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Study of Pinch-Off Locations during Drop-on-Demand Inkjet Printing of Viscoelastic Alginate Solutions Changxue Xu, Zhengyi Zhang, Jianzhong Fu, and Yong Huang Langmuir, Just Accepted Manuscript • Publication Date (Web): 30 Apr 2017 Downloaded from http://pubs.acs.org on May 6, 2017

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Study of Pinch-Off Locations during Drop-on-Demand Inkjet Printing of Viscoelastic Alginate Solutions

Changxue Xu1,2, Zhengyi Zhang3, Jianzhong Fu4, Yong Huang2* 1

Department of Industrial, Manufacturing, and Systems Engineering, Texas Tech University, Lubbock, TX 79409, USA

2

Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA 3

School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

4

Department of Mechanical Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, China

* Corresponding author, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA, Phone: 001-352-392-5520, Fax: 001- 352-392-7303, Email: [email protected]

Abstract The ligament pinch-off process of viscoelastic fluids during jetting is a key step for various biotechnology and drop-wise three-dimensional printing applications. Various pinch-off locations have been investigated as a function of material properties and operating conditions during the drop-on-demand (DOD) inkjet printing of viscoelastic alginate solutions. Four breakup types are identified based on the location of first pinch-off position: front pinching is mainly governed by a balance of inertial and capillary effects, exit pinching is affected by the 1 ACS Paragon Plus Environment

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external actuation-induced hydrodynamic instability and mainly governed by a balance of elastic and capillary effects, middle pinching usually occurs any place along a uniform thin ligament under dominant viscous and elastic effects, and hybrid pinching happens when the front pinching and exit pinching occurs simultaneously as a special case.

1. Introduction and Background Pinch-off during fluid dispensing refers to the process during which a fluid jet or ligament disintegrates into droplet(s). The ligament pinch-off process, especially of viscoelastic fluids,1 has received considerable attention recently because it is a key step for a variety of technological applications in biotechnology and drop-wise three-dimensional (3D) printing. There has been a great practical and scientific interest to understand the physics underlying ligament/filament pinch-off which is a complex process controlled by capillary, viscous, elastic, and inertial effects.2

The pinch-off process of viscoelastic polymer solutions has been extensively studied during dripping,3 continuous jetting,4-5 drop-on-demand (DOD) inkjet printing6 and liquid bridge breakup.6-9 The thinning process of viscoelastic polymer ligaments during the aforementioned processes usually includes three consecutive stages: inertio-capillary thinning, elasto-capillary thinning, and finite extensibility; their duration and dominance may vary due to material properties and operating conditions. During inertio-capillary thinning, the polymer chains start being stretched, and the elastic stress is still small. The capillary pressure is mainly balanced by inertial acceleration in the thinning ligament, resulting in a ligament diameter as a power-law function of jetting time.3 During elasto-capillary thinning, the polymer stretching-induced elastic stress shadows the inertial effect and competes with the capillary stress as the main stress 2 ACS Paragon Plus Environment

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component, resulting in an exponential ligament thinning function of jetting time.3, 8-10 During finite extensibility, the polymer chains are fully stretched. The fluid behaves like a very viscous anisotropic Newtonian fluid characterized by the steady extensional viscosity of the fluid, leading to a linear ligament diameter decay.10-12

Pinch-off location can be different along a liquid ligament, for example, end pinching at the both ends of a polystyrene-diethyl phthalate liquid bridge,6 pinching at the mid-filament position of a polystyrene-diethyl phthalate liquid bridge if the polystyrene concentration is high enough,13 front pinching (near the ligament head/forming droplet) and exit pinching (near the orifice) during inkjetting sodium alginate solutions,14 and even any place along a liquid polystyrene bridge.6

The pinch-off location may even switch depending on not only the fluid viscoelasticity6 but also the liquid bridge/ligament dimension,15 inertia/stretching velocity,15-16 electric field17-19 and surfactant,20 to name a few. In particular, Vadillo et al.6 studied the ligament pinch-off behavior of polystyrene solutions as a liquid bridge, and three different pinch-off behaviors were presented depending on the polymer concentration: at low polymer concentrations, pinch-off happened around both the two bridge ends; at intermediate polymer concentrations, the ligament thinned until the Rayleigh instability appeared, and the pinch-off locations were any place along the thin ligament; and at high polymer concentrations, a long lasting uniform ligament was observed without identifiable pinch-off locations. For liquid bridge studies, both the bridge dimension and the inertia/stretching velocity matter. Yildirim et al.15 computationally investigated the pinch-off of a shear-thinning liquid during liquid bridge and reported that the pinch-off location was sensitive to the initial bridge aspect ratio, switching from the vicinity of 3 ACS Paragon Plus Environment

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the bridge bottom to its moving top with the increase of initial bridge length. Zhang et al.16 computationally investigated the effect of disk stretching velocity on pinch-off of glycerol bridges: at a low stretching velocity, the thread broke first at the lower fixed end due to the larger capillary pressure caused by a larger curvature of the interface there; at a critical velocity, the thread broke at its two moving and fixed ends simultaneously; and at a high disk velocity, the thread broke first at the upper moving end. External energy fields such as the electric field control the pinch-off location too. Zhang et al.17 experimentally carried out a detailed study of the dynamics of droplet formation of sodium chloride solutions in the presence of an electric field during dripping: with the increase of electric field, the pinch-off locations switched from the lower receiving end to the nozzle exit end due to the switch of the highest curvature caused by the electric field. Such a pinch-off location switch was also computationally validated during dripping.18 Xu et al.19 further reported the pinch-off location switch along the jetting direction during the electric field-assisted DOD printing of water. The pinch-off location may be affected by surfactants. Ambravaneswaran et al.20 studied the effects of insoluble surfactants on pinch-off of stretching liquid bridges and reported that the critical stretching velocity for the pinch-off location switch depended on the Peclet number which represents the importance of convection of surfactant relative to its diffusion along the free surface. While various pinch-off locations and their switch have been investigated, the possible pinch-off locations during the inkjet printing of viscoelastic fluids have been largely ignored, which should be systematically examined for the better inkjet fabrication of monodisperse droplets.

The objective of this work is to study various pinch-off locations as a function of material properties and operating conditions during DOD inkjet printing of viscoelastic sodium alginate

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solutions. Four types of pinch-off have been observed and their associated mechanisms have been analyzed. The resulting knowledge should be applicable to any dilute (or semidilute) viscoelastic polymer solutions.

2. Experimental Design 2.1 Materials As a versatile biomaterial,21-22 alginate hydrogel has been used as scaffolds for tissue engineering, as delivery vehicles for drugs, and as model extracellular matrices for basic biological studies. Alginate, in particular, sodium alginate (NaAlg or simply as alginate herein), has been used as a constituent of bioink in bioprinting.22-25 For its broad bioprinting applications, sodium alginate solution has been chosen as a model system to study the pinch-off process during DOD inkjet printing in this study.

The sodium alginate solutions were prepared by dissolving sodium alginate (Sigma-Aldrich, St. Louis, MO) into deionized water to make the solutions with different concentrations of 0.10 – 2.00% (w/v). The molecular weight of the sodium alginate used in this study is in the range of 12 – 40 kDa. The density was measured by averaging the weight of 1 ml sodium alginate solution five times. The shear viscosity of sodium alginate solutions was based on the average of three measurements, which were acquired using a rotational rheometer (ARES, TA Instrument, New Castle, DE, 0.1 µN·m accuracy) in a Couette geometry (bob diameter of 25 mm and cup diameter of 27 mm). The surface tension was measured based on the pendant drop method using a drop shape analysis system (Attension Theta Lite, Biolin Scientific, Linthicum Heights, MD, 0.01 mN/m accuracy) at room temperature and determined based on five measurements. The


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longest relaxation time was determined based on the elasto-capillary thinning mechanism during dripping using a Photron camera (Photron Fastcam MC2.1, Photron, San Diego, CA).

Three timescales are considered herein: inertio-capillary or Rayleigh timescale τ c = ρR 3 / γ , visco-capillary timescale τ v = µ R / γ , and polymer longest relaxation timescale λ representing the elastic effect, where ρ is the density and R is the nozzle radius of the inkjetting system (60 µm). These timescales help define two material property-related nondimensional numbers: Ohnesorge number ( Oh =

τv µ λ = ) and Deborah number ( De = , where τ% is the τc τ% ρ Rγ

characteristic process time.). Depending on whether the inertial or viscous effect is dominant (Oh less than 1 or not8, De0 =

λ = τc

), τ% is either τc or τν, resulting in the intrinsic Deborah number

26

λ 2γ λ λγ and the elasto-capillary number Ec = = . The Appendix (Table A1) 3 ρR τv µR

also provides the values of these nondimensional numbers of the alginate solutions studied.

2.2 Method and experimental conditions The DOD inkjet printing system herein was composed of three key sub-systems: a MicroFab nozzle dispenser with an orifice diameter of 120 µm (MJ-ABL-01-120-6mx) and its associated Jet Driver (MicroFab, Plano, TX), a pneumatic controller (MicroFab, Plano, TX), and an imaging system (ImageXpert, Nashua, NH). The excitation waveform was controlled using the MicroFab Jet Driver, and the pneumatic controller was used to adjust the backpressure of the fluid reservoir to obtain an ideal meniscus for good droplet formation. Once a pulsed voltage is applied to the nozzle piezoelectric element, a pressure wave is generated to squeeze the nozzle,


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finally ejecting some fluid out to form droplets in a DOD mode. The droplet formation process was captured by the imaging system for time-resolved image analysis, and the jet velocity and breakup time were determined from the images captured. The image resolution herein is 1032 × 778 pixels, and one pixel is 3.2 µm, the minimum achievable feature resolution. The ligament length was determined using the ImageJ software developed by the National Institutes of Health. More DOD inkjetting setup details can be found from a previous study.14

During DOD inkjet printing, an excitation waveform was applied to the nozzle dispenser to form droplet(s), and the typical excitation waveform is bipolar, which consists of a succession of positive/negative square-wave pluses.27 The bipolar excitation waveform used in the study is defined as follows: excitation voltages in the range from 30V to 70V with an interval of 5 V, voltage rise/fall time 3 µs, dwell time 30 µs, echo time 30 µs, and frequency 50 Hz.

2.3 Key characteristics of a droplet formation process During the droplet formation process, some key features are defined in Fig. 1. Two important locations are the origin x0 which is the exit position of nozzle orifice and the jet/droplet leading point xl, and these two locations are used to determine the droplet velocity ( U =

xl − x 0 ) herein. ∆t

Before the jet disintegrates from the nozzle, the connecting fluid thread is called ligament. After jet pinch-off, the trailing fluid behind the primary droplet is called tail.


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Fig. 1. Illustration of a forming droplet 3 Pinch-off during DOD Inkjet Printing 3.1 Pressure wave inside nozzle chamber During DOD inkjet printing, the amplitude of excitation-induced pressure wave can be studied based on the force equilibrium inside the nozzle chamber. Fig. 2 shows a representative pressure wave at the nozzle orifice during inkjetting. In order to form a droplet, the pressure at the nozzle tip has to overcome the steady and unsteady inertia, viscous resistance, elasticity, and capillary pressure.28 For the pressure wave shown in Fig. 2, the first negative pressure pulse due to the rising edge of the excitation waveform retracts the meniscus, which is known as the fill-beforefire action.28 It is reflected at the reservoir inlet to become a positive pressure which is amplified by the falling edge of the excitation waveform to become a larger positive pressure to drive the fluid out from the nozzle. The second negative pressure pulse due to the echo of the excitation waveform is to cancel some of residual acoustic oscillations that may remain in the nozzle chamber. The detailed description of DOD inkjetting mechanism can be found in other relevant documents.28-29


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1.4×105

Pressure (Pa)

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First positive pressure

70 µs

Time

-7.0×104 First negative pressure for meniscus retraction before firing

Second negative pressure

Residual pressure wave

Fig. 2. Schematic prepared based on a representative pressure wave28

During DOD inkjet printing, the generated pressure pulses propagate inside the nozzle reflecting at the reservoir and orifice, resulting in an oscillating pressure wave. Ligament thinning has been studied extensively theoretically30-31 and experimentally such as dripping,3, 32 continuous jetting,5, 33

and liquid bridge breakup.6-7 However, the high-frequency oscillating pressure wave makes the

pinch-off process during DOD inkjet printing different from those aforementioned. Some careful examinations of the pinch-off process during DOD inkjetting are greatly needed.

3.2 Possible pinch-off locations According to the Young-Laplace equation, the capillary pressure is proportional to the curvature of the interface, and pinch-off usually occurs at the positions with the largest variation of the curvature where the pressure gradient is largest.28 During the DOD droplet formation process, the initial curvature variation may be generated at two locations: near the ligament head and near the nozzle orifice. At the location near the ligament head, the initial curvature variation results from a supercritical acceleration at the beginning of the droplet formation, which generates an additional maximum velocity in the ligament head to move it away from the rest of forming 9 ACS Paragon Plus Environment

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droplet.28 At the location near the nozzle orifice, the initial curvature variation originates from the jet constriction due to the acceleration.34 The acceleration by the pressure wave affects the fluid near the nozzle orifice,34 causing an inward motion of the free surface near the orifice, which leads to a constriction. In addition to the aforementioned two pinch-off locations, a uniform thin ligament may be formed before pinch-off under some special conditions such as printing of highly elastic fluids, and eventually it breaks up due to the Rayleigh instability.6 Then the pinch-off location can be some place along the thin ligament. These three pinch-off locations may combine and further determine possible pinch-off types during DOD inkjet printing. It should be pointed out that the axial location of the pinch-off region can shift over time, and is mainly affected by the meniscus oscillation. The meniscus oscillation is driven by the pressure wave illustrated in Fig. 2, and significantly affects the ligament pinch-off at the location near the nozzle orifice. The systematic effects of meniscus oscillation on pinch-off behavior of viscoelastic fluids will be investigated in details as part of the future work.

Pinch-off location

Pinch-off locations

Pinch-off location

Fig. 3. Possible pinch-off locations during DOD inkjet printing

3.3 Four pinch-off types during DOD inkjet printing After the pressure wave-induced initial curvature variation generates, the thinning process follows along the entire ligament under the interplay of the capillary, viscous, elastic and inertial stresses. During the DOD inkjetting of sodium alginate solutions, four different pinch-off types 10 ACS Paragon Plus Environment

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have been observed as shown in Fig. 4: front pinching, hybrid pinching, exit pinching, and middle pinching depending on the sodium alginate concentration and excitation voltage. It implies that different pinch-off mechanisms may prevail during the printing of viscoelastic fluids, which depends on the material properties and operating conditions, in particular, the sodium alginate concentration and excitation voltage.

It is noted that only the first pinch-off event during a droplet formation process is of the interest herein. In particular, during front pinching, the first pinch-off of ligament occurs near the ligament head/forming droplet (Fig. 4(a)). During exit pinching, the first pinch-off of ligament occurs near the nozzle orifice (Fig. 4(c)). Under a critical condition, the first pinch-off of ligament occurs simultaneously near both the ligament head and the nozzle orifice, which is called hybrid pinching (Fig. 4(b)). During middle pinching, the ligament thins until its diameter is under the resolution of the imaging system. Eventually, the uniformly thin ligament breaks up, pinch-off occurs along the thin ligament but no exact pinch-off location(s) can be clearly identified. The nature of front pinching is due to a balance of inertial and capillary effects as observed during the beginning of typical ligament diameter thinning process following a 2/3 scaling law,35-37 and the nature of exit pinching is the hydrodynamic instability due to the external high-frequency pressure wave. It is noted that hybrid pinching is a crossover between front and exit pinching when the breakup times at the front-pinching and exit-pinching locations are the same; middle pinching is a special case when the fluid in the ligament has enough time to drain into the forming droplet(s) and/or the nozzle orifice.38 It is noted that the axial location


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Fig. 4. Four pinch-off types during DOD printing: (a) front pinching, (b) hybrid pinching, (c) exit pinching, and (d) middle pinching. Sodium alginate concentration and excitation voltage are listed as follows: (a) 0.30% and 35 V, (b) 0.30% and 42 V, (c) 1.00% and 50 V, and (d) 2.00% and 50 V. Each pinch-off location is marked using a dashed circle

4. Analysis of Pinch-off Phenomena The viscoelastic ligament thinning process is affected by the interplay of different forces at different length scales. At the beginning of the ligament thinning, the ligament thinning is mainly governed by a balance of inertial and capillary effects, which results in a ligament thinning process following the two thirds power-law function. The elastic stress is generated when the alginate polymer chain is stretched and is only large enough to balance the capillary stress when


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the diameter length is reduced to the critical ligament diameter Delastic =

1 3

µ D0

4 3

( 4λγ )

1 3

, where D0 is the

nozzle diameter. As the ligament diameter approaches to zero, the viscous effect starts to become more and more important.39-40

4.1 Pinch-off at front-pinching location Pinch-off at the front-pinching location during DOD inkjet printing is also usually observed during continuous inkjet (CIJ) printing.33,

41-42

Front pinching usually occurs using sodium

alginate solutions with a very low concentration such as 0.10 – 0.20% under the entire voltage range of 30 – 70V (Weber number We =

ρ RU 2 = 5.58 – 88.15). The breakup time at the frontγ

pinching location is usually shorter than that at the exit-pinching location. In this section, the mechanism of front pinching is further explored by analyzing the ligament thinning process.

4.1.1 Effects of viscous and elastic forces During the DOD inkjet printing of a viscoelastic fluid, the droplet formation process is always determined by the inertial, viscous, capillary, and elastic effects, and the influence of some effects may dominate over that of others. It is noted that the gravitational effect is negligible due to a very small Bond number ( Bo =

ρgR 2 ~10-3 1.00 and El > 1.00, meaning the dominant viscous and elastic effects. During middle pinching, the ligament thins until its diameter is below the resolution of the imaging system (3 µm). The ligament further thins and breaks up due to the Rayleigh instability. As summarized before, the breakup may occur any place along the thin ligament. 22 ACS Paragon Plus Environment

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The ligament thinning process near the ligament head/forming droplet is governed by a balance of viscous, elastic and capillary effects. However, near the nozzle orifice, the viscoelastic behavior of the fluids is affected by the high-frequency pressure wave, and the ligament thinning process is exponential and governed by the elasto-capillary thinning mechanism as shown in Fig. 7. Ligament diameters near the orifice and the forming droplet (µm)

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120

Near the forming droplet Near the orifice

100 80 60

Exponential decay

40 20 D = 78.66e-0.009t

0 0

100

200 Time (µs)

300

400

Fig. 7. Middle-pinching diameter information using 1.50% sodium alginate solution at 45V. The ligament thinning at the location near the nozzle orifice is fitted by an exponential function, which confirms the exponential decay near the nozzle orifice

Middle pinching actually is a special case when the fluid of the ligament has enough time to flow into both the nozzle orifice and the main forming droplet. Two characteristics of middle pinching are observed: fluid drainage back into the nozzle, and low, oscillating head velocity (Fig. 8) of the forming droplet. The head velocity oscillates between 0 and around 2 m/s during the time of 100-305 µs, which is mainly due to the meniscus oscillation (the meniscus oscillating velocity is 23 ACS Paragon Plus Environment

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measured as ±1.08 m/s with a standard deviation of 0.62 m/s). During middle pinching, it is also observed (Fig. 9) that the ejected volume starts decreasing after 100 µs, indicating that the fluid of the ligament starts flowing back to the nozzle orifice due to the pressure difference caused by surface tension.52-53

14

Head velocity of forming droplet (m/s)

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12 10 8 6

Oscillating velocity 4 2 0 0 -2

50

100

150

200

250

300

Time (µs)

Fig. 8. Head velocity of forming droplet using 1.50% sodium alginate solution at 45 V

Apparently, long breakup time and low head velocity facilitate the drainage of the fluid of the ligament.54-56 The breakup time near the orifice should be long enough for the capillary pressure to drive some of the ligament fluid to flow back to the nozzle. The head velocity of the forming droplet should be small enough so that the fluid of the ligament can stay connected with the ligament head. Only in this way can a uniformly thin ligament be formed before pinch-off, which eventually results in middle pinching. It is observed in this study that the middle-pinching process only occurs using the 1.50 – 2.00% sodium alginate solutions under low excitation voltages (for example, 50 V for the 1.50% solution and 55 V for the 2.00% solution (We around 0.72 for both)). 24 ACS Paragon Plus Environment

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8000 7000

Ejected ligament volume (pL)

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6000

1%, 65V 2%, 50V

5000

Exit pinching

4000 Middle pinching 3000 2000 1000 0 0

100

200 Time (µs)

300

400

Fig. 9. Ejected fluid volume as a function of time

4.4 Hybrid pinching Hybrid pinching happens when the front pinching and exit pinching occurs simultaneously. The breakup times at the front-pinching and exit-pinching locations compete with each other to determine the pinch-off type, which depends on the sodium alginate concentration and initial ligament diameter. Under certain conditions, the two breakup times may be the same, resulting in hybrid pinching. For low-concentration alginate solutions, the viscous and elastic effects are relatively small when compared to the inertial and capillary effects. As the sodium alginate concentration increases, the viscous and elastic effects start showing their influence by delaying the breakup time of front pinching, which may be close to that of exit pinching. While it is not common, hybrid pinching is observed using the 0.30% sodium alginate solution at the excitation voltage within the range of 40 – 55 V (We = 15.11 – 39.63) and the 0.35% sodium alginate solution at the excitation voltage within the range of 34 – 36 V (We = 5.56 – 9.02).


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5. Conclusions and Future Work This work has studied various pinch-off locations as a function of material properties and operating conditions during DOD inkjet printing of viscoelastic sodium alginate solutions. Four breakup types have been identified: front pinching, hybrid pinching, exit pinching, and middle pinching. Some main conclusions are drawn as follows: (1) for very low alginate concentrations such as 0.10 – 0.20%, front pinching prevails. The ligament thinning process is governed by a balance of inertial and capillary effects, following a power-law function with an exponent of 2/3; (2) for low concentrations such as 0.25 – 0.35%, hybrid pinching occurs within a specific range of We when the viscous and elastic effects start showing their influence by delaying the breakup time of front pinching, which may be close to that of exit pinching; (3) for intermediate concentrations such as 0.50 – 1.00%, exit pinching occurs. The ligament thinning process is governed by a balance of elastic and capillary effects, resulting in the exponential decay process; and (4) for high concentrations such as 1.50 – 2.00%, middle pinching occurs at low We. The ligament thinning process near the ligament head/forming droplet is governed by a balance of viscous, elastic, and capillary effects, while the ligament thinning process near the orifice is governed by a balance of elastic and capillary effects due to the high-frequency pressure wave.

Future work may include: 1) investigation of the effect of meniscus oscillation during DOD inkjet printing of viscoelastic fluids, 2) analytical and computational modeling of ligament thinning process as well as regime transitions during DOD inkjet printing of general viscoelastic fluids to understand the underlying pinch-off physics, and 3) construction of phase diagrams based on dimensionless numbers to classify the regimes for different pinch-off types by considering both material properties and 3D printing conditions.


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Acknowledgements The work was partially supported by the National Science Foundation (CMMI-1314834). C. Xu thanks J. Yan and C.L. Herran for rheological measurement assistance.

Appendix Table A1. Sodium alginate solution rheological properties and related nondimensional values Sodium alginate concentration (w/v)

Density ρ (g/cm3)

Average zero-shear viscosity µ (cP)

Surface tension γ (mN/m)

Longest relaxation time λ

De Oh

El De0

Ec

(µs)

0.10%

1.001

2.8

72.1±0.1

320

0.04

5.84

0.25

0.15%

1.002

3.7

71.7±0.3

380

0.06

6.92

0.39

0.20%

1.002

4.5

71.5±0.3

390

0.07

7.09

0.49

0.25%

1.003

5.5

70.8±0.3

400

0.08

7.23

0.61

0.30%

1.004

6.0

69.9±0.8

410

0.09

7.36

0.68

0.35%

1.005

6.7

67.4±0.9

420

0.11

7.40

0.78

0.50%

1.005

10.2

52.6±1.2

430

0.18

6.69

1.21

1.00%

1.010

31.1

47.5±0.2

650

0.58

9.59

5.56

1.50%

1.014

75.2

45.7±0.5

920

1.43

9.32

19.00

2.00%

1.021

139.5

44.6±0.3

1650

2.67

8.79

62.62

References: (1) Wagner, C.; Amarouchene, Y. A.; Bonn, D.; Eggers, J. Droplet Detachment and Satellite Bead Formation in Viscoelastic Fluids. Phys. Rev. Lett. 2005, 95, 164504.


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TOC Graphic

Pinch-off location

Pinch-off location

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Pinch-off locations

Study of Pinch-Off Locations during Drop-on ... - ACS Publications

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