Electrohydrodynamic jet (e-jet) printing is a high-resolution additive manufacturing process that uses an electric field to ex- tract polarizable ink from a nozzle. The high-resolution capa- bilities of e-jet printing are very favorable for the fabrication of printed electronics and biosensors, which is typically achieved using a highly controllable pulsating jet. In this regime, high voltage pulses are superimposed over a baseline DC voltage, which primes the meniscus for the subsequent pulse. While a higher baseline voltage reduces the response time of the system, values above a certain threshold can cause the printing to transi- tion toward an uncontrollable jetting regime in which the natural dynamics of the ink instigate pulsating jet behavior. To charac- terize the effect of these unwanted transitions on the final print, key parameters of the natural pulsating jet mode must be identi- fied. This work presents findings on the relevant time constants and volume measurements of jet printing at various subcritical voltages. While the impingement time of the jet was found to be proportional to the applied voltage, the volume of the initial droplet increasingly varied. Conclusions regarding permissible pulse widths and system predictability as a function of voltage were made. 1 Introduction Additive manufacturing (AM) is the layer-by-layer process of merging materials together using an energy source [1]. Com- pared to traditional manufacturing techniques, AM has the ca-pability to fabricate more complex devices with a far greater ef- ficiency and less material waste [2]. Recent advancements in AM have improved the precision of micro- and nano-scale de- vices, which constitute numerous applications across a variety of engineering disciplines. Electrohydrodynamic jet (e-jet) print- ing is an emerging AM technique that demonstrates promising properties for micro-scale fabrication. With resolution capabili- ties reaching below 100 nm [3, 4], e-jet has been favored as the printing method for various applications, such as printed elec- tronics [5, 6], biosensors [7, 8], and tissue engineering [9, 10]. During the e-jet printing process, a potential difference is applied between the conductive micro-nozzle and the grounded substrate. As a result, mobile charges within the ink begin to ac- cumulate on the ink-air interface until the meniscus deforms into a Taylor cone. As the potential difference further increases, the Coulombic repulsion between the mobile ions overcomes the sur- face tension of the ink, and a discrete jet is released. In contrast with traditional inkjet printing techniques, the deposited droplet size can be several orders of magnitude smaller than the noz- zle [11]. Figure 1(a) presents a labelled schematic diagram of a sample e-jet printer used for experimental analysis. Various regimes of e-jet printing have been identified using a set of dimensionless parameters as a function of applied volt- age and nozzle flow rate [12]. The vast majority of device fab- rication utilizes the cone-jet regime, characterized by the steady emission of a contiguous jet of ink from the nozzle. Drop-on- demand printing can be achieved through custom modification of the input shape of the applied voltage, which typically involves 1 Copyright © 2023 by ASME 900 VCameraFunction Generator Ampliﬁer SubstrateLightNozzle xyz (a) V oltage TimeV oltage Time V oltage TimeBaseline V oltageV oltage Pulses + (b) FIGURE 1 : (a) Schematic figure of an e-jet printing setup and (b) an illustration of the signal pulse decomposition. the alternation of two or more voltages at varying pulse widths. As a mechanism for reducing the response time of the system, baseline voltages which do not instigate droplet ejection are used in conjunction with high voltage pulses. A illustrated decompo- sition of the voltage signals used in pulse printing is provided in Fig. 1(b). Although the high-resolution properties of e-jet printing are favorable for a wide variety of micro-scale applications, one fac- tor that hinders its commercial expansion is a relatively low pro- duction speed [13]. Therefore, efforts to foster a greater manu- facturing speed are indispensable. Choi and Khan demonstrated that a multi-nozzle printer setup can be used to accomplish this [14, 15]; however, the velocity of the ejected droplet is dictated by various material properties of the ink and the system inputs. Though the system inputs can be adjusted [16], there is also an upper limit for their impact on the printing behavior. The ap- plied high voltage is constrained by the potential to transition toward less controllable printing regimes, such as multi-jet or tilted jet [11]. Additionally, Stachewicz et.al. [17] demonstrated that the pulse frequency is confined by the hydrodynamic be- havior inside the capillary. One potential solution which has not been widely studied is the effect of the baseline voltage, which is commonly used to prime the meniscus for the subsequent pulse, lowering the response time of the system. However, the upper limit of this input is limited by the transition toward an uncon- trollable regime known as natural pulsation.The natural pulsation regime occurs when the applied volt- age exceeds the threshold for droplet ejection, but falls below the critical value required for a sustained cone-jet. This regime is characterized by an initial deposit followed by the natural repet- itive process of jet breakup, retraction, charge accumulation, and jet impingement [18]. Empirical analysis on the steady state be- havior of this regime has been widely performed, and the re- lationships between jet diameter and pulsation frequency as a function of applied voltage are well established [19]. However, these studies disregard the characteristics of the initial deposi- tion, which differ from steady state behavior. Defining certain aspects of this regime’s initialization allows for the use of natural pulsation voltages as the baseline voltage in pulse printing, which reduces the response time of the system. Specifically, the elapsed time between the voltage pulse and jet impingement provides in- sight into the appropriate design parameters of the voltage input shape. Additionally, the consistency of the initial deposit’s vol- ume following natural breakup indicates the controllability of the system in this state. This paper presents a case study on the relevant time con- stants and volume measurements of the natural pulsation regime with regards to manufacturing applications. The main contri- butions of this work are (1) Identifying the maximum length of time a natural pulsation voltage can be applied until droplet ejec- tion occurs and (2) Characterizing the predictability of the initial droplet size in the natural pulsation regime. The rest of the paper is organized as follows: Section 2 provides descriptions of the experimental setup and methods, Section 3 outlines the experi- mental results, and Section 4 contains concluding arguments and details future work. 2 Materials and Methods 2.1 Experimental Setup All experiments are performed using a custom-built e-jet printer developed by the Barton Research Group. The setup consists of a motion system, a print head, and high-speed imag- ing equipment. For the motion system, a single-axis lift stage (Aerotech, ANT130) is superimposed on a two axis linear stage (Aerotech, Planar DL) to provide controlled X-Y-Z positioning of the silicon wafer substrate. The wafer rests suctioned on an electrically-grounded aluminum disc. A custom 3D printed syringe holder containing high voltage electrical connections is mounted on the print head, where a servomotor controls its Z- axis location (Aerotech, BMS60). Mounted adjacent to the mo- tion system is a high-speed camera (Vision Research, Phantom VEO-410L) and a high intensity coaxial LED light (Advanced Illumination, SL162). The substrate is a silicon wafer with a resistivity of 0.005- 0.02 Ohm-cm. Three glass nozzles with inner diameters of 30 µmare sputter coated with 0.05 nm gold to ensure good conduc- tivity. The printing ink is Norland Optical Adhesive (NOA) 81, 2 Copyright © 2023 by ASME FIGURE 2 : The experimental setup used for printing. a dielectric polymer. The nozzle’s electric potential is generated using a voltage amplifier (TREK, 677B) and controlled with a function generator (RIGOL, DG1032Z), which supplies the triggering mechanism for the high-speed imaging. The voltage waveform is monitored using an oscilloscope (Tektronix, TDS 2024B). The nozzle is positioned 150 µmabove the substrate. The high-speed camera is configured to record at 10,000 Hz to fully capture the jetting dynamics. Due to the chosen frame rate, the sample time is constrained to 741 ms. Because typical pulse printing occurs at time scales of less than 102ms [20], this con- straint does not impact the analysis of the experimental results, and a high voltage pulse of 741 ms is applied to initiate natural pulsation. Each frame has a 1024 by 512 pixel size and is cap- tured with an exposure time of 99 µs. A 100x lens attachment provides a resolution of 0.2µm px. A labeled image of the experi- mental setup is provided in Fig. 2. 2.2 Experimental Procedure As part of the initialization process for each nozzle, DC volt- ages ranging from 1000V to 1200V are applied for several min- utes while the substrate is moved in a raster formation. A con- tinuous jet is maintained throughout the duration of this process, which serves as a method for clearing potential blockages within the nozzle. To record a lower bound for the experimental volt- ages, the applied voltage is gradually increased from zero until initial jet formation. Due to the similarity of initiation voltages, an experimental lower bound of 700 V is chosen for each nozzle. Three trials at increasing increments of 50 V starting from 700 V are recorded until continuous jet behavior was observed. The triggering signal for the high-speed camera is coupled with the applied voltage pulse.2.3 High-Speed Video Image Processing In order to extract volume measurements of the initial deposited droplets, image processing techniques with MATLAB are used to outline the droplet contour in each frame. Minimal user-defined regions are required to assist the algorithms. The computation steps along with their corresponding MATLAB functions are provided below. 1)Convert 3D Grayscale Image to Binary: A locally adaptive threshold ( adaptthresh ) with a tolerance of 0.55 is computed for each frame and used in correspondence with MATLAB’s binary conversion function ( imbinarize ). This step results in the foreground objects (ink and nozzle) appearing black in front of a white background. 2)Apply a Noise Filter: The droplet boundary tracing al- gorithm dictates that the image pixels in the region below the substrate must contain a value of 0. To achieve this requirement, the user defines a point ( drawpoint ) on an image just below the line corresponding to the substrate. This is found by displaying a frame ( imshow ) where one or more droplets have been deposited and identifying a point just below the line of reflection. Once the frames are cropped, a 2-D median filter (medfilt2 ) is applied to reduce the overall noise of each frame. 3)Identify Jet-Substrate Contact: The natural pulsation regime is characterized by cyclic phases of a contiguous ink connection between the nozzle and the substrate followed by the advancement or recession of the jet. When the jet is contacting the substrate, the deposited volume is transient, and volume measurements during this phase require advanced operational procedures. However, the period when the jet is moving above the substrate (whether receding or advancing) defines a constant droplet volume which can be measured. Differentiation of these two phases can be achieved by tracing the interface of the black and white regions of the frames ( bwtraceboundary ) and recording the number of pixels along the boundary. The starting pixel of the boundary tracing is chosen to be the top left corner of the image. Upon application of high voltage, the meniscus retracts toward the substrate, forming a jet, and the length of the boundary increases. The initial frame depicting jet contact with the substrate corresponds to a sharp decline in the boundary length, as the tracing cannot map pixels on the right side of the frame. The instigation of jet breakup then drastically increases the number of traced boundary points. The detection of these abrupt changes ( ischange ) can identify phases of the natural pulsation behavior, and, therefore, define frames when the droplet volume is constant. Sample frames and the progression of the boundary point count are shown in Fig. 3. Note that the sharp changes in the plot provided in Fig. 3(c) correspond to the transition to and from a contiguous jet connecting the nozzle to the substrate. The duration between jet breakup and impingement is known as the contact time of the jet, which directly correlates to the volume of the deposition. 3 Copyright © 2023 by ASME Boundary points(a) Boundary points (b) 0 5 10 15 20 Time (ms)200040006000800010000 12000 Number of Boundary Points Contiguous jet Jet impingement Jet breakup Contact timeAdvancing jetReceding jet (c) FIGURE 3 : Sample frames with traced boundary before (a) and during (b) jet contact with the substrate. (c) Boundary point count progression with labeled regions. 4)Droplet Contour Modelling and Volume Measure- ments: The user defines a rectangle in which the droplet may be found ( drawrectangle ). Boundary points lying within the rectangle constitute the droplet’s contour. The droplet’s horizontal cross section is assumed to be circular, and the overall shape is modelled as a stack of conical frusta with a height of 1 pixel. The volume of each frustum can be summed, as shown in Eq. 1, Vd=n−1 ∑ i=1π 3(R2 i+RiRi+1+R2 i+1) (1) where Vdis the volume of the deposited droplet [ µm3] and Riand Ri+1are the radii of sequential frusta [ µm]. Figure 4 presents a side-by-side comparison of a frame pre- and post-processing. Note that the shaded region in Fig. 4(b)indicates the region modelled by the computer vision algorithm to compute the droplet’s volume. Nozzle Nozzle tip Substrate lineInk droplet Droplet reflection Taylor cone (a) Modelled region (b) FIGURE 4 : (a) Labeled comparison of raw image frame and (b) processed frame used for computer vision algorithm. 3 Results Figure 5(a) presents a box plot of the initial jet impingement times as a function of the applied voltage. As expected, an in- versely proportional relationship exists between these variables. Applying a higher voltage to the nozzle results in a greater charge accumulation rate on the meniscus, and, subsequently, a faster ejection. Additionally, the spread of the impingement times re- duces with voltage. This relationship is likely resultant of the unstable jet formation behavior that exists near the critical volt- age values required for ejection [21]. The distributions in Fig. 5(a) provide insight into the possible shapes of the applied volt- age input. Specifically, a baseline voltage applied for a duration that exceeds the impingement time would result in an undesired ejection. The results imply that a larger range of permissible widths exists for baselines of lower voltage magnitudes. For ex- ample, as observed in Fig. 5(a), reducing the baseline voltage from 750 V to 700 V results in a two fold increase in the im- pingement time, which expands the design space of the input shape. This principle is illustrated in Fig. 6, which depicts a series of high voltage pulses superimposed on baseline voltages of varying magnitudes. Note that the temporal widths of the el- evated baseline voltages ( τ2andτ3) differ in accordance with their respective voltage magnitudes ( V2andV3). To avoid unde- sired droplet ejection while simultaneously reducing the system response time, these widths must be limited to experimentally- determined impingement times. 4 Copyright © 2023 by ASME 700 750 800 850 900 950 DC Voltage (V)1020304050607080Impingement time (ms)DC E-Jet Printing - Average Diameter 30 m(a) 700 750 800 850 900 950 DC Voltage (V)010203040506070Contact time (ms)DC E-Jet Printing - Average Diameter 30 m (b) FIGURE 5 : (a) Summary of the jet impingement times and (b) contact times as a function of applied voltage. Due to the existence of temporal uncertainties for all experi- mental applied voltages, it becomes pertinent to examine the con- sequences of surpassing this time constant. The jet’s contact time provides insight to the volume of the initial deposition. This pa- rameter is presented as a function of applied voltage in the form of a box plot in Fig. 5(b). In contrast to the inverse relationship seen in Fig. 5(a), the mean value and variance of the contact time are observed to increase with voltage. This result concurs with prior expectations, as the applied voltages near the maximum of the experimental range likely fall within a transition region bor- dering the natural pulsation and cone-jet regimes. A box plot displaying these volume measurements is pro- vided in Fig. 7. As expected, these results mimic the function- ally increasing behavior of the contact times seen in Fig. 5(b) and indicate proportionality between the applied voltage and the uncertainty of the initial droplet’s volume. It is evident that a trade-off relationship exists regarding the controllability of e-jet printing in the initial moments of the natural pulsation regime. Reducing the applied baseline volt- V oltage TimeV1 V1V3V2 2τ 3τ Vi= i Baseline V oltageth iτ= i Baseline Pulse WidththHigh V oltagesFIGURE 6 : A sample applied voltage input shape containing a series of baseline and pulsed voltages. 700 750 800 850 900 950 DC Voltage (V)05101520Initial Droplet Volume (pL)DC E-Jet Printing - Average Diameter 30 m FIGURE 7 : Summary of volume measurements of the initial de- position as a function of applied voltage. age allows for a greater range of permissible widths and low volumetric uncertainties, but the temporal characteristics asso- ciated with jet formation and impingement remain difficult to predict. In contrast, a higher baseline voltage provides a faster system response time, but the volumetric analysis of the initial droplet demonstrates the existence of high uncertainties. There- fore, user-defined p