International Journal of Multiphase Flow 38 (2012) 17–26

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International Journal of Multiphase Flow

journal homepage: www.elsevier .com/ locate / i jmulflow

Drop-on-demand drop formation of colloidal suspensions

Xi Wang a, Wallace W. Carr b,⇑, David G. Bucknall b, Jeffrey F. Morris c

a FUJIFILM Dimatix, Inc., Lebanon, NH 03766, USAb School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USAc Department of Chemical Engineering & Levich Institute, The City College of New York, New York, NY 10031, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 14 September 2010Received in revised form 9 September 2011Accepted 11 September 2011Available online 16 September 2011

Keywords:Inkjet printingDrop-on-demand drop formationColloidal suspension

0301-9322/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijmultiphaseflow.2011.09.001

⇑ Corresponding author. Tel.: +1 404 894 2538; faxE-mail address: chuck.carr@mse.gatech.edu (W.W

The drop formation dynamics in the drop-on-demand (DOD) inkjet process is studied for model inksincluding a Newtonian liquid and colloidal dispersions. The ink shear viscosity is a parameter oftenadjusted in tuning the DOD drop formation process. Apparent shear viscosity measured at low shear ratesis currently used to characterize inkjet inks throughout both the inkjet industry and academia. However,during the ejection process in inkjet printing, very high shear rates (above 1 � 105 s�1) are involved. Inthis paper, the drop formation characteristics at 10 kHz drop formation rate in a DOD mode of a simpleNewtonian liquid are compared with those of a colloidal suspension system which has the same low-shear-rate viscosity as the simple Newtonian liquid, but significantly different high-shear-rate viscosity.Under conditions of good jetting, the drop formation dynamics of the colloidal suspension is similar tothat of the simple Newtonian liquid of similar low-shear viscosity, with only slight systematic differencesobserved. Good jetting is, however, difficult to obtain in the colloidal particle inks, with non-straight tra-jectories and non-axisymmetric ligaments commonly observed. These observations suggest that evapo-ration, nonuniform wetting, and particle-related changes in properties play a role when poor jettingbehavior is observed for colloidal inks.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Drop-on-demand (DOD) inkjet printing involves managing theejection of droplets, less than 100 lm in diameter, onto a targetedlocation. Where the process is successful, inkjet printing may beutilized in a wide range of applications (Beecher et al., 2007;Gamerith et al., 2007; Liu et al., 2007; Ng et al., 2007; Reis et al.,2005; Ringeisen et al., 2006; Roy, 2007; Sumerel et al., 2006; Wanget al., 2004; Zaugg and Wagner, 2003).

DOD drop formation involves a number of physical processesincluding liquid ejection, capillary breakup, thread retraction, andsatellite formation; these processes have been studied by a numberof groups (e.g. Burton et al., 2004; Dong et al., 2006a; Eggers, 1997;Kowalewski, 1996; Notz et al., 2001). Several investigations of dropformation are discussed below; however, it should be pointed outthat the mentioned relationships are only valid for specific cases,e.g. certain combinations of printheads and inks, and that theseare not general design rules. Dong et al. (2006a, 2006b) used highspeed flash photography imaging to study DOD drop formation ofpure Newtonian fluids in detail. They found that DOD drop forma-tion of pure fluids is highly reproducible with a drop-to-drop posi-tional variation of 1 lm. Their work indicates that primary drop

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: +1 404 894 8780.. Carr).

size scales with the size of the inkjet nozzle and increases slightlywith increasing surface tension and/or decreasing viscosity. It wasalso shown that when the signal amplitude of the inkjet nozzle pie-zoelectric transducer is increased, the variation of primary dropsize is insignificant; however, both the number and sizes of satel-lite drops change significantly and the total volume of the satellitesincreases. The waveform of the actuating signal can also greatlyaffect DOD drop formation dynamics. Chen and Basaran (2002)showed that by manipulating the signal waveform driving the pie-zoelectric element, it is possible to reduce the ejected drop radiuswithout reducing nozzle radius. As a result, a reduction in theliquid volume greater than a factor of 10 was achieved. This issignificant in practice, considering the difficulties of precisely man-ufacturing smaller nozzles for obtaining reduced size drops.

Compared to the study of DOD drop formation of simple liquids,DOD drop formation of particle-laden suspensions has not receivedmuch attention to date. de Jong et al. (2006a, 2006b) found thatsmall particles may lead to a distorted droplet formation, as a filmformed by accumulated particles on the nozzle plate leads to airentrapment and nozzle failure in the printheads. Furbank andMorris (2004, 2007) investigated millimeter-size drop formationdynamics from particle-laden suspensions. The particles utilizedin their study were on the order of 100 lm and the orifice fromwhich the drops were formed was on the order of 1 mm. Theyfound that the particles in the necking thread slowed down the

18 X. Wang et al. / International Journal of Multiphase Flow 38 (2012) 17–26

thinning process and the number of particles involved in the neck-ing process determines either a stabilizing or a destabilizing effecton the thread compared to the behavior of a Newtonian fluid.While certain aspects of the problem may be captured by studyof these larger-scale drops, in the DOD drop formation process,the nozzle size and particle size are typically smaller than100 lm and 1 lm, respectively. The practical application of DODis therefore in a regime where colloidal forces and Brownian mo-tion are present and likely to be of some are importance. Experi-mental investigation of the effect of individual colloidal particlesor a group of colloidal particles on the evolution of an ejected li-quid thread is difficult, particularly considering the short durationof DOD drop formation process (�O (100 ls)). Hence, this workconsiders the bulk properties of the colloidal dispersion in analyz-ing the effect of colloidal scale pigments on drop formationdynamics.

With the addition of colloidal particles to a Newtonian liquid,the colloidal suspension normally will have higher apparent low-shear rate viscosity and it may also exhibit various non-Newtonianbehaviors, such as dependence of viscosity on shear rate and/orshearing time, viscoelasticity, and varying extensional viscosity.To study the effect of adding colloidal particles on the DOD drop for-mation process, it is important to separate effects of the non-New-tonian behavior from that of increasing the apparent low-shear-rate viscosity since two pure Newtonian fluids with different vis-cosities may show significant differences in the DOD drop forma-tion process (Dong et al., 2006a). As an example, a colloidalsuspension with low-shear viscosity of 5 cP can be prepared by dis-persing colloidal particles in a 1-cP Newtonian liquid. When this inkis ejected by an inkjet nozzle, it is reasonable to expect that the DODdrop formation process for the colloidal suspension will differ fromthat of the 1-cP liquid, but should it be expected to be similar to thatof a 5-cP Newtonian liquid? Considering that when inkjet ink isejected through a nozzle, it suffers a shearing field with shear rateshigher than 1 � 105 s�1, it is also important to address what is therole of the extremely high shear rate properties. In this paper, workconducted to answer these questions is presented. Colloidal sus-pensions were prepared by dispersing colloidal particles in a 1-cPNewtonian liquid. Then, the shear viscosities of the colloidal sus-pensions were measured for shear rates from 10 to 2 � 105 s�1,and the drop formation characteristics of the colloidal suspensionsystems were compared with those of simple Newtonian liquidmixtures having the same low-shear-rate viscosities. In the follow-ing section we describe the experimental techniques, and in Section3, we present results showing that there is a great deal of similarityin the drop-on-demand process for colloidal dispersion inks andNewtonian liquids with similar viscosity (low-shear value for thedispersion), but obtaining good jetting in the colloidal dispersioncase is much more difficult than in a simple liquid.

2. Experimental

2.1. Sample preparation and fluid properties

Three fluids, termed here as ink samples (see Table 1), havingalmost identical low-shear-rate viscosities, were used in the tests.

Table 1Inkjet ink samples used for studying DOD drop formation of particle suspension.

Sample Pigment, (vol.%) Base fluid

Glycerin (vol.%) DI water (vol.%) V

#1 0 48.4 51.6 6#2 5.7 35.5 58.8 3#3 15.0 0 85.0 1

Sample #1 was a Newtonian liquid mixture of water and glycerin.It contained no pigment and was used as a reference. Ink samples#2 and #3 were prepared by adding inkjet preparation CAB-O-JET�

200 (Cabot Corp.) to mixtures of water and glycerin. This ink prep-aration contained about 20% w/w pigment (10.3 vol.%, with pig-ment density of 1.95 g/ml), 0.2% w/w anti-foaming agent, about79.8% w/w water and a concentration of sodium of 4952 ppm/sol-ids. The surface of the pigment particles has covalently grafted –SO3Na� groups which render the particles stable in water withoutsurfactants, dispersion aids or polymers. The pH and surface ten-sion of the inkjet ink preparation were 7.53 and 70.4 mN/m,respectively. The mean particle size is about 130 nm.

The three samples have similar values of low-shear-rate viscos-ity, surface tension and density; however, the volume fraction ofpigment and high-shear-rate shear viscosity vary significantly.The static surface tension was measured using a KRUSS BubblePressure Tensiometer BP2 at temperature of 22 �C. The viscosity re-quired two methods to obtain the full variation of shear rate up tolevels encountered in an inkjet nozzle. The low-shear-rate viscositywas measured using a Brookfield LVDVI + Couette viscometer atshear rate of 52.3 s�1 and temperature of 22 �C. A capillary viscom-eter (Wang et al., 2010) was used to measure, at the same temper-ature, the shear viscosity of the samples at shear rates up to2 � 105 s�1. In Fig. 1, shear viscosity is plotted against shear rate.The shear viscosities of samples #2 and #3, containing 5.7% and15% by volume pigment, respectively, drop from 6.4 to 5.7 cP andfrom 6.3 to 3.5 cP, respectively, as shear rate was increased from10 to 2 � 105 s�1.

Since no polymeric dispersant or surfactant was present in thethree samples, dynamic surface tension, measured using a KRUSSBubble Pressure Tensiometer BP2 at bubble frequencies up to10 Hz, was found to be the same as the static surface tension. Sam-ple #1 contains no pigment, and it is reasonable to expect that thedynamic surface tension remains constant even under very highsurface deformation. For samples #2 and #3 pigment particlesmay adsorb to the air-suspension interface; if so, it is likely the dy-namic interfacial tension would change at high rate as the processof bringing particles to or from the interface would be slower thanthe stretching rate (values of this stretching rate based on our dataare detailed in Section 3). No commercially available instrument iscapable of measuring dynamic surface tension at the surface dila-tational rate (higher than 10,000 s�1) encountered in the DOD dropformation process.

2.2. Experimental protocol and image analysis

A push-mode piezoelectric printhead (Trident-ITW, Inc.) wasused in this study. Detailed information related to the printheadand the double-peak waveform used can be found in Dong et al.(2006a). The high-speed flash photography imaging system origi-nally developed by Dong et al. (2006b) was used for obtainingthe drop formation images, but a much higher rate of drop forma-tion was employed. The jetting frequency in Dong’s study was20 Hz, but for pigmented inks at frequency of 20 Hz, clogging ofthe nozzle and unstable jetting was observed. Jetting behavior forthe ink sample with high pigment loading was significantly

Shear viscosity at shearrate of 52.3 s�1, (cP)

Surface tension(mN/m)

Density(g/ml)

iscosity (cP)

.4 6.4 67.8 1.14

.7 6.4 69.5 1.19

.0 6.3 71.0 1.24

2

3

4

5

6

7

10 100 1000 10000 100000 1000000

Shear rate, 1/s

Shea

r vis

cosi

ty, c

P

Sample #1: 0 vol%Sample #2: 5.7 vol%Sample #3: 15.0 vol%

Measured by Couette viscometer

Measured by capillary viscometer

Fig. 1. Shear viscosity of ink samples described in Table 1 as a function of shear rateat temperature of 22 �C. Low-shear data is from a Couette viscometer and that athigh rate from a capillary viscometer described in Wang et al. (2010) (permissiongranted by American Institute of Physics).

Fig. 2. Images of non-ideal jetting conditions frequently encountered in studyingDOD drop formation of highly pigmented inkjet inks used in this study.

X5(t)

X2(t)

X4(t) X3(t)

X1(t) Tail of ejected liquid, Point 2

Leading point of satellite, Point 4

End of primary drop, Point 3

Leading point, Point 1

Tip of liquid due to reflection of pressure wave, Point 5

Nozzle exit

Fig. 3. Five representative points used for quantitatively discussing DOD dropformation dynamics.

X. Wang et al. / International Journal of Multiphase Flow 38 (2012) 17–26 19

improved by increasing the jetting frequency, and the imaging sys-tem was modified so that a jetting frequency of 10,000 Hz (10 kHz)could be used for the experiments reported here.

It is important to note that good jetting behavior is more diffi-cult to obtain for inks containing colloidal particles than simpleNewtonian liquids. Continuous jetting over a period of approxi-mately 30 min is required to obtain a full set of data using ourimaging system. Good jettability was achieved by using a jettingfrequency of 10 kHz, and the ‘‘good jetting’’ data were used to com-pare the DOD drop formation process of the colloidal suspensionswith Newtonian liquids. Although good jettability was obtained forsufficiently long periods of time to study the DOD drop formationprocess for the pigmented inks, there were periods over which thejettability of the pigmented inks was poor. When poor jettabilitywas observed, the inkjet nozzle often jetted a ligament with non-straight flying trajectory and/or highly non-axisymmetric ligamentformation, as shown in Fig. 2. Characteristics of the poor jettingperformance are discussed in more detail in the Section 3.

To allow the most direct comparison, the same nozzle was usedfor testing all three ink samples. The test temperature was21 ± 1 �C, very close to the 22 �C at which properties of viscosityand surface tension were measured. The data were obtained at a

jetting condition where the inkjet nozzle continued firing for a per-iod of more than 5 h at a frequency of 10 kHz with consistent jet-ting behavior, exhibiting good reproducibility, straightness oftrajectory and axisymmetry of the jetted liquid ligament. The dataused for discussion were collected through a trial-and-error ap-proach until optimum jetting conditions were reached.

Four signal amplitudes (24.7, 27.8, 30.9, and 36.5 V) were usedto drive the piezoelectric actuator for all samples. The sequence ofadjusting signal amplitude was as follows: 36.5 ? 30.9 ?27.8 ? 24.7 ? 36.5 V. The last step was used to compare withthe first in order to ensure jetting consistency during the test.Experimental procedures were carried out to ensure the liquid jet-ted from the nozzle had the same material composition as that inthe liquid in the ink reservoir.

During experiments where data were collected, the nozzle wasfired continuously, and thus the so-called ‘‘first drop problem’’(Dong et al., 2006a) did not appear. The first drop problem is acommon issue in inkjet printing, particularly for volatile inks suchas aqueous and solvent inks. While idle, one or more of the inkcomponents evaporate from the inkjet nozzle, affecting ink proper-ties. When the inkjet nozzle is triggered under such a pre-condi-tion, the first few drops ejected may have lower drop velocity. Asimilar problem may also occur at a very low jetting frequencywhere the evaporation of one or more than one of the ink compo-nents is faster than the replenishing process from the jettingprocess.

The method of studying the dynamics of DOD drop formationused here is now described. For each drop, time was measuredstarting from the moment when the liquid ligament emerged fromthe nozzle. More than 20 images, all of which were highly repro-ducible, were taken at each time after ejection, and images col-lected in increments of 1 ms. At an exposure time of 1 ls, thespatial variation was less than 2.0 lm. A typical image of anejected liquid thread is shown in Fig. 3, showing dimensions,X1(t) through X5(t), representing the distances from the character-istic positions to the nozzle exit. These positions were tracked as afunction of time (t) in order to quantify the DOD drop formationdynamics. The meaning of each of these points X1–X5, which formcurves when plotted as functions of time as shown in Fig. 5, is asfollows: X1 is the leading edge of the entire material ejected duringone actuation event; X2 is the position of the trailing edge when adiscrete volume separates from the nozzle due and thus first

20 X. Wang et al. / International Journal of Multiphase Flow 38 (2012) 17–26

appears at the time of thread pinchoff at the nozzle (time labeledtb1); X3 is the position of the trailing edge of the primary drop whenan end-pinch event occurs to form a primary and satellite drop; X4

appears at the same time as X3 and is the position of the leadingedge of the satellite drop (with trailing edge given by point X2);and finally X5 is the tip of the liquid protruding from the nozzle ori-fice following the ejection of the bolus which travels away.

Analysis of the curves obtained by plotting these five pointsprovides a fairly complete picture of the drop formation dynamics.

Fig. 4. Sequence of images of DOD drop formation for sample #3 in Table 1 usingthe double-peak waveform (Dong et al., 2006a) with signal amplitude = 30.9 V andjetting frequency = 10 kHz. Interframe time = 3 ls and image size = 87 lm �418 lm.

0 20 40 60900

800

700

600

500

400

300

200

100

0

Dis

tanc

e fro

m n

ozzl

e, µ

m

Tim

Ejection speed

Breakup length of thread from

nozzle exit

Time of thread pinch-off from

nozzle exit

Time of end-pinch

Fig. 5. Curves of DOD drop formation for sample #3 in Table 1 corresponding to the imagdrop ejection, retreating of thread tail, satellite drop, and primary drop.

3. Results and discussion

3.1. General description of DOD drop formation

A sequence of images illustrating the typical DOD drop forma-tion process for a pigmented ink with both primary and satellitedrop formation is presented in Fig. 4. DOD drop formation typicallyinvolves: (a) ejection and stretching of liquid thread (images 1–4),(b) necking and pinch-off of liquid thread from the nozzle (images5–10), (c) recoil of free liquid thread (images 11–13), (d) breakupof the free liquid thread (images 14–16), and (e) formation of pri-mary drop and satellite(s) (images 17–22).

In Fig. 5, a typical time evolution of ejected liquid ligament isshown for the five characteristic points, X1 through X5 describedat the end of Section 2. Fig. 5 can be used to calculate parametersrelated to the drop formation; we compute the speed of the repre-sentative points at various positions, speeds of the primary dropand satellites, pinch-off length and time for the liquid thread fromthe nozzle exit, time of breakup of liquid thread into satellites andprimary drop, and sizes of primary drop and satellite (see Donget al., 2006a for further details).

3.2. Ejection and stretching of liquid thread

In Fig. 6, sequential images of the ejection and stretching of thethree inks at two signal amplitudes of V = 24.7 and 30.9 V areshown. Although pigment loading varies from 0 vol.% to15.0 vol.%, there is no significant difference in this stage for thethree inks. The first breakup time, tb1 (when the thread detachesfrom the nozzle) of these three samples (static surface tension of69 ± 2 mN/m and low-shear-rate shear viscosity of 6.3 ± 0.1 cP) atfour different signal amplitudes is 30 ± 2 ls. In Dong et al.(2006a), the first breakup time of the glycerin/water mixture (sur-face tension of 68 mN/m and viscosity of 5.0 cP) was 28 ls at dif-ferent signal amplitudes. The slightly longer first breakup time inthis study is attributed to the higher shear viscosity of the inkjetink samples and the resulting stronger resistance to the fluidmotion.

In Fig. 7, a detailed comparison for the three inks at t = 4 ls andsignal amplitude of 30.9 V, is made by plotting the position of theleading edge in more detail than elsewhere in this work: here the

Satellite drop speed

80 100 120 140 160

e, µs

Point 1 Point 2 Point 3 Point 4 Point 5

Retreating speed of thread tail

Satellite drop size

Primary drop size

Primary drop speed

es shown in Fig. 4. The slopes of the curves are analyzed to determine the speeds for

Fig. 6. Sequential images of ejection and stretching of three inkjet ink samples (seeTable 1) using the double-peak waveform (Dong et al., 2006a) with signalamplitude = 24.7 and 30.9 V and frequency = 10 kHz. Image size = 87 lm � 418 lm.

0 10 20 30 40 500

10

20

30

40

50 0 vol% 5.7 vol% 15.0 vol%

Posi

tion

of le

adin

g ed

ge

from

noz

zle

exit,

µm

Radial position along the nozzle exit, µm

Fig. 7. Position of leading edge of samples #1, #2 and #3 in Table 1 at time = 4 ls,signal amplitude = 30.9 V and frequency = 10 kHz. X-axis is the radial position alongthe nozzle exit, and Y-axis is the distance of the leading edge from the nozzle exit.

0 5 10 15 20 25 30 350

40

80

120

160

200

240

Time, µs

0 vol% @24.7 V 5.7 vol% @24.7 V 15.0 vol% @24.7 V 0 vol% @30.9 V 5.7 vol% @30.9 V 15.0 vol% @30.9 V

X1, µ

m

Fig. 8. Temporal variation of point 1 in Fig. 3 before pinch-off from the nozzle exitfor three samples tested using the double-peak waveform (Dong et al., 2006a) withsignal amplitudes = 24.7 and 30.9 V and frequency = 10 kHz. Highest time shownfor each plot corresponds to the time of pinch-off from nozzle exit, tb1.

Table 2Ejection speed, speed of point 1 at pinch-off from nozzle exit, and traveling time of inkthrough the nozzle based on ejection speed.

Pigmentloading(vol.%)

Voltage,(V)

Ejectionspeed,me (m/s)

Speed of point1 at pinch-offfrom nozzleexit, mb1 (m/s)

Traveling timeof ink through thenozzle, based onejection speed, te (ls)

0 24.7 8.0 2.5 9.427.8 9.1 4.4 8.230.9 10.4 5.2 7.236.5 12.9 8.8 5.8

5.7 24.7 8.1 2.1 9.327.8 9.2 3.6 8.230.9 10.3 5.1 7.336.5 12.4 7.8 6.0

15.0 24.7 5.8 2.1 12.927.8 7.8 3.9 9.630.9 8.1 5.7 9.336.5 10.0 6.7 7.5

X. Wang et al. / International Journal of Multiphase Flow 38 (2012) 17–26 21

position is measured from the nozzle exit versus the radial positionmeasured from the left wall of the nozzle. A slight difference isseen as flatness of the center region of the profiles increases withpigment content. The position of the leading edge at this short timeafter exiting the orifice mirrors the exit velocity. A flattening of thevelocity profile is expected because the pigmented ink exhibits ashear-thinning viscosity; for a shear thinning fluid, the materialat the center of the orifice where the shear stress is smaller has ahigher effective viscosity than the wall material. It thus shears lessrapidly, i.e., the velocity profile is flatter near the center than itwould be in a simple Poiseuille flow (as seen for the Newtonianink sample #1). Note that the wall shear rate is on the order of

2 � 105 s�1 as discussed below (see Fig. 10), and for this shear ratethe highly pigmented sample has an effective viscosity of below4 cP, whereas the pure liquid sample has a viscosity of 6.3 cP.While the differences are small, Fig. 7 shows a higher wall shearrate for the highly pigmented sample, and the difference in shearrates is consistent with these differences in viscosity.

In Fig. 8, the temporal variations of X1, the leading edge of thematerial ejected by the actuator pulse, are shown for the threesamples at signal amplitudes of 24.7 and 30.9 V. Pinch-off occursat the last point shown in each of the plots. The liquid pinch-offlength, lb = X1(t = tb1), increases with the driving signal amplitude.The speed, dX1/dt, is larger for a higher driving voltage and de-creases as the primary drop moves away from the nozzle. The firstbreakup time, tb1, is slightly shorter for the ink sample with pig-ment loading of 15 vol.% than for ink samples with pigment load-ings of 0 and 5.7 vol.%.

Ejection speed, me = dX1/dt, was roughly constant for the firstfew micro-seconds during the ejection process, and is used to char-acterize the hydrodynamic motion of the ink. The time, te, taken forthe ejected liquid to pass through the L = 75-lm length inkjet noz-zle used in this study is approximately equal to L/ve. The speed ofthe leading edge at pinch-off from the nozzle exit is defined as mb1.These parameters are given in Table 2. When compared to ink sam-ples with pigment loadings of 0 and 5.7 vol.%, sample #3 with

0 10 20 30 40 50 60 70 800

15

30

45

60

75

90

105

24.7 V

27.8 V

30.9 V

36.5 V

Volu

me,

pL

Time, µs

(a)

0 10 20 30 40 50 60 70 800

3000

6000

9000

12000

15000

18000

24.7 V

27.8 V

30.9 V

36.5 V

Surfa

ce a

rea,

µm

2

Time, µs

(b)

Fig. 9. Volume (a) and surface area (b) of ejected liquid vs. time for sample #3(15.0 vol.%) in Table 1 with signal amplitudes = 24.7, 27.8, 30.9 and 36.5 V andfrequency = 10 kHz. Marker ‘‘+’’ indicates the time of liquid separation from thenozzle exit. The error bar stands for one standard deviation.

0 2 4 6 8 10 12 14 16104

105

24.7 V 27.8 V 30.9 V 36.5 V

Shea

r rat

e, s

-1

Time, µs

Fig. 10. Magnitude of shear rate vs. time using the data in Fig. 9a and Eq. (1) forsample 3 (15.0 vol.%) in Table 1 with signal amplitudes = 24.7, 27.8, 30.9, and 36.5 Vand frequency = 10 kHz.

22 X. Wang et al. / International Journal of Multiphase Flow 38 (2012) 17–26

pigment loading of 15 vol.% exhibited a lower ejection speed andconsequently a longer te; however, mb1 is similar for all three sam-ples. For the three inks, te ranged from 6 to 13 ls at various signalamplitudes. Clearly, the time over which shear stress is applied tothe ink in the nozzle is very short.

The volume and surface area of liquid ejected as a function oftime were determined for sample #3 at signal amplitudes of24.7, 27.8, 30.9 and 36.5 V and a jetting frequency of 10 kHz (seeFig. 9). Notice that the volume increases to a maximum valueand then decreases. This occurs because there is a negative pres-sure wave in the inkjet chamber and nozzle, which is generatedby the second small pulse (we used a double-pulse signal). The ef-fects from this negative pressure are to accelerate breakup, to re-duce the tail volume and thus satellite volume, and to activelycontrol the meniscus bounce for a more stable jet trajectory. Theresults indicate that the higher the signal amplitude, the higherthe volume, and correspondingly, a larger surface area of theejected liquid thread. Before the first breakup, the liquid volumefirst increases and then decreases since part of the liquid body issucked back into the nozzle until pinch-off at the nozzle exit oc-curs, after which the liquid drop volume remains constant.

The shear rate that the ink experiences during the ejection pro-cess was estimated for the inkjet nozzle used in our experiments,using the data in Fig. 9a. The scale of shear rate, �_r, is given by

�_r � VRnoz� Q=Anoz

Rnozð1Þ

where V is the averaged speed of liquid ligament jetted from thenozzle, Q is the volumetric flow rate calculated from the data of

Fig. 9 as the rate of change of the volume, while Anoz and Rnoz arethe cross-section area and the radius of the inkjet nozzle, respec-tively. In Fig. 10, the computed �_r vs. time during the ejection processis given. Increasing signal amplitude leads, as expected, to highershear rates. It is of some interest to note that although the shearrate is on the order of 1 � 105 s�1 for the first few micro-seconds,it drops quickly to 1 � 104 s�1 at about 15 ls.

The data in Fig. 9b are used to estimate the average rate of sur-face dilatational deformation, _kexp (Mourougou-Candoni et al.,1997), as follows,

_kexp �DA

Amax

1Dt

ð2Þ

where Amax is the maximum surface area the liquid ligamentreached during the ejection process and is determined using themaximum value in each plot shown in Fig. 9b, DA is the differencebetween the maximum surface area and the minimum surface areaAmin, and Dt is the time taken for the surface area to reach to themaximum value. The value of Amin is defined simply as the cross-section area of the inkjet nozzle. Based on this definition, the valuesof _kexp with signal amplitudes of 24.7, 27.8, 30.9 and 36.5 V areapproximately 25,000, 28,300, 28,500 and 29,700 s�1, respectively.This indicates that the time of surface aging is no more than �O(100 ls). Thus if surfactant is used for adjusting the surface tensionof the inkjet ink, with such a short period of surface aging, dynamicsurface tension (DST) may become an important parameter. How-ever, as noted, no commercial instrument is available for measuringDST at surface aging time of less than 100 ls. After the surface areaof the ejected liquid thread reaches its maximum value at about30 ls, surface area changes slowly with time as can be seen inFig. 9b.

The volume and surface area of liquid ejected as a function oftime are shown in Fig. 11 for all three ink samples. The plots forthe three samples are very similar; however, the total volumeejected for the inkjet ink with pigment loading of 15.0 vol.% isslightly higher.

3.3. Breakup and contraction of liquid thread

In DOD drop formation, two kinds of liquid thread breakup havebeen observed (Dong et al., 2006a). One is end-pinching at the rearof the primary drop, and the other is capillary breakup due towave-like instability. Under the signal amplitudes used in thisstudy, no capillary breakup of ejected liquid thread was observed.

Fig. 12 shows enlarged images focusing on the location of thesecondary breakup for the three ink samples. Each image is

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

0

15

30

45

60

75

90

0 vol%

5.7 vol%

15.0 vol%

Volu

me,

pL

Time, µs

(a)

0

3000

6000

9000

12000

15000

0 vol%

5.7 vol%

15.0 vol%

Surfa

ce a

rea,

µm

2

Time, µs

(b)

Fig. 11. Volume (a) and surface area (b) of ejected liquid vs. time for all threesamples in Table 1 with signal amplitude = 30.9 V and frequency = 10 kHz. Marker‘‘+’’ indicates the time of liquid separation from the nozzle exit. The error bar standsfor one standard deviation.

(a) Sample #1 (pigment

loading of 0 vol%)

(b) Sample #2 (pigment

loading of 5.7 vol%)

(c) Sample #3 (pigment

loading of 15.0 vol%)

Signal amplitude = 30.9 V

Signal amplitude = 36.5 V

Fig. 12. Cropped last image before the instant of liquid thread break up into aprimary drop (having a diameter of approximately 45 lm) and a secondary threadfor the three ink samples. Signal amplitudes of 30.9 and 36.5 V, and frequency of10 kHz.

40 60 80 100 120 140 160 1800

20

40

60

80

100

120

140

160

180

Seco

ndar

y liq

uid

thre

ad le

ngth

, µm

Time, µs

0 vol% 5.7 vol% 15.0 vol%

Fig. 13. Length of the contracting/recoiling secondary liquid thread vs. time forthree ink samples. Signal amplitude = 30.9 V and frequency = 10 kHz.

X. Wang et al. / International Journal of Multiphase Flow 38 (2012) 17–26 23

cropped and magnified from an image similar to No. 16 in Fig. 4.After the secondary breakup, a primary drop is formed and a sec-ondary liquid thread contracts. In Fig. 12, the shapes at the breakuppoint for all three samples at different voltages are similar. The li-quid thread formed after the secondary breakup has a cone-shapedleading point where the high local surface curvature and resultinghigh local capillary pressure leads to fast liquid thread contraction/recoiling toward the center of the thread (for example, images17–22 in Fig. 4). The lengths of the contracting/recoiling secondaryliquid thread as a function of time are shown in Fig. 13. For all sam-ples, the secondary liquid thread contracts and oscillates to form asingle satellite in a similar manner.

Using the assumption that the first breakup of the liquid thread(pinch-off from the nozzle exit) and the second breakup (or end-pinching) are both caused by the most unstable disturbance alongthe liquid thread, Dong et al. (2006a) showed in a simplified anal-ysis that the time at which the liquid thread pinches off can beapproximated by

tb ¼ Ctca

a�maxð3Þ

where C ¼ ln Rnozemax

� �and tca ¼ qR3

nozc

� �1=2and is referred to as the cap-

illary time. Here emax is the (typically unknown) initial amplitude ofthe disturbance corresponding to growth rate of the most unstabledisturbance, Rnoz is the radius of the inkjet nozzle, q is density and c

is surface tension. The first breakup (tb1) was calculated by subtract-ing the eject time, te, from the experimental breakup time becauselittle stretching occurs in the ejected liquid during the ejectionstage, since the ratio of the surface area to volume of ejected liquidis almost constant during the ejection stage (see Fig. 9a and b). Thefirst and second breakup times for the three ink samples are givenin Table 3. In this study, C1 and C2 are in the ranges of 0.2–0.3 and0.5–0.7, respectively, which are similar to the values obtained byDong et al. (2006a), but are slightly smaller. The lower value of C1

is attributed to the different mechanisms between the two break-ups. Since the first breakup (tb1) takes place when the liquid threadis ejected out from the nozzle and is being stretched, C1 is related tothe actuating waveform since the fluid motion inside the ejected li-quid thread starts during the ejection process and part of the liquidis sucked back towards the nozzle. Both tb1 and tb2 of the inkjet inkwith pigment loading of 15.0 vol.% are slightly shorter compared tothose of the other two samples.

Table 3Breakup times of three liquid threads and related parameters.

Pigmentloading (vol.%)

Voltage(V)

tb1 (ls) tb1 (ls) tcaa�max

b (ls) C1 C2

0 24.7 31 47 65.1 0.26 0.5127.8 29 49 0.23 0.5430.9 29 50 0.23 0.5536.5 30 54 0.25 0.61

5.7 24.7 32 48 65.2 0.28 0.5327.8 30 49 0.25 0.5530.9 30 51 0.25 0.5836.5 30 54 0.25 0.63

15.0 24.7 29 N/Aa 65.2 0.25 N/Aa

27.8 28 45 0.24 0.5330.9 28 44 0.24 0.5136.5 28 48 0.24 0.58

a No secondary breakup.b Calculated using shear viscosity measured at low shear rate.

24 X. Wang et al. / International Journal of Multiphase Flow 38 (2012) 17–26

3.4. Speeds and sizes of primary and satellite drops

The speed, size and kinetic energy of primary and satellite dropsof all three samples for four different signal amplitudes and a jet-ting frequency of 10 kHz are given in Table 4. The results indicatean interesting influence of the particle-induced rheology changes.As one would expect, because it is of substantially lower viscositythan the pure liquid, the 15% dispersion has higher kinetic energyat the same driving voltage: less energy is dissipated. The surpriseis that despite the lower shear viscosity at high shear rates of the5.7% dispersion, the kinetic energy of drops of this material are re-duced relative to the pure liquid. The decrease in kinetic energy forthe lower-solids dispersion is not readily explained but reproduc-ible, as seen from the data at different voltages. It may be due toinfluence of the particulate structure on extensional rheologywhich we have not measured.

In cases where signal amplitude is low (24.7 and 27.8 V for ourstudy), corresponding to a low primary drop speed, only one satel-lite or even no satellite is formed, and recombination of primarydrop and satellite occurs. However, in a typical industrial inkjetprinting process, primary drop speed needs to be sufficiently high(�8 m/s) to obtain satisfactory impaction accuracy of the DODdrops. Thus reducing signal amplitude to eliminate satellite dropsis probably not practical for many inkjet applications.

Table 4Size, speed, and kinetic energy of primary and satellite drops for three samples at signal a

Pigmentloading(vol.%)

Voltage(V)

Primary dropsize dp (lm)

Primary dropspeed vp (m/s)

Primary dropkinetic energy(J � 10�10)

Satellite dropsize ds (lm)

0 24.7a 44.3 ± 1.0 �2.6c �1.8 26.1 ± 1.027.8a 4.1 4.4 32.6 ± 1.030.9 5.4 7.6 36.5 ± 1.036.5 7.5 14.6 43.9 ± 1.0

5.7 24.7a 43.8 ± 1.0 �2.2c 1.3 25.7 ± 1.027.8a 3.7 3.6 31.3 ± 1.030.9 5.0 6.5 36.5 ± 1.036.5 7.1 13.2 43.9 ± 1.0

15.0 24.7a 45.7 ± 1.0 �2.6b �2.1 N/Ab

27.8a 3.5 3.8 29.1 ± 1.030.9 7.0 15.2 37.4 ± 1.036.5 8.1 20.3 41.3 ± 1.0

a Recombination of primary and satellite drop occurred.b No satellite formation.c Value is shown as �because a satellite merged with the primary drop just before se

3.5. Drop formation dynamics and high-shear-rate rheology

The three ink samples studied here differ in pigment loading,base fluid composition, and viscosity as shown by Table 1. TheDOD drop formation processes for the three inks were similar;however, there were differences. When DOD drop formationdynamics of sample 3 (pigment loading of 15 vol.%) are comparedwith those of the other two samples, the three noticeable differ-ences are: (1) the first breakup time, tb1, is slightly shorter forthe ink sample with pigment loading of 15 vol.%; (2) the secondbreakup time, tb2, of the inkjet ink with pigment loading of15.0 vol.% is slightly shorter; (3) the total volume ejected for theinkjet ink with pigment loading of 15.0 vol.% is slightly higher thanthat for the other two samples.

It is possible that the first and second differences are associatedwith dried pigment particles accumulating on the nozzle exit anddecreasing the nozzle diameter, leading to a thinner ejectedligament diameter and reduced tb1 and tb2. However, under thesame jetting conditions, slightly higher ejected liquid volumes wereobtained with Sample #3, which argues against this possibleexplanation.

Another explanation for all three differences is that sample 3exhibited a lower apparent shear viscosity compared to those ofthe other two samples at the nozzle shear rates; this is becausethe mixtures are matched in their low-shear rate viscosity, muchof which is contributed by a fragile structure for the high-solidsample #3. Such an argument is consistent with the high shear-rate shear viscosity data shown in Fig. 1. The shear rate experi-enced by the ink in the nozzle is about 2 � 105 s�1 (see Fig. 10).At a shear rate of 2 � 105 s�1, the shear viscosity of sample 3 de-creases from 6.3 to 3.5 cP. In the work of Dong et al. (2006a), sucha decrease in viscosity for Newtonian liquids led to much largerchanges in the DOD drop formation process than were observedhere, so the differences noted in the prior paragraph are likelydue to the effective viscosity.

The smallness of the differences between the samples studiedhere raises the question of the value of high shear-rate data in pre-dicting DOD drop formation dynamics. The answer to the questionmay be related to the manner in which the high shear-rate data areobtained. The viscometer used for obtaining the data is based onsteady state conditions. The capillary is long enough that the flowthrough the capillary is fully-developed. It is conjectured thatbreakdown of agglomerates subjected to high shear rates is themechanism of the shear thinning behavior shown in Fig. 1. A

mplitudes of 24.7, 27.8, 30.9, and 36.5 V and jetting frequency = 10 kHz.

Satellite dropspeed, vs (m/s)

Satellite dropkinetic energy(J � 10�10)

Total kineticenergy (J � 10�10)

Ratio of kineticenergy of each inkto that of the base fluid

�4.6 �1.1 2.9 1.04.5 2.1 6.5 1.05.0 3.6 11.2 1.06.1 9.4 24.0 1.0

�4.6 1.1 2.4 0.84.5 1.9 5.5 0.94.8 3.5 10.0 0.95.9 9.2 22.4 0.9

N/Ab N/Ab N/Ab N/Ab

4.4 1.5 5.3 0.85.1 4.4 19.6 1.86.5 9.7 30.0 1.3

quence of images ended so that the data for calculating speed were limited.

X. Wang et al. / International Journal of Multiphase Flow 38 (2012) 17–26 25

period of time (or total strain, the product of time and shear rate)under sufficiently high hydrodynamic stress is needed to breakdown the microstructure of the colloidal suspension. The lengthof the capillaries used in the capillary viscometer provides suffi-cient time for the microstructure in the colloid suspension to re-spond to the high shear-rate field and reach a steady statestructure. However, this may not be the case for inkjet ink ejectionthrough the nozzle. As shown in Table 2, the traveling time, te, ofink through the nozzle at the maximum speed, i.e., ejection speed,me, is estimated to range from 6 to 13 ls, depending on signalamplitude. During this period of time, the shear rate applied tothe inkjet ink being ejected from the nozzle is at its maximum va-lue (�2 � 105 s�1), yielding a strain of approximately 2. Comparedto the period of time (>1000 ls) for the inkjet ink sample to flowthough the capillary viscometer, te (6–13 ls) is extremely short.The strain in the viscometer is approximately 100 times larger,so that structural breakdown taking place under the capillary vis-cometer condition may not occur in the inkjet nozzle. In this case,the low shear-rate viscosity would retain relevance in setting thebehavior of the material leaving the nozzle, although the differ-ences seen in the samples suggests that the thinning of the viscos-ity due to structural breakdown does play a role. Further work isneeded to determine whether some recovery of the structure fol-lowing exit from the nozzle may play a role as well.

3.6. Non-ideal jetting behavior of pigmented inks

It would be misleading to suggest that the jetting behavior of acolloidal ink is essentially the same as a Newtonian liquid of sim-ilar low-shear viscosity. There is a great deal of similarity underideal jetting conditions, but more often than not, the colloidal inksexhibit non-ideal jetting. In Sections 3.1–3.5, the DOD drop forma-tion process for good jettability, i.e. ideal jetting conditions, is dis-cussed. Only the data taken when the jetting problems occurredwere included in the discussion of the DOD process discussed inSections 3.1–3.5. Although good jettability was obtained forsufficiently long periods of time to study the DOD drop formationprocess for the pigmented inks, there were periods over whichthe jettability of the pigmented inks was bad. When poor jettingoccurred, the temporal duration of the continuous firing processof an individual inkjet nozzle was usually very short, ranging fromseveral seconds to a few minutes. Ideal jetting behavior wasrare and in most cases the jetting behavior was non-ideal in termsof: (1) non-straight flying trajectory, (2) non-axisymmetricligament formation, (3) insufficient period of duration of excellentjetting behavior, and (4) long duration of inconsistent jettingbehavior.

The non-ideal jetting behavior is attributed to the accumulatedparticles and non-ideal wetting condition on the nozzle plate asdiscussed by de Jong et al. (2006b). The formulation of the ink sam-ple was simple with no chemical added to control the wettingbehavior on the nozzle plate. No surfactant or humectant wasadded to control surface tension and evaporation rate, respectively.Moreover, the pigment volume fraction was high and the pigmentloading of sample #3 was significantly higher than industrial stan-dard pigment loading. Evaporation at the nozzle can lead to full orpartial nozzle clogging; in addition, asymmetric wetting aroundthe nozzle may result. If the nozzle is clogged fully, clearly no jet-ting is observable. If the nozzle is clogged partially or the asym-metric wetting boundary condition around the nozzle occurs,then the ejected liquid ligament may resemble the images shownin Fig. 2. Considerable effort was expended in repeatedly usingone particular nozzle until good jettability so that all three samplescould be studied under the same jetting conditions.

4. Conclusions

This work has addressed the drop-on-demand process for mod-el inks, including both colloidal dispersions of pigment solids andNewtonian liquids. These model ink samples were designed tohave equivalent low-shear rate viscosity and surface tension. Apractical conclusion is that obtaining good jetting behavior fromthe colloidal pigmented inks is not straightforward, as we oftenfound poor jetting behavior. However, when jetting is regular,the characteristics are very similar to the behavior of a simple li-quid of similar viscosity. The low shear-rate viscosity was foundto be a reliable parameter to describe the behavior, and despite sig-nificant differences in the steady effective viscosity at shear ratesseen in the nozzle, the sample inks studied behaved similarly.

It is important to note that the frequent occurrence of poor jet-ting behavior for the pigmented inks indicates that processes sep-arate from the jetting hydrodynamics, lead to difficulties andirregularities in the DOD process. Nonuniform nozzle plate wettingand evaporation coupled to particle-fraction dependence of prop-erties are the most likely candidates. The influence of evaporationupon material properties can be especially important for colloidalparticles which undergo aggregation, as a small loss of solventcan lead to gelation.

Although the properties of the three samples discussed in this pa-per are different in terms of pigment loading, base fluid compositionand viscosity, the DOD drop formation process for the three inkswere similar as noted. However, when DOD drop formation dynam-ics of sample 3 (pigment loading of 15 vol.%) are compared withthose of the other two samples, some differences are observed.The three most important differences are: (1) the first breakup time,tb1, is slightly shorter; (2) the second breakup time, tb1, is slightlyshorter; (3) the total volume ejected is slightly higher. It appears thatshear viscosity measured at high shear rates in a capillary viscome-ter is not the most relevant measure of the viscosity for the DOD dropformation process for the colloidal suspensions studied. This is be-lieved to be due to the insufficient shearing time (or total strain)for changing and stabilizing the microstructure of the suspensionduring DOD drop formation process. The low-shear rate viscositywith consideration for deviations caused by initial shear thinningis more representative of the material properties associated withthe sub-100 lm nozzle orifice. The work presented here serves asa guide to the key issues in colloidal ink DOD: one must considerthe geometry of the device used and the stress and total strainnecessary to break down any structure in order to properly accountfor rheology on the process of drop formation in the DOD mode.

Acknowledgments

The authors wish to acknowledge the financial sponsorshipfrom National Textile Center. The authors also wish to acknowl-edge the suggestions from Dr. Hongming Dong of School of Mate-rials Science and Engineering, Georgia Institute of Technology.

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