###### 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.  
electrohydrodynamic jetting; drop-on-demand; jetting frequency; damping ratio; natural frequency  
with lower pulse voltage also increases [3; 4; 5]. By changing the applied voltage and flow rate, jet type was also studied such that, as the flow rate and voltage increase, the jet-mode changes from dripping, to pulsating, to cone-jet, to tilted-jet, and to multi-jet [6; 7]. Also, a number of studies investigated the effects of amplitude and frequency of electric voltage pulse on the jetting and printing characteristics for drop-on-demand (DOD) printing systems with various inks and nozzles [8; 9; 10; 11; 12; 13; 14]. In those previous studies, examined jetting frequency was relatively low (typically less than 100 Hz) because an EHD system has little means to stabilize the motion of the meniscus right after the detachment of the drop. This is because filling the nozzle with ink takes some time to form a stabilized drop for repeatable jetting. Understanding the movements of ink inside the nozzle is, therefore, crucial to achieve high speed jetting with small drops in advanced manufacturing.  
[PERSON] et al. [15] proposed a useful model to describe the electro-hydro-dynamic movements of ink in the nozzle as an oscillatory system to explain the jetting stability with the electric pulse frequency, which introduces the natural frequency and damping ratio of the system as a function of ink property and nozzle geometry. They clearly showed that, in their underdamped jetting system with 50 \(\upmu\)m diameter nozzle, the maximum jetting frequency is limited by the natural frequency. Interestingly, if the nozzle diameter decreases sufficiently, the damping ratio can increase to make this an overdamped system. Compared with the underdamped system, the overdamped system might be stable at the higher jetting frequency. However, direct evidence for the higher stability of the overdamped system has not been given yet.  
Considering this background, for EHD jetting of Ag nanoparticle ink, this study investigates the effect of the damping ratio on the stability against pulsating frequency. EHD nozzles having various damping ratios were tested by adopting different nozzle geometries; the relation between jetting frequency and pulsating frequency was measured. The results for the overdamped system 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.