Chapter 5. Conclusions and future work
5.1 Conclusions
We conducted numerical simulations to investigate the effect of actuation conditions on the drop ejection of a printhead (Picojet) of DOD type that is commercially available. According to numerical results of the finite-element simulation, the temporary displacement function of the piezoelectric diaphragm displays a trapezoidal shape with higher-order vibration ignored and is divisible into six stages – supply, refill, forward, pause, backward, and equilibrium. The fluid is assumed to be an isothermal, incompressible Newtonian fluid of constant physical properties – density and viscosity. The dynamics of the drop ejection are governed by these independent parameters: We , s We , f We , b Ds, Df, Db, ∆τp1, ∆τp2 and
Ohnesorge number Oh, in which We represents Weber number, D the maximum displacement of the piezoelectric diaphragm, ∆τ the duration of the different stages of a single transducer pulse and the subscripts s, f, b, p1, and p2 depict supply, forward, backward, refill, and pause stages, respectively.
For the investigation of the forward stage, the flow inertia, i.e. Wef , must be
large enough that a DOD drop can be formed in accordance with intuition. The simulations also show that the volume of the primary drop increases as Df increases.
118
These results are consistent with the fact that the larger is the volume displacement of the ink chamber, the larger is the volume of liquid ejected from the DOD nozzle.
Increasing We might produce an increased velocity of the primary drop. The drop f
velocity slightly increases when the volume of the ejected drop increases. This result is explicable on assuming that an increased volume of the ejected drop might cause a decreased curvature of the liquid interface, thus accounting for the decreased restoring effect of surface tension.
From the investigation of the backward stage, the velocity and the volume of the primary drop seem to depend weakly on the varied conditions of the backward stroke.
The extent of tube invasion by the retracting meniscus is closely related to We and b
τb
∆ . From the investigation of the pause stage, the velocity and the volume of the primary drop remain constant but the formation of the satellite drops tends to be suppressed as ∆τp2 decreases. There is a strong possibility that decreasing ∆τp2
might decrease the length lb of the liquid thread at pinching off and increase the
upper limit lb* for the free thread length without satellite formation. This maximum limit lb* depends strongly on the time tb1 at which the liquid thread pinches off from nozzle outlet, time tb2 at which the free liquid thread breaks up into primary drop and secondary liquid thread and the average speed vr of the retreating thread tail. Moreover, the pinch-off time tb1 and breakup time tb2 are shown to be
119
significantly associated with the waveform of the transducer pulse.
Based on the non-dimensional analysis of the system parameters and variables in the present theoretical models, the effect of liquid viscosity can be related to Ohnesorge number Oh=µ/ ρRnozσ , which measures the important of viscous
force relative to surface tension force. As Oh increases with constant actuation conditions, the pinching-off and breaking-up time of the ejected liquid increase slightly, while the liquid thread length at pinching off decreases slightly. The primary drop volume tends to be constant with Oh. In addition, a drop ejected at larger Oh tends to move at a slower speed. In some cases with larger Oh, drop breakup may not occur and more powerful actuation is required.
In order to investigate the effect of liquid hydrophobicity and nozzle passage curvature on the drop formation process without interference from the complicated geometry of the interior flow channels in ink jet printheads, we designed a system of a nozzle plate connected to a flat-plate piezoelectric material. A numerical model was constructed and validated by the comparison of simulation results with experimental
observation. When the diameter of the orifice equals 34 µm or 24 µm, the liquid strands seem to be expelled continuously and drops with uniform size distribution can be formed in the absence of satellite drops. In contrast, when the orifice diameter
equals 14 µm or 4 µm, a primary drop with a few satellite drops are observed. The
120
drop volume increased and average drop velocity decreased with increasing orifice diameter. Among varied curvatures of the nozzle wall, the linear type seems to have a larger drop velocity, a smaller drop volume and a smaller pinching-off period because of a larger pressure difference between water and ambient air. When the dynamic contact angle was altered from 7.1o to 170o, the drop velocity slightly increased and the volume decreased. The period to pinch off a drop tends to be relatively small when the contact angle is extremely large and small.
The most popular application of ink-jet printheads is to print digital data onto a medium at high resolution. The drop size should hence be as small as practicable, but an ink-jet printhead designed to deliver a small drop size for high resolution undergoes a severe restriction of throughput for an application at poor resolution. A reliable approach to decrease the drop size for one case but not others should hence extend the applicable areas of the specific ink-jet printhead. A prospectively unique capability of piezoelectric printheads is modulation of the drop size with a single transducer pulse having complicated positive and negative parts to manipulate the fluid motion in the nozzle. The results of this work might yield physical insight into the components of the transducer pulse and lead to the development of modulation of the drop size in piezoelectric DOD ink-jet printheads.
121