves showed slower
absorption than the experimental ones, presumably because of the effect of swelling of cellulosic materials, which resembles
that of an absorbent polymer.
The experimental curves shown in Fig. 10 deviated downward to some extent from a linear regression for the sized paper.
This deviation is presumably attributed to the evaporation of water from the micro-droplet surfaces. If the evaporation rate is
assumed to be roughly proportional to the area of a water/air interface and this area does not change much until near the endof the absorption process, the water micro-droplet volume decreases as a linear function of time by evaporation. If theevaporation effect is put on the absorption curves, the volume reduction curves in Fig. 10 will deviate downward on a scaleof a square root of time. The effect of evaporation should be examined precisely because it is closely related tomicrostructure formation after drying.

Absorption of a water micro-droplet on a wet surface
Coincidentally, several water micro-droplets landed close to each other on sample PM. Fig. 12a shows video frames
recording four water micro-droplets that landed continuously on the surface. The first droplet (0 to 6 ms) and the third droplet(200 to 216 ms) appear on the left, the second (124 to 130 ms) appears in the middle, and the fourth (210 to 216 ms) appearson the right. The second and fourth water droplets landed at a distance from the first and second, respectively, ofapproximately half the radius of the circular contact area. The absorption patterns of the second and fourth water droplets
were similar to that of the first droplet, which landed on a dry surface, in terms of the change in the volume of the on-paper
spherical cap, the radius of the circular contact area, and the contact angle. When an area of about one-third of that of thecircular contact area is already wetted, it does not seem to affect a droplet’s absorption behavior. However, for the third
droplet, which happened to land on exactly the same location as the first one, the volume decreased more slowly than for theother droplets, and the contact angle was lower at the same time after landing. Wet pore walls are believed to have low
contact angles θ and to absorb water more quickly than dry ones. However, absorbed water might remain inside the pores andplug them for longer times than expected for diffusion and evaporation.

Micro-sizing degree
In Fig. 2a, the spherical cap of a micro-droplet was recorded in only two frames. In this case, the MSD was 2 ms. It
follows that in order to standardize the sizing degree, we can assume that n frames including a micro-droplet in contact with apaper surface indicate that the MSD is n ms on average, with maximum errors of ±1 ms at 1000 frames/s. Therefore, lower
MSDs tend to have relatively larger experimental errors. For samples other than the laboratory sheets treated with size H, themulti-nozzle type head was used. From this head, satellite (small) and coalesced (large) droplets were sometimes generated.
The MSDs for every clearly recorded micro-droplet were determined irrespective of the droplet size, and the mean values
were calculated. Table 1 lists the mean MSDs with 95% confidence intervals for all the samples examined. Therefore, thecalculated MSDs have relatively broad distributions. When 0.10% or less of AKD L was added, the MSD did not varysignificantly. When 0.20% was added, however, it increased to extremely high values. Ink-jet papers having an ink-receptive
layer that contains silica or alumina particles are known to absorb water quickly. However, the hydrophilic fiber surfaces of7

an unsized or even weakly sized laboratory sheet absorbed water much more quickly. Sample HG showed the lowest MSD
among the silica-coated ink-jet papers used.
AKD particles melt under heat treatment and cover the paper’s surface, but only a certain ratio of the entire area [9].
Exposed unsized surfaces might be wetted easily by water micro-droplets and trigger quick absorption even on strongly sized
paper. Therefore, it was predicted that for micro-droplets, sizing agents such as AKD might not function properly. Emulsified
particles of AKD are adsorbed on the fiber surfaces during dehydration in the papermaking process. However, for thelaboratory sheets with 0.20% of added AKD H, it takes several tens of milliseconds for every micro-droplet to be completely
absorbed. This is significantly longer than the time required on the laboratory sheets with 0.10% or less of added AKD H.
Thus, strongly AKD-sized paper exhibits homogeneous water repellency of micro-droplets with diameters of as small as afew micrometers.

Conclusion
The micro-sizing degree (MSD) is defined as the period of time between when a micro-droplet of water ejected from an
ink-jet head lands on a paper surface and its complete disappearance by absorption. MSD values were evaluated using
microscopic high-speed video images of a side view for several grades of commercially available ink-jet paper and laboratory
sheets having different levels of water repellency. The laboratory sheets were prepared from a kraft pulp with added AKD.
The MSD of commercial ink-jet papers, which are known to absorb water very quickly, was approximately 3–6 ms. In
contrast, it was approximately 2–3 ms for uncoated laboratory sheets with 0.10% or less of added AKD H. The MSD forlaboratory papers with 0.20% of added AKD H was approximately 45 ms. The absorption of water micro-droplets wasanalyzed considering the capillary pressure with and without the Laplace pressure as driving forces. The difference due toconsidering or ignoring the Laplace pressure became remarkable when the capillary pressure was reduced by the presence oflarger pore sizes or higher contact angles, that is, for common uncoated printing paper. The MSD of a wet surface where apreceding micro-droplet had already landed was higher than that of a dry or partially wet surface. The knowledge obtained in
the study will be useful in the design and fabrication of microstructures on commercial paper.

Acknowledgment
The authors express special thanks to Mr. Kazumasa Matsumoto, Konica Minolta, for giving us the opportunity to use theKIE-2 system. They also thank the Japan Society for the Promotion of Science (JSPS) and the Japanese Society of Printing
Science and Technology (JSPST) for their financial support: Grant-in-Aid for Scientific Research (B) No. 22380092 (2009)
and Research Fund for Printing Technology (2009 and 2011), respectively.

8

Table 1 MSD values of commercially available ink-jet
papers and laboratory sheets sized to different degrees
Type of paper

MSD, ms

Commercially available ink-jet paper
QP

6.3±1.4PM

4.8±1.0

Landing on dry or partially wet surface

7.3±1.3

Landing on wet surface

18

HG

3.3±0.7

Laboratory sheets
Unsized2.1±0.4

Sized by AKD L addition, %No AKD addition

2.1±0.4

0.05

3.4±2.50.10

2.3±0.70.20

44.9±21.2

Sized by AKD H addition, %No AKD addition

3.1±1.1

0.10

380±1200.15

420±700.20

450±609Microscope
Lens
Paper

Water
dropletSamplestage
Backlight

Fig. 1 Multi-nozzle (top) and single-nozzle (middle) ink-jet heads andmicroscopic high-speed video camera system (bottom)

10

(a)

(b)

-2 ms

-1 ms

5 ms

-1 ms

0 ms

1 0 ms0 ms

1 ms

1 5 ms1 ms

2 ms

2 0 ms3 ms

4 0 ms4 ms

6 0 ms

2 ms

10 μ m10 μ mFig. 2 Landing of water micro-droplets on laboratory sheets preparedwith (a) 0.05% and (b) 0.20% added AKD

11

0 ms

2 ms

4 ms

6 ms

8 ms

10 ms
10 μm

Fig. 3 Changes in projected spherical cap of water micro-droplet
on sample QP recorded every 2 ms

12

90
80

Water droplet volume, pL

12

70
10

60

8

50

Volume40

6Contact Angle
30

Radius420
2Height (μm) , Radius of contact area( μm) and Contact Angle (º)

1410Height
0

0
0

2

4

6

8

10

Time, ms

Fig. 4 Changes in volume and shape parameters of a single water micro-droplet
recorded in video images shown in Fig. 2

13

100

Water droplet volume, pL

(a)
80

60

40

20

0
0

5

10

15

20

25

Time, ms
100

Water droplet volume, pL

(b)
80

60

40

20

0
0

1

2

3

Square root of time, ms

4

5

0.5

Fig. 5 Changes in volume of water micro-droplets on sample QP with (a)time and (b) square root of time14

Fig. 6 Schematic of water micro-droplet absorption mechanism

15

50

Water droplet volume, pL

40

30

20

10

0
0

1

2

3

4

Square root of time, ms 0.5

Fig. 7 Changes in volume of water micro-droplets on
sample PM with square root of time

16

50

2 ms
4 ms
6 ms

Water droplet volume, pL

0 ms

40
30
20
10
0
0

1

2

3

4

Square root of time, ms 0.5

Fig. 8 Changes in projected spherical cap of water micro-droplet on sample
HG recorded every 2 ms (left) and changes in volume of droplets withsquare root of time (right)

17

10

No AKD addition

Water
dropletVolume,pLvolume, pL

WaterdropletVolume,pL volume, pL

10
9
8
7
6
5
4
3
2
1
0

8
7
6
5
4
3
2
1
0

0

1

2

3

Square root of time, ms

4

0

5

0.5

1

2

3

4

5

Square root of time, ms 0.5

1010
AKD addition 0.10 %

9

Water
dropletVolume,pLvolume, pL

WaterdropletVolume,pLvolume, pL

AKD addition 0.05 %

9

8
7
6
5
4

8
7
6
5
4

2

3
2

1

1

0

0

3

0

1

2

3

4

AKD addition 0.20 %

9

0

5

1

2

3

4

Square root of time, ms 0.5

Square root of time, ms 0.5

Fig. 9 Volume changes with square root of time in water micro-droplets above surface plane oflaboratory sheets prepared by adding different amounts of AKD sizing to dry pulp mass

18

5

18
AKD 0.20%
AKD 0.15%
AKD 0.10%
No AKD addition

Water droplet volume, pL

16
14
12
10
8
6
4
2
0
0

5

10
15
20
0.5
Square root of time, ms

25

Fig. 10 Volume changes with square root of time in water microdroplets after landing on laboratory sheets prepared with AKD size H.
Error bars indicate 95% confidence intervals.

19

18

Sized, Laplace P considered
Sized, Laplace P neglected
Unsized, Laplace P considered
Unsized, Laplace P neglected

Water droplet volume, pL

16
14
12
10
8
6
4
2
0
0

5

10

15

20

25

Square root of time, ms 0.5

Fig. 11 Predicted volume changes of water micro-droplets on laboratory sheets. For sized
sheets, a = 21.3 μm, r = 21.6 μm, θ = 80.4°, and φ = 0.547 are assumed. For unsized sheets, a= 22 μm, r = 27.5 μm, θ = 53.1°, and φ = 0.557 are assumed.

20

50

(a)
1st 2nd
0 ms
2 ms
4 ms
6 ms

Volume,pL
Water droplet
volume,pL

1st water drop
2nd, away from 1st by half

40

3rd, same with 1st
4th, away from 2nd by half

30

(b)

20
10
0
0

124 ms1

2

3

4

Square root of time, ms 0.5

128 ms
130 ms200 ms
202 ms
204 ms
206 msRadius of circular conta carea, μm

126 ms

50

(c)
40
30
20
10
0
0

3rd

4th

Contact angle, degree

216 ms

3

4
0.5

60

210 ms

214 ms2

Square root of time, ms

208 ms212 ms

1

(d)

50
40
30
20
10
0
0

1

2

3

Square root of time, ms

4
0.5

Fig. 12 (a) First water droplet in initial frames, second droplet away from the firstby half the drop size, third droplet on the same location as the first droplet, andfourth droplet away from the second by half the drop size, with graphs of (b)volume, (c) radius of circular contact area, and (d) contact angle

21

References

22

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ISO 535:1991 Paper and board — Determination of water absorptiveness — Cobb method

5)

TAPPI TEST METHODS T 530 om-02 Size test for paper by ink resistance (Hercules-type
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Kuga S, Kataoka H, Enomae T, Onabe F, Yagi N, Fukami O (1994) Development andapplication of dynamic scanning absorptometer—Rapid and improved measurement ofBristow’s method. Japan TAPPI J 48:730-734 [in Japanese]

7)

TAPPI TEST METHODS T 835 om-03 Water absorption of corrugating medium: water drop
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Asakura K, Iwamoto M, Isogai A (2005) Effects of fatty acid components present in AKD
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Yip KL, Lubinsky AR, Perchak DR, Ng KC (2002) Measurement and modeling of drop
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2319) Enomae T, Onabe F, Usuda M (1990) Surface properties and pore structure of coated paper
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