Motivation and objectives

As the preceding review illustrates, most previous work has focused on the influence of the diameter of the nozzle exit, the electrically driven signal and the

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properties of the dispensed liquid on the drop ejection of ink-jet printheads. The quality of ink-jet printers is closely related by the volume of a primary drop, the creation of an unwanted secondary drop, known as the satellite drop and asymmetric drop formation. The primary drop volume determines the resolution of the printed pattern on a substrate or the quantity of microfluidic deposition; however, the occurrence of the satellite drop would disturb the primary drop charging and degrade the printing resolution by impacting the substrate in undesired locations. The asymmetric drop formation skews the drop trajectory and causes drop misregistration at designated sites, thereby decreasing the accuracy of drop placement. The primary drop volume tends to be affected by the nozzle size and electrically driven signal, and the formation of the satellite drop by the signal waveform and liquid properties.

Moreover, the signal waveform and the roundness of nozzle opening seem to have a great effect on the skew phenomena of drop ejection. In most DOD applications, the voltage waveform to drive the piezoelectric actuator is a square-wave pulse or a succession of two square-wave pulses. The effect of the voltage signal on drop ejection has been investigated experimentally and numerically. From an experimental point of view, authors ^{36, 37} focused mainly on the influence of the maximum amplitude and the frequency of voltage signals on the drop-ejection behavior and on seeking an optimal range of operating conditions in which satellite drops fail to form,

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based on an iterative method. Because of machine restrictions, the variable range of operation conditions was constrained. In contrast numerical calculations in research ^23,

38 focused on a fundamental understanding of the fluid mechanics of DOD ink-jet

printing that in general involves the elucidation of a competition between the flow directed toward the nozzle outlet and that directed away from it, based on a simplified printhead configuration and an ideally imposed flow rate or pressure pulse as a function of time upstream of the nozzle outlet.

Using numerical simulations we have systematically divided a single transducer pulse with a so-called bipolar waveform composed of two square-wave pulses in succession – the first positive and the second negative – into components and investigated the effects of these components and their various combinations on the ejection of a drop in terms of volume, speed and period of decomposition of the primary drop and the formation of satellite drops. According to Rayleigh’s pioneering works⁶, a liquid jet emanating from a nozzle tends to form drops at some distance from the nozzle due to the instability created by the existence of liquid surface tension.

This instability leading to the breakup of the liquid jet and then drop formations originate from the growth of an infinitesimal disturbance along the liquid jet, which reduces the surface area and energy. Following Rayleigh⁶, there is the most rapidly growing disturbance which sets the sized drops formed under one excitation of

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external noises and reduces the surface area of the liquid jet the most. The environmental disturbances produced at the nozzle and convected down the jet tend to be random. Therefore, the drop formation frequency and the distance from the nozzle where drops first appear alter at random. According to previous researches^{6, 7}, the formation of drops can be forced to happen at a well-defined frequency and distance from the nozzle by flustering the jet periodically with sufficient power in order that random environmental disturbances are ignorable. One way to perturb the liquid jet periodically is to introduce a periodic pressure change at the liquid side of the nozzle.

In the drop formation of a piezoelectric ink jet printhead, the pressure variation in the nozzle can be driven by the electrically controlled solid wall movements. This motivates us to investigate the effect of a transducer pulse on the drop formation and microfluidic control of a piezoelectric ink jet printhead.

The literature review also shows that little is known about the effect of the wetting condition of the nozzle wall and its curvature on drop formation through the ink-jet print heads. Furthermore, when an ink-jet print head is fabricated in progressively smaller size for the purpose of enhancing resolution, the capillary effects including the vapor- liquid interfacial tension and the wetting condition on the solid wall, coupled with curvature of that wall, play an increasingly important role on the drop ejection. In the present work we performed numerical simulations to

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investigate the detailed process of formation of a droplet when considering various dynamic contact angles (various dynamic contact-angle patterns represent varied wetting conditions) and curvature of the nozzle wall. To simplify the models stemming from the complicated geometry of the interior flow channels in ink-jet print heads, we adopted a model of a nozzle plate connected with a flat-plate piezoelectric material; we compared the numerical results with experimental measurements to validate the present computer code. The results of this work might yield suggestions for the design of ink-jet printheads and contribute to a fundamental understanding of the fluid mechanics of DOD ink-jet printing.

The rest of the thesis is organized as follows. Chapter 2 describes the theoretical models and computational methods used in this study. Chapter 3 presents computational results and discusses the effect of a transducer pulse on the DOD drop formation. Chapter 4 considers the influence of liquid hydrophobicity and nozzle passage curvature on a drop ejection process. In this chapter, firstly, the physical models and solution methods are described. Secondly, the description of the experimental setup and conditions are given. Next, a comparison of numerical results with experimental observations is presented. Finally, numerical results and a discussion of the effect of the orifice diameter, the curvature of the nozzle passage and wall wetting conditions on the drop ejection are provided. Chapter 5 presents the

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conclusions and future work.

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