## 2 Experimental Setup  
Figure 1a is a schematic of the experimental setup for the EHD printing system. In this study, we used silver ink (DGP 40 LT-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 11-12 \(\upmu\Omega\)-cm, such that the ink can easily be used to produce electronics. Density, surface tension, and viscosity of ink are 1450 kg/m\({}^{3}\), 35 mN/m, and 15 mPa-s, respectively. Three glass nozzles having different dimensions were tested, as shown in Table 1.  
Figure 1: (**a**) Schematic of electro-hydro-dynamic (EHD) drop generation system; (**b**) Waveform applied to EHD system: bias voltage (\(V_{b}\)) is applied to the nozzle, lower than the onset voltage (\(V_{om}\)), and pulsed voltage (\(V_{p}\)) is applied to the stage.  
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 voltage, bias voltage was applied at 90% of onset voltage, \(V_{an}\), at which point EHD-jet starts to form, as shown in Figure 1b [4; 5]. The following equation estimates the value of \(V_{on}\)[16; 17]  
\[V_{on}\,\sim\,d_{n}\ln\left(\frac{8h}{d_{n}}\right)\sqrt{\frac{\left(\frac{4 \gamma}{d_{n}}-\Delta P\right)}{8\varepsilon}} \tag{1}\]  
where \(d_{n}\) is the inner diameter of the nozzle, \(h\) is the distance between the nozzle and the substrate, and \(\gamma\) is the surface tension of the ink; according to the Young-Laplace equation, capillary pressure in a tube is \(4\gamma/d_{n}\), \(\Delta P\) is the hydrostatic pressure, and \(\varepsilon\) is the permittivity of air, which was assumed to be \(8.859\,\times\,10^{-12}\) F/m at room temperature [18]. The value of \(V_{on}\) calculated using Equation (1) is compared with the experimental results using nozzle A, as shown in Figure 2; the results agree to each other.  
A complex-waveform driver (MicroFab INC., Plano, TX, USA, JetDrive III) is used to generate 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, \(V_{p}\) having a duration of 500 \(\upmu\)s, 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 \(\upmu\)m. Therefore, the ratio of the pulsation frequency to the jetting frequency of the ink could be obtained by measuring the printed drop spacing divided by 40 \(\upmu\)m.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{2}{c}{**Nozzle \#**} & \\ \cline{2-4}  & **A** & **B** & **C** \\ \hline Approximate ink column height, \(H\) (m) & 0.2 & & \\ Distance between nozzle and substrate, \(h\) (\(\upmu\)m) & 100 & & \\ Inner diameter of nozzle, \(d_{n}\) (\(\upmu\)m) & 30 & & 15 \\ Radius of the capillary far above the nozzle, \(b\) (\(\upmu\)m) & 375 & 120 & 60 \\ Total length of the thinnest part, \(l\) (mm) & 3.0 & 1.2 & 1.2 \\ Bias voltage, \(V_{b}\) (V) & 650 & 620 & 450 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the experimental set-up.  
Figure 2: Onset voltage, \(V_{on}\), as a function of distance between nozzle and substrate. Calculated data is based on Equation (1), and experimental data were obtained using Nozzle A (\(d_{n}\) = 30 \(\upmu\)m).