Literature survey

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An experiment to investigate the fluid mechanics of a drop ejection depends mainly on stroboscopic observation. The basic principle of this method is that the region of interest, in which liquid emerges in the form of a jet that subsequently disintegrates into drops, is illuminated with a pulsed light such as a light-emitting diode (LED). The images of the ejected liquid are recorded with a camera incorporating a charge-coupled device (CCD) associated with a microscope. The stroboscope light is generally synchronized with the CCD camera. Many experimenters have visualized the liquid jet and the formation of a drop from DOD ink-jet printheads ^11-16; for instance, Meinhart et al. ¹⁴ utilized a particle-image-velocimetry system with micrometer resolution to measure

simultaneously the velocity flow field with spatial resolution to 5-10 µm and temporal resolution to 2-5 µs. Fan et al. ¹² assessed the drop quality from a temporal sequence of magnified images recorded with a CCD camera and a stroboscopic technique while varying the nozzle size, voltage signal and liquid properties. Kwon et al. ¹³ developed edge-detection techniques for the jet speed and drop diameter using CCD camera images with a varied trigger interval. Moreover, Dong et al. ¹⁶ used the stroboscopic photography to capture sequential images of the drop ejection process from a piezoelectric ink-jet printhead. In this study, several key stages of DOD drop formation were identified and quantitative analysis of the dynamics of drop formation

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was developed.

The prediction of droplet formation, which can not only validate theoretical models with experimental observation but also provide insight into asymptotic conditions, constitutes a substantial challenge to numerical simulation. Early models failed to predict the temporal evolution of the velocity, shape and trajectory of a drop because models of interfacial physics were inadequate and topology variations were complicated ^17-21. As numerical methods have developed and computing power has advanced, computational fluid dynamics (CFD) has become a promising tool to overcome the limitations of theoretical models. Among diverse approaches, the volume-of-fluid (VOF) method proposed by Hirt and Nichols ²² has proven to be effective for its simplicity and robustness ^23-29. Wu et al. ²⁸ demonstrated the feasibility of the full cycle of ink-jet printing including the ejection, formation and collision of drops against a target substrate with their custom program; employing a finite-difference-based method to solve fluid dynamics and the VOF method to capture the variation of the interface, this program was validated with experimental observation. Liou et al. ²⁵ simulated the ejection of a printhead (SEAJet) by applying commercial CFD software (COMET, StarCD Suite) based on the VOF method to handle free-surface problems. The software discretizes governing equations by means of a finite-volume approach and exploits the continuum-surface-force (CSF) model to

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account for the effect of surface tension; the predicted evolution of the meniscus inside the printhead was compared with published experimental results. Pan et al. ²⁷ used commercial CFD software (Flow-3D) to simulate the drop formation of a drop ejector with a micro-electro-mechanical diaphragm and provided useful information concerning the design of this ejector; the software was tested to be capable of modeling the free-surface problems, employing the finite-volume approach to solve the governing equations of fluid flow and the VOF method to track effectively the interface deformations. Feng ²³ conducted various numerical experiments to find design rules of ink-jet devices utilizing the same software (Flow-3D); the volume, velocity and shape of drops were chosen to evaluate the jet performance. Yang et al. ²⁹ exploited commercial software (CFD-ACE+), also applying the VOF approach for interface tracking to explore numerically the drop ejection of a printhead (Picojet); 17 simulation cases were undertaken to reveal the design concept of the printhead.

Anantharamaiah et al. ³⁰ employed the CFD code from Fluent Inc. to investigate the relationship between the nozzle inlet roundness and the diameter of ejected liquid jet in the applications of hydroentangling. The interfacial flow model used in this study was VOF method along with CSF model to consider the surface tension effect. The paper of Anantharamaiah et al. ³¹ provide extensive discussions of the effect of nozzle geometry on the formation of constricted waterjets, which have an air gap between the

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liquid and nozzle wall. In this study, the VOF method together with CSF model was used as the two-phase flow model. Although other numerical methods have been proposed ^{32, 33}, the VOF methods are considered to be commonly used for the modeling of the drop formation in DOD ink-jet printheads.

The full theoretical model of the piezoelectric DOD ink-jet printhead involves the coupling of structural, electric and interfacial flow fields. The direct coupled-field simulation of this printhead might require substantial computing power and cost. An alternative method, so-called load transfer, coupling multiple fields on applying results from one analysis as load in another analysis, might be effective to simulate the multiphysics of a piezoelectric DOD ink-jet printhead. Several authors 19, 28, 29, 33, 34 have shown the feasibility of the load-transfer method to simulate the full system of

the piezoelectric printhead. Wu et al. ²⁸ used the propagation theory of acoustic waves before the simulation of interfacial flow of piezoelectric ink-jet printing to estimate the temporal variation of pressure imposed at a location upstream from the nozzle outlet as a boundary condition on pressure. Yu et al. ³³ coupled an interfacial flow solver with an equivalent circuit model that transfers the effect of the ink cartridge, supply channel, vibration plate, and piezoelectric actuator into the pressure at the nozzle inflow with a given voltage signal. Kim et al. ³⁴ measured the displacement waveform from a piezoelectric actuator with a laser Doppler vibrometer (LDV); this

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waveform information then served as input data at the piston-moving boundary for the three-dimensional simulation of an ink jet. Chen et al. ¹⁹ used the finite-element software (ANSYS) to determine the temporally dependent averaged moving velocity of the piezoelectric diaphragm; this velocity was imposed as an inflow boundary condition in a drop ejection simulation of an ink-jet printhead. Yang et al. ²⁹ reported that the transient displacement function of the piezoelectric diaphragm determined (with ANSYS) was imposed as a prescribed moving-boundary condition to investigate the drop ejection of a printhead (Picojet).

In competitive industrial printing markets, a commercially available piezoelectric DOD ink-jet printhead (Picojet) is known for its enduring reliability, diverse fluid compatibility and structural durability. This printhead comprises several stainless-steel plates bonded together to form inner flow channels and cavities with ultrasonic bonding, and uses the bending-mode design of a piezoelectric actuator. As a micro-fluidic dispenser, this printhead is capable of discharging up to 18000 drops per second with a discrepancy of drop volume below 10 %^{29, 35}.