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Applied Sciences
, Volume 8 (2) – Jan 24, 2018

/lp/multidisciplinary-digital-publishing-institute/effect-of-meniscus-damping-ratio-on-drop-on-demand-electrohydrodynamic-NMQQDdXQgR

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- Multidisciplinary Digital Publishing Institute
- Copyright
- © 1996-2019 MDPI (Basel, Switzerland) unless otherwise stated
- ISSN
- 2076-3417
- DOI
- 10.3390/app8020164
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- See Article on Publisher Site

applied sciences Article Effect of Meniscus Damping Ratio on Drop-on-Demand Electrohydrodynamic Jetting 1 2 2 2 2 Samuel Haedong Kim , Heuiseok Kang , Kyungtae Kang , Sang Ho Lee , Kwan Hyun Cho 2 , and Jun Young Hwang * Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA; samuel.h.kim@gatech.edu Korea Institute of Industrial Technology, Cheonan 31056, Korea; hskang@kitech.re.kr (H.K.); ktkang@kitech.re.kr (K.K.); sholee7@kitech.re.kr (S.H.L.); khcho@kitech.re.kr (K.H.C.) * Correspondence: jyhwang@kitech.re.kr; Tel.: +82-10-5285-7074 Received: 15 December 2017; Accepted: 23 January 2018; Published: 24 January 2018 Abstract: Drop-on-demand (DOD) electrohydrodynamic (EHD) jet printing uses a nozzle and pulsated electric ﬁelds to eject small ink droplets of functional material to the appointed spot of a substrate at the appointed time, which offers solutions of high resolution patterning for fabrication of printed electronics, bioengineering, and display. Because the EHD jet connects ﬁne drops to yield a ﬁne pattern, it is essential to realize high throughput by generating drops quickly and reliably. In this study, the characteristics of jetting frequency were experimentally investigated as a function of nozzle dimensions by measuring response of jetting frequency to pulsating frequency which is varying from 1 Hz to 2000 Hz. The results showed that, even when the nozzle diameter is the same, the other dimensions of the nozzle signiﬁcantly change the response of jetting to high pulsating frequency. Using a linear damping model describing hydrodynamic motion of ink inside the nozzle, the different behavior of the jetting frequency was explained via the different damping ratio of the oscillating ink: contrary to an underdamped system, an overdamped system supports a jetting frequency higher than the natural frequency. Keywords: electrohydrodynamic jetting; drop-on-demand; jetting frequency; damping ratio; natural frequency 1. Introduction Direct printing of functional electronic materials has attracted considerable interest. This method combines simple additive processing with low-cost materials and have a potential to drastically lower the cost of electronics fabrication, especially compared to that for conventional silicon processing [1]. Inkjet printing, which represents a highly established direct printing method, has been demonstrated to be capable of printing all materials required for electronics, display, optics, bioengineering, and other areas. However, there is a critical challenge of inkjet printing in that practically feasible resolution is as low as 20–30 m. On the other hand, electro-hydro-dynamic jet (EHD-jet) printing provides high-resolution patterning (<10 m), which means that this process has potential for application in nano-systems such as NEMS and biotechnology [2]. EHD-jet printing is a technique that uses electric ﬁelds between the nozzle and an opposing conducting substrate to make the functional electronic material ﬂow from a nozzle via electro-hydro-dynamics. There have been studies to understand the fundamental mechanism of EHD-jet printing; however, the physics of EHD-jet printing and the parameters that affect the printing are not yet clearly understood, and these parameters will be signiﬁcant for high resolution, uniform, and reproducible printing. Meniscus deformation was investigated by changing the imposed voltage such that when the bias voltage increases, not only the meniscus height increases, but also the chance of jetting of smaller drops Appl. Sci. 2018, 8, 164; doi:10.3390/app8020164 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, x FOR PEER REVIEW 2 of 8 Appl. Sci. 2018, 8, 164 2 of 8 Meniscus deformation was investigated by changing the imposed voltage such that when the bias voltage increases, not only the meniscus height increases, but also the chance of jetting of smaller drops with lower pulse voltage also increases [3–5]. By changing the applied voltage and flow rate, with lower pulse voltage also increases [3–5]. By changing the applied voltage and ﬂow rate, jet type jet type was also studied such that, as the flow rate and voltage increase, the jet-mode changes from was also studied such that, as the ﬂow rate and voltage increase, the jet-mode changes from dripping, dripping, to pulsating, to cone-jet, to tilted-jet, and to multi-jet [6,7]. Also, a number of studies to pulsating, to cone-jet, to tilted-jet, and to multi-jet [6,7]. Also, a number of studies investigated the investigated the effects of amplitude and frequency of electric voltage pulse on the jetting and effects of amplitude and frequency of electric voltage pulse on the jetting and printing characteristics printing characteristics for drop-on-demand (DOD) printing systems with various inks and nozzles for drop-on-demand (DOD) printing systems with various inks and nozzles [8–14]. In those previous [8–14]. In those previous studies, examined jetting frequency was relatively low (typically less than studies, examined jetting frequency was relatively low (typically less than 100 Hz) because an EHD 100 Hz) because an EHD system has little means to stabilize the motion of the meniscus right after system has little means to stabilize the motion of the meniscus right after the detachment of the drop. the detachment of the drop. This is because filling the nozzle with ink takes some time to form a This is because ﬁlling the nozzle with ink takes some time to form a stabilized drop for repeatable stabilized drop for repeatable jetting. Understanding the movements of ink inside the nozzle is, jetting. Understanding the movements of ink inside the nozzle is, therefore, crucial to achieve high therefore, crucial to achieve high speed jetting with small drops in advanced manufacturing. speed jetting with small drops in advanced manufacturing. Stachewiez et al. [15] proposed a useful model to describe the electro-hydro-dynamic Stachewiez et al. [15] proposed a useful model to describe the electro-hydro-dynamic movements movements of ink in the nozzle as an oscillatory system to explain the jetting stability with the electric of ink in the nozzle as an oscillatory system to explain the jetting stability with the electric pulse pulse frequency, which introduces the natural frequency and damping ratio of the system as a frequency, which introduces the natural frequency and damping ratio of the system as a function of function of ink property and nozzle geometry. They clearly showed that, in their underdamped ink property and nozzle geometry. They clearly showed that, in their underdamped jetting system jetting system with 50 μm diameter nozzle, the maximum jetting frequency is limited by the natural with 50 m diameter nozzle, the maximum jetting frequency is limited by the natural frequency. frequency. Interestingly, if the nozzle diameter decreases sufficiently, the damping ratio can increase Interestingly, if the nozzle diameter decreases sufﬁciently, the damping ratio can increase to make to make this an overdamped system. Compared with the underdamped system, the overdamped this an overdamped system. Compared with the underdamped system, the overdamped system system might be stable at the higher jetting frequency. However, direct evidence for the higher might be stable at the higher jetting frequency. However, direct evidence for the higher stability of the stability of the overdamped system has not been given yet. overdamped system has not been given yet. Considering this background, for EHD jetting of Ag nanoparticle ink, this study investigates the Considering this background, for EHD jetting of Ag nanoparticle ink, this study investigates effect of the damping ratio on the stability against pulsating frequency. EHD nozzles having various the effect of the damping ratio on the stability against pulsating frequency. EHD nozzles having damping ratios were tested by adopting different nozzle geometries; the relation between jetting various damping ratios were tested by adopting different nozzle geometries; the relation between frequency and pulsating frequency was measured. The results for the overdamped system were jetting frequency and pulsating frequency was measured. The results for the overdamped system compared with those for the underdamped system. The effect of pulsating amplitude on jetting were compared with those for the underdamped system. The effect of pulsating amplitude on jetting stability was also investigated for both overdamped and underdamped systems. stability was also investigated for both overdamped and underdamped systems. 2. Experimental Setup 2. Experimental Setup Figure 1a is a schematic of the experimental setup for the EHD printing system. In this study, Figure 1a is a schematic of the experimental setup for the EHD printing system. In this study, we used silver ink (DGP 40LT-15C), which contains 30~35% silver particles dissolved in Triethylene we used silver ink (DGP 40LT-15C), which contains 30~35% silver particles dissolved in Triethylene Glycol Monoethyl Ether (TGME), from ANP Co., Ltd. (Sejong, Korea) Specific resistivity of the ink is Glycol Monoethyl Ether (TGME), from ANP Co., Ltd. (Sejong, Korea) Speciﬁc resistivity of the ink 11~12 μΩ-cm, such that the ink can easily be used to produce electronics. Density, surface tension, is 11~12 W-cm, such that the ink can easily be used to produce electronics. Density, surface tension, and viscosity of ink are 1450 kg/m , 35 mN/m, and 15 mPa-s, respectively. Three glass nozzles having and viscosity of ink are 1450 kg/m , 35 mN/m, and 15 mPa-s, respectively. Three glass nozzles having different dimensions were tested, as shown in Table 1. different dimensions were tested, as shown in Table 1. (a) (b) Figure 1. (a) Schematic of electro-hydro-dynamic (EHD) drop generation system; (b) Waveform Figure 1. (a) Schematic of electro-hydro-dynamic (EHD) drop generation system; (b) Waveform applied applied to EHD system: bias voltage (Vb) is applied to the nozzle, lower than the onset voltage (Von), to EHD system: bias voltage (V ) is applied to the nozzle, lower than the onset voltage (V ), and pulsed on and pulsed voltage (Vp) is applied to the stage. voltage (V ) is applied to the stage. p Appl. Sci. 2018, 8, 164 3 of 8 Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 8 Table 1. Parameters of the experimental set-up. Table 1. Parameters of the experimental set-up Nozzle # Parameter Nozzle # A B C Parameter AB C Approximate ink column height, H (m) 0.2 Approximate ink column height, H (m) 0.2 Distance between nozzle and substrate, h (m) 100 Distance between nozzle and substrate, h (μm) 100 Inner diameter of nozzle, d (m) 30 15 Inner diameter of nozzle, dn (μm) 30 15 Radius of the capillary far above the nozzle, b (m) 375 120 60 Radius of the capillary far above the nozzle, b (μm) 375 120 60 Total length of the thinnest part, l (mm) 3.0 1.2 1.2 Total length of the thinnest part, l (mm) 3.0 1.2 1.2 Bias voltage, V (V) 650 620 450 Bias voltage, Vb (V) 650 620 450 Bias voltage is applied to the nozzle by a high voltage DC power supply (ConverTech, Gyeonggi, Bias voltage is applied to the nozzle by a high voltage DC power supply (ConverTech, Gyeonggi, Korea, SHV 300R). To minimize the droplet size and facilitate generation of drops with low pulse Korea, SHV 300R). To minimize the droplet size and facilitate generation of drops with low pulse voltage, bias voltage was applied at 90% of onset voltage, V , at which point EHD-jet starts to form, on voltage, bias voltage was applied at 90% of onset voltage, Von, at which point EHD-jet starts to form, as shown in Figure 1b [4,5]. The following equation estimates the value of V [16,17] on as shown in Figure 1b [4,5]. The following equation estimates the value of Von [16,17] u 4g − DP 88ℎ h d n (1) V ~ d lnln (1) on n d 88# where dn is the inner diameter of the nozzle, h is the distance between the nozzle and the substrate, where d is the inner diameter of the nozzle, h is the distance between the nozzle and the substrate, and γ is the surface tension of the ink; according to the Young–Laplace equation, capillary pressure and g is the surface tension of the ink; according to the Young–Laplace equation, capillary pressure in a tube is 4γ/dn, ΔP is the hydrostatic pressure, and ε is the permittivity of air, which was assumed in a tube is 4g/d , DP is the hydrostatic pressure, and " is the permittivity of air, which was assumed −12 to be 8.859 × 1012 F/m at room temperature [18]. The value of Von calculated using Equation (1) is to be 8.859 10 F/m at room temperature [18]. The value of V calculated using Equation (1) is on compared with the experimental results using nozzle A, as shown in Figure 2; the results agree to compared with the experimental results using nozzle A, as shown in Figure 2; the results agree to each other. each other. Experiment Calculation 0 50 100 150 200 250 300 350 Distance between nozzle and substrate, h (μm) Figure 2. Onset voltage, Von, as a function of distance between nozzle and substrate. Calculated data Figure 2. Onset voltage, V , as a function of distance between nozzle and substrate. Calculated data is on is based on Equation (1), and experimental data were obtained using Nozzle A (dn = 30 μm). based on Equation (1), and experimental data were obtained using Nozzle A (d = 30 m). A complex-waveform driver (MicroFab INC., Plano, TX, USA, JetDrive III) is used to generate a A complex-waveform driver (MicroFab INC., Plano, TX, USA, JetDrive III) is used to generate rectangular step-function signal, which is sent to the power amplifier (TREK INC., Lockport, NY, a rectangular step-function signal, which is sent to the power ampliﬁer (TREK INC., Lockport, NY, USA, TREK 2220) for 200 V/V amplification to make the voltage pulse, Vp having a duration of 500 USA, TREK 2220) for 200 V/V ampliﬁcation to make the voltage pulse, V having a duration of 500 s, μs, as shown in Figure 1b. In this experiment, pulsation frequency was varied from 1 to 2000 Hz while as shown in Figure 1b. In this experiment, pulsation frequency was varied from 1 to 2000 Hz while moving speed of the stage was set to the pulsation frequency multiplied by 40 μm. Therefore, the moving speed of the stage was set to the pulsation frequency multiplied by 40 m. Therefore, the ratio ratio of the pulsation frequency to the jetting frequency of the ink could be obtained by measuring of the pulsation frequency to the jetting frequency of the ink could be obtained by measuring the the printed drop spacing divided by 40 μm. printed drop spacing divided by 40 m. Onset voltage, V (V) on Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 8 Appl. Sci. 2018, 8, 164 4 of 8 3. Linear Damping Approximation The electrohydrodynamic movements of the ink in the capillary can be described by the equation 3. Linear Damping Approximation of linear damping system [19] The electrohydrodynamic movements of the ink in the capillary can be described by the equation (2) of linear damping system [19] .. . mx + cx + kx = 0 (2) where m is the mass, c is the damping coefficient, k is the spring constant, and x is the ink displacement inside the capillary nozzle. The components of Equation (2), the natural oscillation frequency fc, and where m is the mass, c is the damping coefﬁcient, k is the spring constant, and x is the ink displacement the damping ratio Γ, of the EHD-jet system were modeled by the following equations [19] inside the capillary nozzle. The components of Equation (2), the natural oscillation frequency f , and the damping ratio G, of the EHD-jet system were modeled by the following equations [19] (3) m = d rH (4 (3) ) 8 n c = 8pul (4) 2ℎ 1− (5) 4 2 4 pgd 2h d n m n 2 ℎ k = 1 4 + rgp (5) 4 2 2 2 d 2 n 16b d 2 + h 2 + h m m 4 (6) 1 k f = (6) 2p m G = p (7 (7) ) 2 mk where where H H iis s tthe he approxim approximate ate ink col ink column umn height height, , υ u is t ishthe e viscos viscosity ity of of the ink, the ink, l is the tota l is the total l length length of the of thinnest part, the thinnest part, hm ihs th ise ap thep appr roxim oximate ate memeniscus niscus hei height, ght, which is which is ap appr proxim oximated ated bby y 20% o 20% of f tthe he inner inner diameter o diameter of f n nozzle ozzle [15], [15], bb iis s tthe he rad radius ius o of f tthe he cap capillary illary far far ab above ove tthe he nozz nozzle, le, as as iillustrated llustrated in F in Figur igure e3. 3. All value All values s ar are shown e shown in T in Table able 1. Tab 1. Table le 2 2 show shows s the the c calculated alculated n natural atural fr fre equency quency an and d the d the damping amping ratios of the ratios of the four d four dif ifferent ferent nozzles. nozzles. Reg Regar arding ding th the e d dimensions imensions of t of the he nozzle nozzle an and d the propert the property y of the of the ink, t ink, the he d damping amping r ratios atios o of f nozz nozzle le A an A and d C C are h are higher igher tthan han 1 1, , and and tthat hat of noz of nozzle zle B is B is sm smaller aller tthan han 1 1; ; these value these values s c corr orrespond to espond to over overdamped damped and and under underd damped amped system systems, s, re respectively spectively. . Figure 3. Figure 3. Schematics of nozzle: Schematics of nozzle: ρ r = dens = density ity of ink, of ink,γ = surface tension of in g = surface tension of k,ink, υ = vuiscosity of ink, = viscosity of H ink, = approximate ink colu H = approximate ink column mn height from in height fromk reservoir ink reservoir to free end of nozzle, to free end of nozzle, b b= rad = radius ius of of ccapillary apillary far far above nozzle above nozzle,, h h = = distance bet distance between ween nozzle a nozzle and nd substrate, substrate, h hm = = meniscus height, meniscus height, d dn = inne = inner r diameter of diameter of m n nozzle, and l = total length of thinnest part of nozzle. nozzle, and l = total length of thinnest part of nozzle. Appl. Sci. 2018, 8, 164 5 of 8 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 8 Table 2. Calculated natural frequency and damping ratio of three different nozzles Table 2. Calculated natural frequency and damping ratio of three different nozzles. Nozzle # Nozzle # Parameter Parameter A B C A B C Natural frequency inside the capillary, fc (Hz) 224 224 448 Natural frequency inside the capillary, f (Hz) 224 224 448 Damping ratio of the system, 2.0 0.78 1.6 Damping ratio of the system, G 2.0 0.78 1.6 4. Results and Discussion 4. Results and Discussion Figure 4 compares the patterns of printed drops with various pulsation frequencies for nozzle A Figure 4 compares the patterns of printed drops with various pulsation frequencies for nozzle and nozzle B at the minimum pulse voltage of jetting. The two nozzles have the same diameter dn of A and nozzle B at the minimum pulse voltage of jetting. The two nozzles have the same diameter 30 μm and the same natural frequency fc of 224 Hz, while they have different damping ratios, as d of 30 m and the same natural frequency f of 224 Hz, while they have different damping ratios, n c shown in Tables 1 and 2. For nozzle A, shown in Figure 4a, where the estimated damping ratio is 2.0 as shown in Tables 1 and 2. For nozzle A, shown in Figure 4a, where the estimated damping ratio (overdamped), ink drops are printed at the designed drop spacing of 40 μm for 3, 10, 30 Hz, and even is 2.0 (overdamped), ink drops are printed at the designed drop spacing of 40 m for 3, 10, 30 Hz, for 1 kHz. The pulsed voltage in Figure 4a was 150 V. On the other hand, for nozzle B, shown in and even for 1 kHz. The pulsed voltage in Figure 4a was 150 V. On the other hand, for nozzle B, shown Figure 4b, where the damping ratio is 0.78 (underdamped) and the pulsed voltage is 300 V, the drop in Figure 4b, where the damping ratio is 0.78 (underdamped) and the pulsed voltage is 300 V, the drop spacing becomes multiples of 40 μm as pulsation frequency increases. spacing becomes multiples of 40 m as pulsation frequency increases. Figure 4. Printed drops of Ag ink with various pulsation frequencies of 1, 10, 30, and 1000 Hz for (a) Figure 4. Printed drops of Ag ink with various pulsation frequencies of 1, 10, 30, and 1000 Hz for overdamped system (Nozzle A; Γ = 2.0) and (b) underdamped system (Nozzle B; Γ = 0.8) at the (a) overdamped system (Nozzle A; G = 2.0) and (b) underdamped system (Nozzle B; G = 0.8) at minimum pulse vo the minimum pulse ltages of voltages jetting of of jetting 150 V ofand 300 150 V and V, respective 300 V, respectively ly. The two nozzle . The twos have the nozzles have same the diameter same diameter dn of 30 μdm and the same natural frequency of 30 m and the same natural fr fc of 224 Hz, while th equency f of 224 Hz, ey have differe while they have nt damping different n c ratios. damping ratios. Figure 5 shows the measured jetting frequency as a function of pulsation frequency. When the Figure 5 shows the measured jetting frequency as a function of pulsation frequency. When the system is overdamped (Γ > 1), as shown for nozzle A in Figure 5, jetting frequency is in good system is overdamped (G > 1), as shown for nozzle A in Figure 5, jetting frequency is in good agreement agreement with pulsating frequency because the ink refill time is sufficiently small [15] and the with pulsating frequency because the ink reﬁll time is sufﬁciently small [15] and the meniscus stabilizes meniscus stabilizes quickly after jetting. However, when system is underdamped (Γ < 1), as shown quickly after jetting. However, when system is underdamped (G < 1), as shown for nozzle B in Figure 5, for nozzle B in Figure 5, jetting frequency does not increase with pulsation frequency but is limited jetting frequency does not increase with pulsation frequency but is limited to a few Hz. This is possibly to a few Hz. This is possibly due to the capillary oscillation of the ink inside the nozzle after jetting. due to the capillary oscillation of the ink inside the nozzle after jetting. This result demonstrates that This result demonstrates that the overdamped EHD system is advantageous for high frequency DOD the overdamped EHD system is advantageous for high frequency DOD jetting. In an overdamped jetting. In an overdamped system, the meniscus shape and capillary force gradually change to have system, the meniscus shape and capillary force gradually change to have periodic equilibrium for periodic equilibrium for a given pulsation wave. However, in an underdamped system with high a given pulsation wave. However, in an underdamped system with high frequency, there occurs frequency, there occurs instability due to an interference of capillary and pulsating waves because instability due to an interference of capillary and pulsating waves because the capillary force varies the capillary force varies sinusoidally in between the pulsations. sinusoidally in between the pulsations. Appl. Sci. 2018, 8, 164 6 of 8 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 8 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 8 Nozzle A (Γ = 2.0) Nozzle A (Γ = 2.0) Nozzle B (Γ = 0.78) Nozzle B (Γ = 0.78) f = f f jet = f p jet p f = 224 Hz f c = 224 Hz 0.1 0.1 0.1 1 10 100 1000 104 0.1 1 10 100 1000 10 Pulsation frequency, f (Hz) Pulsation frequency, f p (Hz) Figure 5. Measured jetting frequency as a function of pulsation frequency. Jetting frequency is in good Figure 5. Measured jetting frequency as a function of pulsation frequency. Jetting frequency is in Figure 5. Measured jetting frequency as a function of pulsation frequency. Jetting frequency is in good agreement with pulsating frequency for overdamped system (Nozzle A; Γ = 2.0), while jetting good agreement with pulsating frequency for overdamped system (Nozzle A; G = 2.0), while jetting agreement with pulsating frequency for overdamped system (Nozzle A; Γ = 2.0), while jetting frequency does not increase with pulsation frequency at a few Hz for underdamped system (Nozzle frequency does not increase with pulsation frequency at a few Hz for underdamped system (Nozzle B; frequency does not increase with pulsation frequency at a few Hz for underdamped system (Nozzle B; Γ = 0.8). G = 0.8). B; Γ = 0.8). Interestingly, Figure 5 also shows that, even for the overdamped nozzle A, jetting frequency Interestingly, Interestingly, F Figur igure e 5 5 also also show shows s th that, at, even even f for or the ove the over rda damped mped nozzl nozzle e A A,, jjetting etting f fr req equency uency deviates from the pulsation frequency near the estimated natural oscillation frequency, fc. In order to deviates from the pulsation frequency near the estimated natural oscillation frequency, fc. In order to deviates from the pulsation frequency near the estimated natural oscillation frequency, f . In order investigate the effect of fc on DOD jetting, Figure 6 shows the jetting frequency as a function of the investig to investigate ate the effect o the effect f fof c on DOD jetti f on DOD jetting, ng, Figure 6 Figur e shows the jetti 6 shows the jetting ng frequenc frequency y as a function o as a function f the of natural frequency ratio for overdamped nozzles A and C. As shown in Tables 1 and 2, the inner natural frequency ratio for overdamped nozzles A and C. As shown in Tables 1 and 2, the inner the natural frequency ratio for overdamped nozzles A and C. As shown in Tables 1 and 2, the inner diameter of nozzle C is 15 μm (one half the diameter of nozzle A) and, therefore, the estimated natural diameter diameter of n of nozzle ozzle C C is 15 is 15μm (one h m (one alf t half he diameter o the diameter f noof zzle nozzle A) and, therefore, t A) and, therefor he estim e, the ated estimated natural frequency is 448 Hz (double the natural frequency of nozzle A). The natural frequency ratios of frequency is 448 Hz (double the natural frequency of nozzle A). The natural frequency ratios of natural frequency is 448 Hz (double the natural frequency of nozzle A). The natural frequency ratios of pulsation α and jetting β are the frequencies normalized by the natural frequency, respectively. puls pulsation ation α and and jetti jetting ng β are the fr are the freque equencies ncies no normalized rmalized by by the n the natural atural fr frequency equency, re , respectively spectively. . Nozzle A (V = 150 V) Nozzle A (V p = 150 V) Nozzle A (V = 250 V) Nozzle A (V p = 250 V) Nozzle C (V = 220 V) Nozzle C (V p = 220 V) Nozzle C (V = 300 V) Nozzle C (V = 300 V) 0.1 0.1 0.01 0.01 0.01 0.1 1 10 0.01 0.1 1 10 Natural frequency ratio of pulsation, α Natural frequency ratio of pulsation, α Figure 6. Natural frequency ratio of jetting as a function of natural frequency ratio of pulsation for Figure 6. Natural frequency ratio of jetting as a function of natural frequency ratio of pulsation for Figure 6. Natural frequency ratio of jetting as a function of natural frequency ratio of pulsation for overdamped nozzles A (fc = 224 Hz) and C (fc = 448 Hz). Pulse voltages of 150 V and 220 V are the overdamped nozzles A (fc = 224 Hz) and C (fc = 448 Hz). Pulse voltages of 150 V and 220 V are the overdamped nozzles A (f = 224 Hz) and C (f = 448 Hz). Pulse voltages of 150 V and 220 V are the c c minimum jetting voltages for nozzles A and C, respectively, while 250 V and 300 V are the increased minimum jetting voltages for nozzles A and C, respectively, while 250 V and 300 V are the increased minimum jetting voltages for nozzles A and C, respectively, while 250 V and 300 V are the increased pulse voltages of jetting for nozzles A and C, respectively. pulse voltages of jetting for nozzles A and C, respectively. pulse voltages of jetting for nozzles A and C, respectively. In Figure 6, pulsed voltages Vp of either 150 V for nozzle A or 220 V for nozzle C are close to the In Figure 6, pulsed voltages Vp of either 150 V for nozzle A or 220 V for nozzle C are close to the In Figure 6, pulsed voltages V of either 150 V for nozzle A or 220 V for nozzle C are close to the minimum voltage that allows DOD jetting shown in Figure 2 and Equation (1). The bias voltage Vb minimum voltage that allows DOD jetting shown in Figure 2 and Equation (1). The bias voltage Vb minimum voltage that allows DOD jetting shown in Figure 2 and Equation (1). The bias voltage V and nozzle-substrate distance h are given in Table 1. With this low pulsation voltage, the electrostatic and nozzle-substrate distance h are given in Table 1. With this low pulsation voltage, the electrostatic pulsation is balanced by capillary oscillation at the nozzle tip. Therefore, when pulsation frequency pulsation is balanced by capillary oscillation at the nozzle tip. Therefore, when pulsation frequency Jetting frequency, f (Hz) Natural frequency ratio of jetting, β Jetting frequency, f (Hz) Natural frequency ratio of jetting, β jet jet Appl. Sci. 2018, 8, 164 7 of 8 and nozzle-substrate distance h are given in Table 1. With this low pulsation voltage, the electrostatic pulsation is balanced by capillary oscillation at the nozzle tip. Therefore, when pulsation frequency approaches the natural frequency (0.5 < < 2), the jetting frequency does not match pulsation frequency due to interference between the electrostatic pulsation and capillary oscillation. On the other hand, the effect of the resonance on distortion of the jetting frequency decreases when pulsed voltage increases to 250 V for nozzle A or 300 V for nozzle C, so that the electrostatic force becomes stronger than the capillary force. 5. Concluding Remarks Characteristics of EHD jetting were experimentally investigated with various pulsating frequencies and nozzle dimensions. A simpliﬁed linear damping model was also adopted to describe the oscillating motion of Ag ink inside the nozzle. Based on the results, the effects of the damping ratio and the natural frequency were discussed. By comparing the results of two nozzles having the same diameter and the same natural frequency, but different damping ratios, it is demonstrated that the overdamped EHD nozzle system is advantageous to support high frequency DOD jetting. When the system is overdamped, jetting frequency was in good agreement with the pulsating frequency up to 2000 Hz. However, when the system is underdamped, the jetting frequency does not increase with the pulsation frequency, but is limited to a few Hz, because capillary oscillation requires time to form a stabilized meniscus in an underdamped system. It is also shown that when the pulsation frequency approaches the natural frequency (0.5 < < 2), mismatch occurs between the jetting frequency and the pulsation frequency due to interference between the electrostatic pulsation and the capillary oscillation. This mismatch is mitigated when the pulsed voltage increases, because the electrostatic force becomes superior to the capillary force. Acknowledgments: This work was supported by an Industrial Technology Innovation program grant no. 10052802 from Korea Evaluation Institute of Industrial Technology, funded by the Ministry of Trade, Industry and Energy of the Korean Government. Author Contributions: S. H. Kim and J. Y. Hwang conceived and designed the experiments; S. H. Kim performed the experiments; All authors discussed the ﬁndings in paper. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Ru, C.; Luo, J.; Xie, S.; Sun, Y. A review of non-contact micro- and nano-printing technologies. J. Micromech. 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Applied Sciences – Multidisciplinary Digital Publishing Institute

**Published: ** Jan 24, 2018

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