A high-resolution high-frequency monolithic top-shooting microinjector ...

0 downloads 0 Views 393KB Size Report
Top-Shooting Microinjector Free of Satellite. Drops—Part I: Concept, Design, and Model. Fan-Gang Tseng, Chang-Jin Kim, and Chih-Ming Ho. Abstract—In this ...
JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 5, OCTOBER 2002

427

A High-Resolution High-Frequency Monolithic Top-Shooting Microinjector Free of Satellite Drops—Part I: Concept, Design, and Model Fan-Gang Tseng, Chang-Jin Kim, and Chih-Ming Ho

Abstract—In this paper, we introduce an innovative microinjector design, featuring a bubble valve, which entails superior droplet ejection characteristics and monolithic fabrication, which allows handling of a wide range of liquids. This new microinjector uses asymmetric bubbles to reduce crosstalk, increase frequency response and eliminate satellite droplets. During a firing, i.e., droplet ejection, the “virtual valve” closes, by growing a thermal bubble in the microchannel, to isolate the microchamber from the liquid supply and neighboring chambers. Between firings, however, the virtual valve opens, by collapsing the bubble, to reduce flow restriction for fast refilling of the microchamber. The use of bubble valves brings about fast and reliable device operation without imposing the significant complication fabrication of physical microvalves would call for. In addition, through a special heater configuration and chamber designs, bubbles surrounding the nozzle cutoff the tail of the droplets being ejected and completely eliminate satellite droplets. A simple one-dimensional model of the operation of the microinjector is used to estimate the bubble formation and liquid refilling. Simulation results show that the reported bubble valve can improve the frequency response at least three times compared with the passive chamber neck design commonly used for commercial devices. [701] Index Terms—Bubble valve, inkjet printing, microinjector, satellite droplet, thermal bubble jet, top shooter.

I. INTRODUCTION

D

ROPLET injectors (or ejectors) have wide application areas, such as inkjet printing [1], [2], biofluid printing, fuel injection [3], drug dosage/micro dosing [4], IC cooling and direct writing. Reliable, high performance and low-cost microinjector arrays are in great demand. High performance for microinjector generally implies high-quality droplets (e.g., no satellite droplets), high-frequency response (over 10 kHz) and high spatial-resolution of nozzles (over 300 dpi). A variety of actuation methods have been reported to eject microdroplets, including thermal bubble [1]–[3], piezoelectric [4], [5], thermal buckling [6], acoustic wave [7] and electrostatic [8]. However, none fulfilled all the three requirements. Thermal bubble Manuscript received June 1, 2001; revised February 20, 2002. This work was supported in part by a grant from the Naval Warfare Center through the Office of Naval Research. Subject Editor N. de Rooij. F.-G. Tseng was with the Mechanical and Aerospace Engineering Department, University of California, Los Angeles, Los Angeles, CA 90095-1597 USA. He is now with the Engineering and System Science Department, National Tsing Hua University, Hsinchu, Taiwan, ROC (e-mail: [email protected]). C.-J. Kim and C.-M. Ho are with the Mechanical and Aerospace Engineering Department, University of California, Los Angeles, Los Angeles, CA 90095-1597 USA (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/JMEMS.2002.802900.

and piezoelectric drive are most mature and common for the commercial inkjet printer [1], [2], [5]. Although commercially successful today, the piezo-based printheads still use bulk piezo material [5], [9] to fabricate inkjet array for enough actuation displacement. Note that the printing resolution has been improved by position controlling of the printhead; the physical resolution of their nozzles is not better than 300 dpi. Electrostatic and thermal buckling means also require large actuator area for the same reason, i.e., to ensure enough displacement of actuation for droplet injection. Their nozzle resolutions and device speeds are highly constrained to typically below 300 dpi and slower than 10 kHz, respectively. On the other hand, acoustic means encounter the problem of precisely controlling the thickness of liquid film for reliable droplet ejection. Among above, only bubble actuation does not have the constraint of actuator displacement, thanks to the bubble freely expanding even in a small actuation area. Therefore, droplet injection by thermally driven bubbles has been one of the most promising means for the application of extremely high resolution (droplet volume smaller than 10 pl, nozzle spatial resolution over 600 dpi), high-speed (over 10 kHz) and low-cost inkjet printhead due to its simplicity (e.g., HP51645A). Capability of very high-resolution array (over 1000 dpi) has been reported [10], [11]. However, some design issues still need to be addressed for the thermal bubble jet to fulfill all three requirements—quality, frequency response, and spatial resolution of droplets. II. DESIGN ISSUES Thermal bubble jets use thermal energy to generate vapor bubbles and employ them as an actuator to eject droplets. Fig. 1 schematically shows a concept of silicon-micromachined highresolution injector based on the principle. A current pulse to the patterned resistor causes the liquid to boil. The expanding bubble functions as a pump and ejects a column of liquid from the chamber through a nozzle. After the bubble collapses, liquid refills the chamber by capillary force. After over 20 years of development [12], thermal bubble jets are enjoying a tremendous commercial success today. However, the demanding requirements of the next generation printers call for further consideration of the following key issues. A. Heat Transfer Issues Most of the commercial thermal bubble jets place heaters directly on a thick substrate [1], [2], [13], losing significant energy to the substrate. Not only it is inefficient, but more im-

1057-7157/02$17.00 © 2002 IEEE

428

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 5, OCTOBER 2002

Fig. 1. Droplet ejection sequence in a thermal bubble jet [3].

portantly, the stray heat raises the overall temperature of the device and limits the operation. In commercial inkjet design, common solutions include adding a thin (1–3 m) insulation layer under the heater [1], [2] or using a poorly conductive material as the substrate (e.g., glass) [14]. However, prevention of heat loss by a thin insulation layer is not so effective and micromachining of glass substrate is rather constrained, not to mention the compatibility problems with IC process. To fast dissipate the residual energy during the cooling cycle, a substrate with a reasonable thermal conductivity is desired. However, a good heat transfer inside the substrate raises a serious problem of “thermal crosstalk” among injectors in a dense array. Compromising among all of the above problems and optimizing the chamber and heater design within the limited choices of materials and tight design constraints are difficult. Ideally, one would like to enhance heat transfer to the vertical direction, either to air or the other side (backside) of the substrate, while minimizing heat transfer to the horizontal direction. B. Hydraulic Crosstalk and Overfilling When inkjet chambers are arranged in a tight array for a high device spatial resolution, they need to share one common liquid supply. As a result, the pressure generated from the firing chamber can affect the menisci at the nozzles of its neighboring chambers, posing “hydraulic crosstalk”. Hydraulic crosstalk makes droplet volume control difficult and even causes unexpected droplet ejection when combined with the thermal crosstalk. Fig. 2(a) illustrates the hydraulic crosstalk. In addition to hydraulic crosstalk, overfilling is another important and related problem. Illustrated in Fig. 2(b), overfilling occurs when liquid fast refills back to chamber after droplet ejection and bubble collapse. Several provisions were reported to address the problem of the hydraulic crosstalk during droplet ejection and the overfill during liquid refilling, such as increasing the chamber length [15], adding a narrow passage (a chamber neck, shown in Fig. 3(a) [16] and placing extra slots as reservoirs (shown in Fig. 3(b) [15]. In the first two designs, the lengthened chamber or the narrowed passage increases the flow resistance into and out of the chamber, producing high pressure drop between the manifold and chamber inside. Although they can reduce

Fig. 2. (a) Crosstalk and (b) overfill.

crosstalk and overfill, the neck or long chamber, unfortunately, slows down the refilling process and thus the period of an ejection cycle, limiting the ejection frequency of the device. The third design of extra slot may reduce some crosstalk problem. However, the extra slot causes meniscus oscillation and as a result, additional time is needed for damping down, again limiting the ejection frequency. What is really desired is a valve mechanism, giving a high flow resistance during ejection to address cross-talk problem, a low resistance during refilling to speed up the refills and then provide a high resistance again at the end of refill to stabilize the meniscus fluctuation in a short time. Indeed, a microvalve has been used despite the added complication in manufacturing processing and operation [17] as well as the limitation the natural frequency of the physical valve poses. We report an elegant solution to this problem, the use of a bubble valve, in this paper. C. Satellite Droplets Satellite droplet formation is one of the most troublesome issues in the top-shooting thermal bubble jet design. The satellite droplets are revealed in Fig. 4(a), which shows the droplet ejection sequence from a commercial inkjet by using the droplet vi-

TSENG et al.: HIGH-RESOLUTION HIGH-FREQUENCY MONOLITHIC TOP-SHOOTING MICROINJECTOR FREE OF SATELLITE DROPS—PART I

429

thermal inkjets, we could not find any droplet speed at which the satellite droplets can be eliminated. We are also not aware of any solution known for the satellite droplet problem of top-shooting thermal bubble inkjets. D. Droplet Size and Initial Speed Limitation The droplet volume commonly used in contemporary commercial high-resolution printing is around 10 pl (27 m in diameter). It usually creates a spot with 30–40 m in diameter on a piece of plain paper. To compete with a laser printer (with spot size around 12 m) or photography (2000–4000 dpi on a 35-mm negative film, giving a spot size 6–12 m on the film), the droplet size needs to be further down to less than 1 pl (12 m spot size). With the materials used in the current commercial inkjet printheads, the maximum water vapor pressure the heater can generate is theoretically around 10–20 atm [19]. With this pressure, the estimated minimum droplet that can be generated by the thermal bubble principle is around 0.07 m in diameter (considering only pressure and surface tension). However, most of the droplets generated by commercial thermal inkjet are larger than 20 m, much larger than the 0.07 m limit, due to the practical limitation in fabrication. In addition to the droplet size limitation, the droplet initial velocity is typically lower than 20 m/s in most of the operation ranges, constrained by the bubble formation speed that the firing heater can sustain. The droplet size and initial velocity highly determine the droplet flying distance (refer to Part II). To obtain enough flying distance, e.g., 1 mm, for printing, a 4- m droplet needs an initial velocity of 20 m/s and a 6- m droplet needs an initial velocity of 10 m/s. It appears not practical to eject a droplet smaller than 1 m into the ambient environment for printing purpose. Noting the resolution of real photo printing, droplets of 12 m in diameter (1 pl in volume) are likely to be small enough in practice. Fig. 3. Provisions to address the problem of crosstalk and overfill. (a) Chamber neck design [16]. (b) Extra open slot design [15].

sualization system developed at UCLA [18]. Each frame of the droplet ejection sequence shows the time after a firing signal, from 50 s to 85 s with 5 s intervals. This typical droplet ejection sequence of commercial bubble jets shows that a long tail separates from the primary droplet and breaks into small satellite droplets. Satellite droplets blur the image in inkjet printing, as shown in Fig. 4(b), a magnified picture of one straight vertical line, i.e., many dots aligned vertically. The blurring comes from the movement of inkjet head. During printing, the inkjet head scans on the paper transversely. After the primary droplet hits the desired location, the satellite droplets arrive on the paper a few s late and hit the paper on the side of the main droplet. In Fig. 4(b), the small extra dots attached to the main ones to the right are the printed images of the satellite droplets. A common attempt to solve this problem is to reduce droplet ejection speed, which may shorten the droplet tail and reduce the break off of the tail from the primary droplet. However, droplets with slow ejection speed suffer from the droplet scattering and the loss of precision in positioning, as a result. Droplet ejection needs a certain minimum energy (for example, 17 J for HP 51626A) to overcome surface tension and viscous force from liquid bath and nozzle wall. After many tests with commercial

E. Frequency Response The frequency response of inkjets is one of the major bottlenecks against increasing printing speed. There are four important time constants related to thermal bubble jets’ frequency response: heating time, bubble growth and collapse time (including cooling) and liquid refilling time. The typical combined time constant from heating to bubble collapse is around 10–60 s, depending on the chamber geometry and does not vary much, i.e., within the same order of magnitude, for different heating and cooling mechanisms. On the other hand, liquid refilling time can vary in 3 orders of magnitude, e.g., from less than 10 s to over 1 s, depending on the refilling path design. In most of the commercial inkjet printhead design, chamber neck [15], elongated chamber channel [14] or physical valve [15] are used to prevent pressure crosstalk problem. However, those designs greatly reduce the refilling time and, as a result, the frequency response. It has become crucial to find a new way to reduce the pressure crosstalk without sacrificing device speed. III. DESIGN OF THE MICROINJECTOR To solve the problems explained above, a new design is proposed. The design is based on the novel concept of a “bubble

430

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 5, OCTOBER 2002

Fig. 4. Satellite drops and the effect on printing. (a) Droplet ejection sequence from an inkjet. (b) A magnified image of a printed vertical line. Note: the blurring of printed image by satellite droplets.

valve” and “droplet tail trimming”, which greatly improves the performance of the thermal bubble jet. The concept is experimentally verified in Part II. A. Prevention of Heat Loss and Thermal Crosstalk In the design of microinjector, the heaters are placed on top of the chamber cover, which is a membrane only 3–4 m thick. Thermal resistance between the heater and the liquid is comparable to that of the usual “heater-at-bottom” design, where the heater is covered with a protective layer anyway. However, thermal resistance to the environment (i.e., heat loss) is dramatically higher for this “heater-on-top” design. Heat loss to air (heater-on-top) is orders-of-magnitude smaller than the loss to silicon substrate (heater-at-bottom)1 . Most of the heat generated from the micro heaters is transferred to the liquid for vapor bubble formation, while the rest is lost to the air and the chamber cover. The heater-on-top design not only gives higher energy efficiency but also reduces thermal crosstalk as it increases the thermal resistance between neighboring chambers. Fig. 5 shows our microinjector schematically. In the microinjector design, liquid is supplied from the backside of the device, through the manifold, into the chamber and droplets are ejected through the nozzle. The heaters are placed above the chamber, instead of at the bottom of the chamber, as described above. Note other differences compared with the one in Fig. 1: deeper and shorter chamber and absence of chamber neck. 1Heat

transfer coefficient, thermal conductivity:

1:57 W/m

k

= 0:026 vs.

k

=

Fig. 5. Micro-injector array.

B. Reduction of Mechanical Crosstalk and Overfill Instead of using a physical chamber neck [e.g., Fig. 3(a)], the concept of a virtual chamber neck is realized by a bubble valve [18]. The bubble valve serves the same function of preventing crosstalk and overfill as the chamber neck but without extending the refill time and sacrificing the ejection frequency. In this new design, bubbles are employed to function not only as a pump but also as a valve regulating the flow resistance between the chamber and the liquid supply. The use of bubbles to regulate flows in microchannels have been conceptually described in [20] and experimentally verified as a valveless micro pumping device [21]. During the ejection phase, a fully-grown bubble

TSENG et al.: HIGH-RESOLUTION HIGH-FREQUENCY MONOLITHIC TOP-SHOOTING MICROINJECTOR FREE OF SATELLITE DROPS—PART I

431

blocks the passage, maintaining high pressure inside chamber and preventing liquid back flow while the second bubble pressurizes the chamber to eject liquid. During the refilling phase, the first bubble collapses first and opens the passage for fast liquid refill. Note the regulation is achieved with no physical moving elements in the system. The following details the operation. The idea of virtual chamber neck can be explained with Fig. 6(a) and (d). Fig. 6(a): It is important to note that the heater at the manifold side is designed narrower than that at the chamber side. When a current pulse goes through these two heaters connected in series, the narrow one generates a bubble faster because of higher power dissipation. The bubble formed under the narrow heater creates a virtual chamber neck, which blocks the liquid passage and isolates chamber as the wide heater starts to generate its own bubble. Expansion of the second bubble transforms into effective liquid ejection because the first bubble blocks the leakage of the liquid from the chamber back to the manifold. Blocking of the leakage also prevents the hydraulic crosstalk with neighboring chambers. Fig. 6(d): After the droplet ejection, the bubble at the manifold side collapses first, opening the virtual camber neck. Liquid refills the chamber fast thanks to the enlarged channel entrance. In addition to isolating active chambers with virtual necks, the connection of each chamber to a manifold with cross section at least 10 times larger also helps reduce crosstalk among chambers, owing to the manifold’s ability to absorb the individual pressure pulses. The combination of virtual chamber neck and manifold connection can efficiently reduce crosstalk and overfill problem. C. Droplet Tail Trimming for Satellite Droplet Elimination Satellite droplets are formed as the long tail of the ejected droplet is broken up by surface tension instability. An obvious method to eliminate satellite droplets is to cut the droplet tail short. However, in thermal bubble jets, a droplet leaves the nozzle within only tens of micro-seconds. In this short time period, it is difficult to implement a mechanism that physically cuts off the tail. It would be more practical if an extra bubble isolates the portion of liquid near the nozzle from the rest in the chamber, as has been proposed for side shooters [22]. In our top shooter design, the multiple bubbles introduced to increase the ejection frequency are strategically positioned to cut off the tail in a different way than that for side shooters [23]. The concept is schematically shown in Fig. 6(b) and 6(c). The heaters on top of the chamber surround the nozzle, as shown in Fig. 5. As groups of bubbles grow and eventually merge under the nozzle, the tail of the ejected droplet dries off in a very short time, from several to tens of microseconds, efficiently preventing the formation of a long tail. The shortened tail trailing the droplet is then drawn back to the leading droplet by surface tension, thus forms only one droplet completely free of satellites. D. Improvement of Frequency Response Different from the physical chamber neck of conventional design, the microinjector uses a bubble to create a virtual neck and

Fig. 6. Principle of microinjector. (a) First set of bubbles generate for virtual neck formation. (b) Droplet ejection. (c) Bubbles meet to cut off long droplet column. (d) Virtual neck colapses for liquid fast refill. The function of virtual cyhamber neck can be decribed by (a) and (d) and the droplet tail cutting by (b) and (c). Virtual neck increases ejection frequency, while tail trimming eliminates satellite droplets.

regulate the flow into and out of the microchamber. Without the physical chamber neck that would slow down the refilling process, the microinjector’s frequency response can be greatly improved. Frequency response as fast as over 35 kHz has been verified with microinjectors of 10 m nozzle, as detailed in Part II. The performance will be improved further if the design is

432

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 5, OCTOBER 2002

optimized. A first-order analysis and comparison of the time responses for microinjector with ideal heating time sequence and for a conventional inkjet are provided in the next section of modeling. E. Micro Injector Array Fig. 5 shows the schematic diagram of an array of microinjectors we developed on a silicon wafer. Notice that each chamber is connected directly to a common liquid manifold with no necking in between in order to minimize the flow resistance. The manifold also absorbs pressure perturbation during chamber firing to help reduce crosstalk among chambers. The heaters are designed on top of the chamber and surround the nozzle. There are three important aspects in the heater design: 1) heater on the chamber top is for preventing heat loss to substrate; 2) heater in different width supports the function of virtual chamber neck; and 3) heater is patterned around the nozzle so that bubbles cut off droplet tail. Note that the narrow heaters on the entrance side of the chamber and wide heaters on the other side of the nozzle are connected serially in our design to simplify the fabrication and operation. However, they can be separated if one wishes to test different firing systems and allow maximum operation flexibility. In addition to the heater design, the depth of the chamber is also important and affects the timing for droplet tail cutting, the damping coefficient in the liquid passage and the droplet volume. In this design, there is no theoretical limitation on the number of chambers connected as an array. The size of an array is limited by the material strength and wafer size. We have successfully fabricated 300 microinjectors in a 30-mm long array on a 4-in diameter silicon wafer. Among those fabricated and tested, two different sizes of the microinjector are reported in this paper, one with nozzle diameter 40 m and the other with 10 m. The spatial resolution of these microinjectors is 200 and 800 dpi, respectively, which is limited by the width a chamber occupies (chamber, nozzle, heater and chamber barrier). IV. MODELING AND ESTIMATION There are four important steps involved in the time response of the injector: 1) bubble generation, 2) bubble growth and droplet ejection, 3) bubble collapse, and 4) liquid refill. The total time constant is the sum of the above four time constants. To estimate the frequency response of our microinjector, the information for bubble formation are adopted from Asai [24] and a simple one dimensional model is used for the estimation of refilling process. A. Bubble Formation Under High-Heat Flux There have been many approaches [19], [24]–[28] on the modeling of bubble dynamics for inkject printers. Asai’s simulation and experiment results [24] showed that the bubble generation time, bubble life time (including bubble growth and collapse) and maximum bubble height are inversely proportional to the amount of heat flux, i.e., the higher the heat flux, the shorter the bubble generation and life time and the smaller the bubble maximum volume. Typical bubble

Fig. 7. Model of micro-injector with different chamber designs: (a) without chamber neck, (b) with physical neck, and (c) with virtual valve.

generation time, bubble life time and maximum bubble volume for commercial water-based inkjets are 4–15 s, 24–45 s m , respectively, depending on the input and 1.5–5 10 heat flux, from 6.5 to 1.62 W/nozzle. The minimum bubble lifetime (the sum of the first three time constants) depends on the maximum heat flux on the heater and the maximum thermal stress the surrounding material can accommodate. For droplets in the diameter of 50–60 m, a total bubble time constant of 30–60 s is typical. B. Liquid Refilling Time While the bubble formation time depends on heat flux and heater material, liquid refilling time is determined by the geometry of liquid passage into and out of the microchamber. To estimate the effect of the proposed virtual valve on the improvement of the droplet injection frequency, three types of liquid passages, shown in Fig. 7, are evaluated. They are a straight chamber without neck [see Fig. 7(a)], chamber with physical neck [see Fig. 7(b)] and chamber with virtual neck [see Fig. 7(c)]. As shown in Fig. 7(a) for the micro channel flow, three forces—inertial, wall shear stress and surface tension of meniscus—exerted on the refilling liquid, are balanced during

TSENG et al.: HIGH-RESOLUTION HIGH-FREQUENCY MONOLITHIC TOP-SHOOTING MICROINJECTOR FREE OF SATELLITE DROPS—PART I

Fig. 8.

Simulated time response for different designs of microinjector: (a) without chamber neck, (b) with physical chamber neck, and (c) with virtual valve.

the liquid refilling process. The one dimensional momentum equation of this system can be expressed as -

and is the surface tension force from the liquid menuscus at the nozzle. Using the concept of equivalent mass by Beasley [29], liquid mass can be further expressed as

(1)

is the average flow velocity in the microchannel, is the total mass of the liquid in the channel, is the coefficient of damping force from channel wall drag

Here

433

(1.1) is the density of liquid and , and are channel where height, width, and length, respectively. is the distance from

434

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 5, OCTOBER 2002

Fig. 9. Simulated time response of different virtual-valve operation, compared to Fig. 8(c), for microinjector with virtual valve: (a) same starting time but shorter valve-on period, (b) same valve-on period but earlier starting time, and (c) same valve-on period but later starting time.

chamber inlet along the chamber length and is the cross section in the chamber region close to nozzle. The damping coefficient in the rectangular channel with varying channel width and height along the channel length can be expressed by using Kyser’s [30] approximation:

and (1.3) The surface tension can be expressed as -

(1.2)

(1.4)

is the liquid surface tension, is the radius of where meniscus sphere, is the radius of nozzle and is the distance

TSENG et al.: HIGH-RESOLUTION HIGH-FREQUENCY MONOLITHIC TOP-SHOOTING MICROINJECTOR FREE OF SATELLITE DROPS—PART I

from the nozzle plane to the meniscus lowest position. Here we assume that the meniscus keeps the shape of a portion of sphere all the time. From the flow continuity equation, the change of gas volume under the nozzle is equal to the liquid flow-in rate: (2) is the volume between the nozzle plane and the meniscus surface. The meniscus volume and channel crosss section can be futher expressed as: (2.1) Notice the volumn can be negative by the definition. By combining (1) and (2), we can have a nonlinear ordinary differential equation (ODE) with respect to meniscus position as follow: (3) where

and the initial conditions are and

(4)

Here we use the parameters of the microinjector with 40 m diameter nozzle to demonstrate the time response of the three configurations in Fig. 7. The chamber width( ), height( ) and length( ) are 140, 20, 210, m, respectively. Water is the ) of working fluid and the properties used are density ( ) of 1 10 Ns m and surface 1000 kg/m , viscosity ( ) of 0.073 N/m. The influence of temperature to tension ( the liquid properties is negelected. The physical chamber neck used in the model has the length, width and height of 70, 30, 20, m, respectively. In the modeling of virtual valve, we set up a high damping value in the microchamber system during the time period of virtual valve operation to simulate the liquid passage blocking effect from bubble expansion. The nonlinear second order one dimensional ODE was then solved by MATLAB. The simulated results for different chamber designs are shown in Fig. 8. Fig. 8(a) illustrates the simulated result of the chamber design without chamber neck, i.e., Fig. 7(a). The meniscus has a large overshoot and several cycles of oscillations before damping down to the ground level, posing overshoot problem and lengthening the waiting time for the next cycle. The total time to quiet down for the refill process is around 200 s. Fig. 8(b) shows the result of the design with physical chamber neck, i.e., Fig. 7(b). The overshoot problem is fully resolved, however, the rising time is long ( 90 s), compared to the rising time ( 22 s) in Fig. 8(a). Fig. 8(c) shows the time response from the design with virtual neck by bubble valve. The valve-on time is between 22 and 62 s with optimized valve starting. Through the valve control, the liquid refill is as fast as the low flow resistance of the under-damped system in Fig. 8(a), yet later the desired high damping is provided to overcome the overshoot problem as in Fig. 8(b), as the

435

valve closes at the desired moment. The time constant, around 22 s, is almost four times shorter than that of commercial inkjet by the traditional design of physical neck [see Fig. 7(b)]. To understand the sensitivity of the starting time and valve-on period of the bubble valve to the damping effect, three different cases of operation are modeled, as shown in Fig. 9. Fig. 9(a) shows the case with very short valve-on period, 3 s, but with the same bubble starting time as in Fig. 8(c). It can be clearly seen that there is no significant response change, suggesting that the damping effect is not sensitive to the bubble lifetime as long as the bubble lifetime is longer than a critical time period, for example, 3 s in the above case. However, in the following two cases, one with the valve starting time 1 s earlier [see Fig. 9(b)] and the other with the valve starting time 1 s later [see Fig. 9(c)], the oscillation of meniscus seems “much” more pronounced. These results led us to conclude that the starting time point of the bubble valve is very important for the liquid damping control. In practical virtual valve design, the bubble starting time can be easily controlled by electronic signal within 1 s resolution. According to the above modeling, the total time constant, including bubble life time and liquid refilling time of our microinjector with 40 m nozzle can be as short as 50–60 s, 3–4 times shorter than that of the commercial design with physical neck. Although the bubble firing time in our fabricated microinjector with 40 m diameter has not been optimized yet, the tested frequency response, 15 kHz ( 67 s/cycle), is already reasonably close to the above simulation. For the microinjectors with smaller chamber and nozzle design, the frequency response is even higher. Microinjector with 10 m diameter nozzle has been operated at the frequency of droplet ejection over 35 kHz. V. SUMMARY The innovative designs of a microinjector have been proposed. The microinjector employs new concepts of “bubble valve” and “droplet tail cutting” to reduce the problems of crosstalk, overfill and satellite droplet formation and enhance the frequency response of droplet ejection. Simulation results have demonstrated that the microinjector can have frequency response at least 3 times higher than those of conventional designs with similar nozzle size. ACKNOWLEDGMENT The authors appreciate the helps from Prof. C. Shih, D. Williams, C.-W. Chiu and Prof. H. J. Sung. REFERENCES [1] I. Endo, Y. Sato, S. Saito, T. Nakagiri, S. Ohno, and Canon, Inc., “Bubble jet recording method and apparatus in which a heating element generates bubbles in multiple liquid flow paths to project droplets,” U.S. Pat. 4 740 796, Apr. 1988. [2] B. J. keefe, M. F. Ho, K. J. Courian, S. W. Steinfield, W. D. Chiders, E. R. Tappon, K. E. Trucba, T. I. Chapman, W. R. Knight, J. G. Mortz, and Hewlett-Packard Company, “Inkjet printhead architecture for high speed and high resolution printing,” U. S. Pat. 5 648 805, Oct. 6, 1994. [3] F.-G Tseng, C. Linder, C.-J Kim, and C.-M Ho, “Control of mixing with micro-injectors for combustion application,” in Proc. MEMS, ASME Int. Mechanical Engineering Congress and Exposition, vol. 59, DSC, Atlanta, GA, Nov. 1996, pp. 183–187.

436

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 5, OCTOBER 2002

[4] M. Fahndrich, B. Hochwind, and A. Zollner, “Fluid dynamics in micro dosing actuators,” in Tech. Dig. 8th Int. Conf. Solid-State Sensors and Actuators (Transducers ’95), Stockholm, Sweden, June 1995, pp. 295–298. [5] S. Sakai, A. Kobayashi, T. Naka, S. Yonekubo, T. Mitsuzawa, S. Shinada, and Seiko Epson Corporation, “Inkjet Recording Head,” European Patent no. 0 573 055A2, April 1993. [6] S. Hirata, Y. Ishii, H. Matoba, and T. Inui, “An ink-jet head using diaphragm micro-actuator,” in Proc. IEEE Micro Electro Mechanical Systems Workshop, San Diego, CA, Feb. 1996, pp. 418–423. [7] X. Zhu, E. Tran, W. Wang, E. S. Kim, and S. Y. Lee, “Micromachined acoustic-wave liquid ejector,” in Tech. Dig. Solid-State Sensor and Actuator Workshop, Hilton Head Island, SC, June 1996, pp. 280–282. [8] S. Kamisuki, T. Hagata, C. Tezuka, Y. Nose, M. Fujii, and M. Atobe, “A low power, small, electrostatically-driven commercial inkjet head,” in Proc. IEEE Micro Electro Mechanical Systems, Heidelberg, Germany, January 1998, pp. 63–68. [9] Y. Erna, H. Fujimoto, T. Amana, and Rohm Co., Ltd., “Inkjet print head and inkjet printer,” U. S. Pat. 5 541 603, August 1993. [10] P. Krause, E. Obermeier, and W. Wehl, “Backshooter—A new smart micromachined single-chip inkjet printhead,” in Tech. Dig. 8th Int. Conf. Solid-State Sensors and Actuators (Transducers ’95), Stockholm, Sweden, June 1995, pp. 325–328. [11] J.-K. Chen and K. D. Wise, “A high-resolution silicon monolithic nozzle array for inkjet printing,” in Tech. Dig. 8th Int. Conf. Solid-State Sensors and Actuators (Transducers ’95), Stockholm, Sweden, June 1995, pp. 321–324. [12] W. L. Buehner, J. D. Hill, T. H. Williams, and J. W. Woods, “Application of ink jet technology to a word processing output printer,” IBM J. Res. Dev., vol. 21, no. 1, pp. 2–9, Jan. 1977. [13] P. A. Torpey, R. G. Markham, and Xerox Corporation, “Thermal inkjet printhead,” U.S. Pat. 4 638 337, January 1987. [14] E. V. Bhaskar and J. S. Aden, “Development of the thin-film structure for the thinkjet printhead,” Hewlett-Packard J., pp. 27–33, May 1985. [15] N. J. Nielsen, “History of thinkjet printhead development-preventing hydraulic crosstalk,” Hewlett-Packard J., p. 9, May 1985. [16] W. A. Buskirk, D. E. hankleman, S. T. Hall, P. H. Kanarek, R. N. Low, K. E. Trueba, and R. Van de Poll, “Development of a high-resolution thermal inkjet printhead,” Hewlett-Packard J., pp. 55–61, Oct. 1988. [17] R. S. Karz, J. F. O’Neill, and J. J. Daniele, “Inkjet printhead with ink flow directing valves,” U.S. Pat. 5 278 585, Jan. 11, 1994. [18] F.-G. Tseng, C.-J. Kim, and C.-M. Ho, “A novel microinjector with virtual chamber neck,” in Proc. IEEE Micro Electro Mechanical Systems, Heidelberg, Germany, Jan. 1998, pp. 57–62. [19] A. Mirfakhraee, “Growth and Collapse of Vapor Bubbles in Ink-Jet Printers,” Ph.D. dissertation, University of California, Berkeley, CA, 1989. [20] F. T. Brown, “Potential building blocks for microhydraulic actuators,” in Proc. Micromechanical Systems, ASME Winter Annual Meeting, vol. 46, DSC, 1993, pp. 21–33. [21] T. K. Jun and C.-J. Kim, “Valveless pumping using traversing vapor bubbles in microchannels,” J. Appl. Phys., vol. 83, no. 11, pp. 5658–5664, June 1998. [22] Z.-Z. Yu, “Dual heaters in a thermal ink jet channel,” Xerox Disclosure J., vol. 16, no. 2, pp. 91–92, Mar./Apr. 1991. [23] F.-G. Tseng, C.-J. Kim, and C.-M. Ho, “A microinjector free of satellite drops and characterization of the ejected droplets,” in Micro-ElectroMechanical Syst., ASME IMECE, vol. 66, DSC, Nov. 1998, pp. 89–95. [24] A. Asai, T. Hara, and I. Endo, “One dimensional model of bubble growth and liquid flow in bubble jet printers,” Jpn. J. Appl. Phys., vol. 26, no. 10, pp. 1794–1801, October 1987. [25] A. Asai, “Bubble dynamics in boiling under high heat flux pulse heating,” ASME J. Heat Transfer, vol. 113, pp. 973–979, Nov. 1991. , “Three-Dimensional calculation of bubble growth and drop ejec[26] tion in a bubble jet printer,” ASME J. Fluids Eng., vol. 114, pp. 638–641, Dec. 1992. [27] , “Application of the nucleation theory to the design of bubble jet printers,” J. Appl. Phys., vol. 28, no. 5, pp. 909–915, May 1989. [28] P. H. Chen, W. C. Chen, and S. H. Chang, “Bubble growth and ink ejection process of a thermal ink jet printhead,” Int. J. Mech. Sci., vol. 39, no. 6, pp. 683–695, 1997. [29] J. D. Beasley, “Model for fluid ejection and refill in an impulse drive jet,” Society of Photographic Scientists and Engineers, vol. 21, no. 2, pp. 78–82, Mar./Apr. 1977. [30] E. L. Kyser, L. F. Collins, and N. Herbert, “Design of an impulse ink jet,” J. Appl. Photogr. Eng., vol. 7, no. 3, pp. 73–79, June 1981.

Fan-Gang Tseng was born in Taichung, Taiwan, ROC, in 1967. He received the B.S. degree in power mechanical engineering from National Tsing Hua University, Taiwan, in 1989 and the M.S. degree from the Institute of Applied Mechanics in National Taiwan University, Taiwan, in 1991. In 1998, he received the Ph.D. degree in mechanical engineering from the University of California, Los Angeles, with an emphasis on MEMS technology. His Ph.D. dissertation was on the design, fabrication and applications of a novel micro droplet injector system. This novel system is currently under technology transfer for commercialization. After one year as a Senior Engineer at the University of Southern California (USC)/Information Science Institute working on a new microfabrication process (EFAB), he has been an Assistant Professor with the Engineering and System Science Department of National Tsing-Hua University, Taiwan, since August 1999. His interests are in the fields of bio-MEMS and microfluidics. He has received five patents, wrote one chapter in MEMS Handbook (Boca Ratone, FL: CRC), published more than 40 technical papers in MEMS, bio-MEMS, and fluid mechanics related fields. Dr. Tseng received one Best Paper Award and Co-Chaired in the technique sessions of IS M, Hong Kong, in 2000 and Transducers’01, Munich, Germany, in 2001. He has been consulted by more than four U.S.-based and three Taiwanbased companies, as well as three Taiwan-based organizations.

Chang-Jin “CJ” Kim received the B.S. degree from Seoul National University, Korea, and the M.S. degree from Iowa State University, Ames, with the Graduate Research Excellence Award. He received the Ph.D. degree in mechanical engineering from the University of California at Berkeley in 1991. Upon joining the faculty at the University of California at Los Angeles (UCLA), in 1993, he has developed several MEMS courses and established a MEMS doctorate major field in the Mechanical and Aerospace Engineering Department. His research is in MEMS and nanotechnology, including design and fabrication of micro/nanostructures, actuators and systems, with a recent focus on the use of surface tension for microdevices. Prof. Kim served as Chairman of the Micromechanical Systems Panel of the ASME DSC Division in 1996 and co-organized the MEMS Symposia between 1994 and 1996 for the ASME International Mechanical Engineering Congress & Exposition. He also organized the 1996 ASME Satellite Broadcast Program on MEMS. He served as General Co-Chairman of the 6th IEEE International Conference on Emerging Technologies and Factory Automation and served in the Technical Program Committees of the IEEE MEMS Workshop (1998) and the SPIE Symposium on Micromachining and Microfabrication (1998–2000). Currently, he is serving in the U.S. Army Science Board, the Technical Program Committee of Transducers’01, the Executive Committee of ASME MEMS Subdivision and as a Subject Editor for the JOURNAL OF MICROELECTROMECHANICAL SYSTEMS. He is the recipient of the TRW Outstanding Young Teacher Award and the NSF CAREER Award.

Chih-Ming Ho received the Ph.D. degree in mechanics from The Johns Hopkins University, Baltimore, MD. He is the Ben Rich—Lockheed Martin Professor of the Mechanical and Aerospace Engineering Department at UCLA and was the Director of the Center for Micro Systems. He has published one hundred eighty papers in the areas of MEMS, micro fluidics, turbulence and unsteady aerodynamics. Professor Ho was elected a member of National Academy of Engineering and a member of Academia Sinica. He was elected Fellow of the American Institute of Aeronautics and Astronautics and Fellow of the American Physical Society. He received six patents in MEMS based transducers, optical sensor and in nozzle design. He was the Chair of Fluid Dynamics Division of APS in 1995–1996. He is a member of the IEEE/ASME JMEMS coordinating Committee. He was an Associate Editor of the ASME Journal of Fluids Engineering and an Associate Editor of the AIAA Journal.