Patent Publication Number: US-8991954-B2

Title: Fluid ejection device with fluid displacement actuator and related methods

Description:
BACKGROUND 
     Fluid ejection devices in inkjet printers provide drop-on-demand ejection of fluid drops. Inkjet printers produce images by ejecting ink drops through a plurality of nozzles onto a print medium, such as a sheet of paper. The nozzles are typically arranged in one or more arrays, such that properly sequenced ejection of ink drops from the nozzles causes characters or other images to be printed on the print medium as the printhead and the print medium move relative to each other. In a specific example, a thermal inkjet printhead ejects drops from a nozzle by passing electrical current through a heating element to generate heat and vaporize a small portion of the fluid within a firing chamber. Some of the fluid displaced by the vapor bubble is ejected from the nozzle. In another example, a piezoelectric inkjet printhead uses a piezoelectric material actuator to generate pressure pulses that force ink drops out of a nozzle. 
     Although inkjet printers provide high print quality at reasonable cost, their continued improvement depends in part on overcoming various operational challenges. For example, the release of air bubbles from the ink during printing can cause problems such as ink flow blockage, insufficient pressure to eject drops, and mis-directed drops. Pigment-ink vehicle separation (PIVS) is another problem that can occur when using pigment-based inks. PIVS is typically a result of water evaporation from ink in the nozzle area and pigment concentration depletion in ink near the nozzle area due to a higher affinity of pigment to water. During periods of storage or non-use, pigment particles can also settle or crash out of the ink vehicle which can impede or block ink flow to the firing chambers and nozzles in the printhead. Other factors related to “decap”, such as evaporation of water or solvent can cause PIVS and viscous ink plug formation. Decap is the amount of time inkjet nozzles can remain uncapped and exposed to ambient environments without causing degradation in the ejected ink drops. Effects of decap can alter drop trajectories, velocities, shapes and colors, all of which can negatively impact the print quality of an inkjet printer. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present embodiments will now be described, by way of example, with reference to the accompanying drawings, in which: 
         FIG. 1  illustrates an inkjet printing system suitable for incorporating a fluid ejection device and implementing methods of circulating fluid in a fluid ejection device as disclosed herein, according to an embodiment; 
         FIG. 2  shows a partial cross-sectional side view of an example fluid ejection device, according to an embodiment; 
         FIG. 3   a  shows a fluid ejection device in a normal drop ejection mode, according to an embodiment; 
         FIG. 3   b  shows the fluid ejection device in a normal fluid refill mode, according to an embodiment; 
         FIG. 3   c  shows a graph of an example voltage waveform (V) applied to actuators to achieve actuator deflections (X) that generate drop ejections and corresponding fluid refills, according to an embodiment; 
         FIG. 4   a  shows a fluid ejection device in a normal drop ejection mode with actuators deflecting into a fluidic channel in forward pumping strokes that generate compressive fluid displacements within the channel, according to an embodiment; 
         FIG. 4   b  shows a fluid ejection device in a normal fluid refill mode with actuators back to an initial or resting state, according to an embodiment; 
         FIG. 4   c  shows a graph of an example voltage waveform (V) applied to actuators to achieve actuator deflections (X) that generate drop ejections and corresponding fluid refills, according to an embodiment; 
         FIGS. 5   a  and  5   b  show a cross-sectional view of a fluid ejection device with fluid displacement actuators operating in a single actuator pumping mode and a graph of example voltage waveforms (V) applied to the actuators, according to embodiments; 
         FIG. 6  shows a cross-sectional view of a fluid ejection device with fluid displacement actuators operating in an alternating multi-pulse actuation mode, according to an embodiment; 
         FIG. 7  shows a cross-sectional view of a fluid ejection device with fluid displacement actuators operating in an alternating multi-pulse actuation mode, according to an embodiment; 
         FIG. 8  shows a cross-sectional view of a fluid ejection device with fluid displacement actuators operating in a simultaneous multi-pulse actuation mode, according to an embodiment; 
         FIG. 9  shows a cross-sectional view of a fluid ejection device with fluid displacement actuators operating in a simultaneous multi-pulse actuation mode, according to an embodiment; 
         FIG. 10  shows a cross-sectional view of a fluid ejection device with fluid displacement actuators operating in a simultaneous in-phase actuation mode, according to an embodiment; 
         FIG. 11  shows a flowchart of an example method of circulating fluid in a fluid ejection device, according to an embodiment; and 
         FIG. 12  shows a flowchart of an example method of circulating fluid in a fluid ejection device, according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Overview of Problem and Solution 
     As noted above, various challenges have yet to be overcome in the development of inkjet printing systems. For example, inkjet printheads used in such systems sometimes have problems with ink blockage and/or clogging. One cause of ink blockage is an excess of air that accumulates as air bubbles in the printhead. When ink is exposed to air, such as while the ink is stored in an ink reservoir, additional air dissolves into the ink. The subsequent action of ejecting ink drops from the firing chamber of the printhead releases excess air from the ink which then accumulates as air bubbles. The bubbles move from the firing chamber to other areas of the printhead where they can block the flow of ink to the printhead and within the printhead. Bubbles in the chamber absorb pressure, reducing the force on the fluid pushed through the nozzle which reduces drop speed or prevents ejection. 
     Pigment-based inks can also cause ink blockage or clogging in printheads. Inkjet printing systems use pigment-based inks and dye-based inks, and while there are advantages and disadvantages with both types of ink, pigment-based inks are generally preferred. In dye-based inks the dye particles are dissolved in liquid so the ink tends to soak deeper into the paper. This makes dye-based ink less efficient and it can reduce the image quality as the ink bleeds at the edges of the image. Pigment-based inks, by contrast, consist of an ink vehicle and high concentrations of insoluble pigment particles coated with a dispersant that enables the particles to remain suspended in the ink vehicle. This helps pigment inks stay more on the surface of the paper rather than soaking into the paper. Pigment ink is therefore more efficient than dye ink because less ink is needed to create the same color intensity in a printed image. Pigment inks also tend to be more durable and permanent than dye inks as they smear less than dye inks when they encounter water. 
     One drawback with pigment-based inks, however, is that ink blockage can occur in the inkjet printhead due to factors such as prolonged storage and other environmental extremes that can result in poor out-of-box performance of inkjet pens. Inkjet pens have a printhead affixed at one end that is internally coupled to an ink supply. The ink supply may be self-contained within the printhead assembly or it may reside on the printer outside the pen and be coupled to the printhead through the printhead assembly. Over long periods of storage, gravitational effects on the large pigment particles, random fluctuations, and/or degradation of the dispersant can cause pigment agglomeration, settling or crashing. The build-up of pigment particles in one location can impede or completely block ink flow to the firing chambers and nozzles in the printhead, resulting in poor out-of-box performance by the printhead and reduced image quality from the printer. Other factors such as evaporation of water and solvent from the ink can also contribute to PIVS and/or increased ink viscosity and viscous plug formation, which can decrease decap performance and prevent immediate printing after periods of non-use. 
     Previous solutions have primarily involved servicing printheads before and after their use, as well as using various types of external pumps for circulating the ink through the printhead. For example, printheads are typically capped during non-use to prevent nozzles from clogging with dried ink. Prior to their use, nozzles can also be primed by spitting ink through them or using the external pump to purge the printhead with a continuous flow of ink. Drawbacks to these solutions include the inability to print immediately (i.e., on demand) due to the servicing time, and an increase in the total cost of ownership due to the consumption of ink during servicing. The use of external pumps for circulating ink through the printhead is typically cumbersome and expensive, involving elaborate pressure regulators to maintain backpressure at the nozzle entrance. Accordingly, decap performance, PIVS, the accumulation of air and particulates, and other causes of ink blockage and/or clogging in inkjet printing systems continue to be fundamental issues that can degrade overall print quality and increase ownership costs, manufacturing costs, or both. 
     Embodiments of the present disclosure reduce ink blockage and/or clogging in inkjet printing systems generally through the use of piezoelectric and other types of mechanically controllable fluid actuators that provide micro-circulation of fluid within fluidic channels and/or chambers of fluid ejection devices (e.g., inkjet printheads). Fluid actuators located asymmetrically (i.e., off-center, or eccentrically) within a fluidic channel, and a controller, enable directional fluid flow through and within the fluidic channels by controlling the durations of forward and reverse actuation strokes (i.e., pump strokes) that generate compressive fluid displacements (i.e., on forward pump strokes) and expansive or tensile fluid displacements (i.e., on reverse pump strokes). 
     In one embodiment, a fluid ejection device includes a fluidic channel having an inlet, an outlet and a nozzle. A first fluid displacement actuator is located asymmetrically within the channel between the inlet and the nozzle. A second fluid displacement actuator is located asymmetrically within the channel between the outlet and the nozzle. A controller controls fluid flow through the channel by generating compressive and expansive fluid displacements of different durations from at least one actuator. 
     In one embodiment, a method of circulating fluid in a fluid ejection device includes generating compressive and expansive fluid displacements of different durations from a first actuator located asymmetrically within a fluidic channel between an inlet and a nozzle, while generating no fluid displacements from a second actuator located asymmetrically within the channel between the nozzle and an outlet. In one implementation, the method includes generating compressive and expansive fluid displacements of different durations from the second actuator while generating no fluid displacements from the first actuator. In another implementation, the method includes alternating activation of the first and second actuators to generate compressive and expansive fluid displacements from both actuators. 
     In one embodiment, a method of circulating fluid in a fluid ejection device includes simultaneously activating a first and second actuator to generate compressive and expansive fluid displacements, where the first and second actuators alternate between compressive and expansive fluid displacements such that they do not generate compressive or expansive fluid displacements at the same time. The first actuator is located asymmetrically within a fluidic channel between an inlet and a nozzle, and the second actuator is located asymmetrically within the channel between the nozzle and an outlet. A nozzle and a chamber are located between the actuators, and the simultaneous activation of the actuators creates a fluidic flow back and forth between the actuators. In one implementation, simultaneously activating the first and second actuator includes activating the first and second actuators to generate concurrent compressive fluid displacements having different compressive displacement magnitudes to eject a fluid drop from the nozzle and create a net directional fluid flow through the channel. 
     Illustrative Embodiments 
       FIG. 1  illustrates an inkjet printing system  100  suitable for incorporating a fluid ejection device and implementing methods of circulating fluid in a fluid ejection device as disclosed herein, according to an embodiment of the disclosure. In this embodiment, a fluid ejection device  114  is disclosed as a fluid drop jetting printhead  114 . Inkjet printing system  100  includes an inkjet printhead assembly  102 , an ink supply assembly  104 , a mounting assembly  106 , a media transport assembly  108 , an electronic controller  110 , and at least one power supply  112  that provides power to the various electrical components of inkjet printing system  100 . Inkjet printhead assembly  102  includes at least one printhead  114  that ejects drops of ink through a plurality of orifices or nozzles  116  toward a print medium  118  so as to print onto print medium  118 . Print media  118  can be any type of suitable sheet or roll material, such as paper, card stock, transparencies, Mylar, polyester, plywood, foam board, fabric, canvas, and the like. Nozzles  116  are typically arranged in one or more columns or arrays such that properly sequenced ejection of ink from nozzles  116  causes characters, symbols, and/or other graphics or images to be printed on print media  118  as inkjet printhead assembly  102  and print media  118  are moved relative to each other. 
     Ink supply assembly  104  supplies fluid ink to printhead assembly  102  from an ink storage reservoir  120  through an interface connection, such as a supply tube. The reservoir  120  may be removed, replaced, and/or refilled. In one embodiment, as shown in  FIG. 1   a , ink supply assembly  104  and inkjet printhead assembly  102  form a one-way ink delivery system. In a one-way ink delivery system, substantially all of the ink supplied to inkjet printhead assembly  102  is consumed during printing. In another embodiment, as shown in  FIG. 1   b , ink supply assembly  104  and inkjet printhead assembly  102  form a recirculating ink delivery system. In a recirculating ink delivery system, only a portion of the ink supplied to printhead assembly  102  is consumed during printing. Ink not consumed during printing is returned to ink supply assembly  104 . 
     In one embodiment, ink supply assembly  104  includes pumps and pressure regulators (not specifically illustrated), enabling ink supply assembly  104  to supply ink to printhead assembly  102  under pressure. In one embodiment, ink is supplied to printhead assembly  102  through an ink conditioning assembly  105 . Conditioning in the ink conditioning assembly  105  can include filtering, pre-heating, pressure surge absorption, and degassing. During normal operation of printing system  100 , ink is drawn under negative pressure from the printhead assembly  102  to the ink supply assembly  104 . The pressure difference between the inlet and outlet to the printhead assembly  102  provides an appropriate backpressure at the nozzles  116 , which is usually on the order of between negative 1″ and negative 10″ of H2O. 
     Mounting assembly  106  positions inkjet printhead assembly  102  relative to media transport assembly  108 , and media transport assembly  108  positions print media  118  relative to inkjet printhead assembly  102 . Thus, a print zone  122  is defined adjacent to nozzles  116  in an area between inkjet printhead assembly  102  and print media  118 . In one embodiment, inkjet printhead assembly  102  is a scanning type printhead assembly. As such, mounting assembly  106  includes a carriage for moving inkjet printhead assembly  102  relative to media transport assembly  108  to scan print media  118 . In another embodiment, inkjet printhead assembly  102  is a non-scanning type printhead assembly. As such, mounting assembly  106  fixes inkjet printhead assembly  102  at a prescribed position relative to media transport assembly  108  while media transport assembly  108  positions print media  118  relative to inkjet printhead assembly  102 . 
     Electronic printer controller  110  typically includes a processor, firmware, software, one or more memory components including volatile and no-volatile memory components, and other printer electronics for communicating with and controlling inkjet printhead assembly  102 , mounting assembly  106 , and media transport assembly  108 . Electronic controller  110  receives data  124  from a host system, such as a computer, and temporarily stores data  124  in a memory. Typically, data  124  is sent to inkjet printing system  100  along an electronic, infrared, optical, or other information transfer path. Data  124  represents, for example, a document and/or file to be printed. As such, data  124  forms a print job for inkjet printing system  100  and includes one or more print job commands and/or command parameters. 
     In one embodiment, electronic printer controller  110  controls inkjet printhead assembly  102  for ejection of ink drops from nozzles  116 . Thus, electronic controller  110  defines a pattern of ejected ink drops which form characters, symbols, and/or other graphics or images on print media  118 . The pattern of ejected ink drops is determined by the print job commands and/or command parameters. In one embodiment, electronic controller  110  includes software instruction modules stored in a memory and executable on controller  110  (i.e., a processor of controller  110 ) to control the operation of one or more fluid displacement actuators integrated within a fluid ejection device  114 . The software instruction modules include single actuation module  126 , multi-pulse actuation module  128 , in-chamber circulation module  130  and drop-eject circulation module  132 . In general, modules  126 ,  128 ,  130  and  132  execute on controller  110  to control the timing, duration and amplitude of compressive and expansive fluid displacements (i.e., forward and reverse pumping strokes, respectively) generated by the fluid displacement actuators in a fluid ejection device  114 . Execution of modules  126 ,  128 ,  130  and  132  on controller  110  controls the direction, rate and timing of fluid flow within fluid ejection devices  114 . 
     In the described embodiments, inkjet printing system  100  is a drop-on-demand piezoelectric inkjet printing system where a fluid ejection device  114  comprises a piezoelectric inkjet (PIJ) printhead  114 . The PIJ printhead  114  includes a multilayer MEMS die stack that includes thin film piezoelectric fluid displacement actuators with control and drive circuitry. The actuators are controlled to generate fluid displacements within fluidic channels and/or chambers. The fluid displacements can force fluid drops out of chambers through nozzles  116 , as well as generate net directional fluid flow through the channels and/or back-and-forth fluid movement within chambers. In one implementation, inkjet printhead assembly  102  includes a single PIJ printhead  114 . In another implementation, inkjet printhead assembly  102  includes a wide array of PIJ printheads  114 . 
     Although fluid ejection device  114  is described herein as a PIJ printhead  114  having piezoelectric fluid displacement actuators, the fluid ejection device  114  is not limited to this specific implementation. Other types of fluid ejection devices  114  implementing a variety of other types of fluid displacement actuators are contemplated. For example, fluid ejection devices  114  may implement electrostatic (MEMS) actuators, mechanical/impact driven actuators, voice coil actuators, magneto-strictive drive actuators, and so on. 
       FIG. 2  shows a partial cross-sectional side view of an example fluid ejection device  114 , according to an embodiment of the disclosure. A blown-up and simplified portion of the fluid ejection device  114   a , discussed below with reference to  FIGS. 3-10 , is set off in  FIG. 2  with dotted lines. In general, fluid ejection device  114  includes a die stack  200  with multiple die layers that each have different functionality. The layers in the die stack  200  include a first (i.e., bottom) substrate die  202 , a second circuit die  204  (or ASIC die), a third actuator/chamber die  206 , a fourth cap die  208 , and a fifth nozzle layer  210  (or nozzle plate). In some embodiments, the cap die  208  and nozzle layer  210  are integrated as a single layer. There is also usually a non-wetting layer (not shown) on top of the nozzle layer  210  that includes a hydrophobic coating to help prevent ink puddling around nozzles  116 . Each layer in the die stack  200  is typically formed of silicon, except for the non-wetting layer and sometimes the nozzle layer  210 . In some embodiments, the nozzle layer  210  may be formed of stainless steel or a durable and chemically inert polymer such as polyimide or SU8. The layers are bonded together with a chemically inert adhesive such as epoxy (not shown). In the illustrated embodiment, the die layers have fluid passageways such as slots, channels, or holes for conducting ink to and from pressure chambers  212 . Each pressure chamber  212  includes a first fluid feed hole  214  and a second fluid feed hole  216  located in the floor  218  of the chamber (i.e., opposite the nozzle-side of the chamber) that are in fluid communication with an ink distribution manifold that includes first fluid manifold  220  and second fluid manifold  222 . The floor  218  of the pressure chamber  212  is formed by the surface of the circuit layer  204 . The first and second fluid feed holes  214  and  216  are on opposite sides of the floor  218  of the chamber  212  where they pierce the circuit layer  204  die and enable ink to be circulated through the chamber  212 . Fluid displacement actuators  224  (i.e., piezoelectric actuators) are on a flexible membrane that serves as a roof to the chamber  212  and is located opposite the chamber floor  218 . Thus, the fluid displacement actuators  224  are located on the same side of the chamber  212  as are the nozzles  116  (i.e., on the roof or top-side of the chamber). 
     The bottom substrate die  202  includes fluidic passageways  226  through which fluid is able to flow to and from pressure chambers  212  via first and second fluid manifolds  220  and  222 . Substrate die  202  supports a thin compliance film  228  configured to alleviate pressure surges from pulsing fluid flows through the fluid distribution manifold due to start-up transients and fluid ejections in adjacent nozzles, for example. The compliance film  228  spans a gap in the substrate die  202  that forms a cavity or air space  230  on the backside of the compliance to allow it to expand freely in response to fluid pressure surges in the manifold. 
     Circuit die  204  is the second die in die stack  200  and is located above the substrate die  202 . Circuit die  204  includes the fluid distribution manifold that comprises the first and second fluid manifolds  220  and  222 . The first fluid manifold  220  provides fluid flow to and from chamber  212  via the first fluid feed hole  214 , while the second fluid feed hole  216  allows fluid to exit the chamber  212  into the second fluid manifold  222 . Circuit die  204  also includes fluid bypass channels  232  that permit some fluid coming into the first fluid manifold  220  to bypass the pressure chamber  212  and flow directly into the second fluid manifold  222  through the bypass  232 . Circuit die  204  includes CMOS electrical circuitry  234  implemented in an ASIC  234  and fabricated on its upper surface adjacent the actuator/chamber die  206 . ASIC  234  includes ejection control circuitry that controls the pressure pulsing of fluid displacement actuators  224  (i.e., piezoelectric actuators). Circuit die  204  also includes piezoelectric actuator drive circuitry/transistors  236  (e.g., FETs) fabricated on the edge of the die  204  outside of bond wires  238 . Drive transistors  236  are controlled (i.e., turned on and off) by control circuitry in ASIC  234 . 
     The next layer in die stack  200  located above the circuit die  204  is the actuator/chamber die  206  (“actuator die  206 ”, hereinafter). The actuator die  206  is adhered to circuit die  204  and includes pressure chambers  212  having chamber floors  218  that comprise the adjacent circuit die  204 . As noted above, the chamber floor  218  additionally comprises control circuitry such as ASIC  234  fabricated on circuit die  204  which forms the chamber floor  218 . Actuator die  206  additionally includes a thin-film, flexible membrane  240  such as silicon dioxide, located opposite the chamber floor  218  that serves as the roof of the chamber. Above and adhered to the flexible membrane  240  are fluid displacement actuators  224 . In the present embodiment, fluid displacement actuators  224  include a thin-film piezoelectric material such as a piezo-ceramic material that stresses mechanically in response to an applied electrical voltage. When activated, piezoelectric actuator  224  physically expands or contracts which causes the laminate of piezoceramic and membrane  240  to flex. This flexing displaces fluid in the chamber  212  generating pressure waves in the pressure chamber  212  that eject fluid drops through the nozzle  116  and/or circulate fluid within and through the chamber  212  and first and second fluid feed holes  214  and  216 . The flexible membrane  240  and fluid displacement actuator  224  (piezoelectric actuator  224 ) are split by descender  242  that extends between the pressure chamber  212  and nozzle  116 . Thus, the fluid displacement actuator  224  is a split actuator  224  having a fluid displacement actuator  224 , or segment of fluid displacement actuator  224 , on each side of the chamber  212 . 
     The cap die  208  is adhered above the actuator die  206  and forms a sealed cap cavity  244  over piezoelectric actuator  224  that encapsulates and protects fluid displacement actuators  224 . Cap die  208  includes the descender  242  noted above, which is a channel in the cap die  208  that extends between the pressure chamber  212  and nozzle  116  that enables fluid to travel from the chamber  212  and out of the nozzle  116  during drop ejection events caused by pressure waves from fluid displacement actuator  224 . The nozzle layer  210 , or nozzle plate, is adhered to the top of cap die  208  and has nozzles  116  formed therein. 
       FIG. 3   a  shows a blown-up and simplified portion of a cross-sectional view of a fluid ejection device  114   a  as in  FIG. 2 , in a normal drop ejection mode, according to an embodiment of the disclosure. In this embodiment, both fluid displacement actuators  224  operate simultaneously with sufficient outward (i.e., convex) deflection and displacement to eject fluid drops of desired speed and volume from the pressure chamber  212  and through nozzle  116 . Both fluid displacement actuators  224  deflect outwardly in forward pumping strokes that temporarily reduce the volume in and around pressure chamber  212 , generating compressive fluid displacements. Pressure waves from the simultaneous compressive fluid displacements of both actuators  224  cause fluid to eject from nozzle  116 , as well as create fluid flow through the first and second fluid feed holes  214  and  216  into manifolds  220  and  222 , respectively (as indicated by fluid flow arrows). 
       FIG. 3   b  shows a blown-up and simplified portion of a cross-sectional view of a fluid ejection device  114   a  in a normal fluid refill mode, according to an embodiment of the disclosure. In this embodiment, a simultaneous reverse or inward deflection of the actuators  224  back to their flat or neutral state draws fluid back into the pressure chamber  212  to refill the chamber in preparation for the next drop ejection. In some implementations, the reverse or inward deflection of the actuators  224  deflects the actuators  224  past their flat or neutral state and up into the cap cavity  244  in a concave deflection. As shown in  FIG. 3   b , both fluid displacement actuators  224  have deflected back to their initial flat or neutral state (i.e., resting state). The deflection back to the initial state retracts the actuators  224  back out of the space in and around pressure chamber  212  in a reverse pumping stroke that increases the volume in the chamber area and generates expansive fluid displacements. The expansive fluid displacements create fluid flow back into the chamber  212  through the first and second fluid feed holes  214  from manifolds  220  and  222 , respectively (as indicated by fluid flow arrows), refilling the chamber  212  with fluid in preparation for the next drop ejection event. During normal drop ejections and fluid refills as shown in FIGS.  3   a  and  3   b , no micro-circulation of fluid occurs other than the movement of fluid to refill the pressure chamber  212 . 
       FIG. 3   c  shows a graph  302  of an example voltage waveform (V) applied to the actuators  224  to achieve the actuator deflections (X) shown in  FIGS. 3   a  and  3   b  that generate drop ejections and the corresponding fluid refills, according to an embodiment of the disclosure. When the applied voltage increases, the actuator  224  deflects in an outward (i.e., convex) deflection that generates a compressive fluid displacement (i.e., the fluid is displaced as it is compressed within the area in and around chamber  212 ). When the applied voltage decreases, the actuator  224  deflects back to its initial flat or neutral state (i.e., resting state) which generates an expansive fluid displacement (i.e., the fluid is displaced as it is pulled back into the increasing volume in and around chamber  212 ). The dotted line voltage waveform in  FIG. 3   c  represents an alternate voltage drive waveform whose negative voltage swing deflects the actuator  224  inward (i.e., concave) past its normal resting state and into the cap cavity  244  of the cap die  208  (see  FIG. 2 ), temporarily increasing the volume in and around chamber  212  further, and generating a greater expansive fluid displacement. Thus, the dotted line voltage waveform drives the actuator  224  to deflect outward into the channel  500  generating a compressive fluid displacement, and then back past its normal resting position in an opposite deflection that extends the actuator  224  up into the cap cavity  244 , generating a greater expansive fluid displacement. Although not illustrated by the voltage waveform of  FIG. 3   c , whenever a piezoelectric actuator is deflected above the flat or neutral position (i.e., concave shape), the voltage is actually much lower than for deflections of the actuator into the chamber (whether for pumping or recirculation). This is to prevent electric fields acting against the polarization of the piezoceramic from degrading the polarization (depoling) which can lessen subsequent deflections, degrading the printing and pumping performance. 
     Although fluid displacement actuators  224  are discussed throughout as being located on the nozzle-side of the chamber  212  (i.e., in the cap die layer  208  on the same side of the chamber  212  as nozzle  116 ), in another embodiment shown in  FIG. 4 , the actuators  224  can be located on the circuit die layer  204  (see  FIG. 2 ) which is opposite the nozzle side. In yet another embodiment (not shown), fluid displacement actuators  224  can be located on both the nozzle-side of the chamber  212  and on the side opposite the nozzle  116 .  FIG. 4  shows a simplified cross-sectional view of a fluid ejection device  114   a  with fluid displacement actuators  224  located on the circuit die layer  204 , opposite the nozzle  116 , according to an embodiment of the disclosure. 
     In  FIG. 4   a  the fluid ejection device  114   a  is shown in a normal drop ejection mode similar to that discussed regarding  FIG. 3   a , with actuators  224  deflecting in outward (i.e., convex) deflections or forward pumping strokes that generate compressive fluid displacements, according to an embodiment of the disclosure. In  FIG. 4   b  the fluid ejection device  114   a  is shown in a normal fluid refill mode similar to that discussed regarding  FIG. 3   b , with actuators  224  deflected back to an initial, flat or neutral state (i.e., resting state), according to an embodiment of the disclosure. The actuators have retracted back in a reverse pumping stroke that generates expansive fluid displacements, refilling the chamber  212  with fluid. 
       FIG. 4   c  shows a graph  400  of an example voltage waveform (V) applied to the actuators  224  to achieve the actuator deflections (X) shown in  FIGS. 4   a  and  4   b  that generate drop ejections and the corresponding fluid refills, according to an embodiment of the disclosure. When the applied voltage increases, it causes an outward (i.e., convex) deflection in the actuator  224  that generates a compressive fluid displacement, and when the applied voltage decreases, it causes an inward (i.e., concave) deflection in the actuator  224  back to its initial, flat or neutral state, generating an expansive fluid displacement. The dotted line voltage waveform in  FIG. 4   c  represents an alternate voltage drive waveform whose negative voltage swing deflects the actuator  224  past its normal resting state and into a cavity (not shown) in the circuit layer  204 , temporarily increasing the volume in and around the chamber  212  and generating an expansive fluid displacement. Thus, the dotted line voltage waveform drives the actuator  224  to deflect outward, generating a compressive fluid displacement, and then back past its normal resting position in an opposite deflection that extends the actuator  224  into the circuit layer  204 , generating an expansive fluid displacement. As noted above with respect to  FIGS. 3   a  and  3   b , during normal drop ejections and fluid refills as shown in  FIGS. 4   a  and  4   b , no micro-circulation of fluid occurs other than the movement of fluid to refill the pressure chamber  212 . 
       FIGS. 5-10  illustrate modes of operation of fluid displacement actuators  224  that provide micro-circulation of fluid within fluidic channels and/or chambers of fluid ejection devices  114  (e.g., inkjet printheads). In general, fluid actuators  224  located asymmetrically (i.e., off-center, or eccentrically) within a fluidic channel, and that are controlled (e.g., by a controller  110 ) to generate compressive and expansive fluid displacements whose durations are asymmetric, function both as fluid drop ejectors to eject fluid drops through nozzles  116  as well as fluid circulation elements (i.e., pumps) to circulate fluid through and within fluidic channels. Accordingly, to facilitate this description, a fluidic channel  500  is defined and shown within the fluid ejection device  114   a  for each of  FIGS. 5-10 . Fluidic channel  500  includes the fluidic volume within fluid ejection device  114   a  that extends from the first fluid manifold  220  at the first fluid feed hole  214  around to the second fluid manifold  222  at the second fluid feed hole  216 . The chamber  212  is part of the fluidic channel  500 , and the fluidic channel  500  runs through chamber  212 . Thus, references herein to the fluidic channel  500  also include the chamber  212  as part and parcel of the channel  500 . Each of the two fluid displacement actuators  224  is located in the fluid channel  500  asymmetrically (i.e., off-center, or eccentrically) with respect to the length of the channel  500 . The chamber  212  is located between the two actuators  224 . 
       FIG. 5  shows a simplified cross-sectional view of a fluid ejection device  114   a  with fluid displacement actuators  224  operating in a single actuator pumping mode, according to an embodiment of the disclosure. In both  FIGS. 5   a  and  5   b , the single actuator  224  on the right side of the figures is arbitrarily shown and discussed as being the actuator operating as a fluidic pump to achieve net fluid flow through channel  500 . The opposite flow effect is achieved when the single actuator  224  on the left side of the figures operates as the fluidic pump. Controller  110  controls the single actuator pumping mode operation of the actuator  224  of  FIG. 5  by execution of software instructions in the single actuation module  126 . Accordingly, controller  110  through execution of module  126  determines which actuator  224  (on the left or the right) operates at any given time to provide a single actuator fluid pumping effect.  FIGS. 5   a  and  5   b  also show a graph of an example voltage waveform (V) applied to the actuator  224  to achieve the illustrated actuator deflections (X) that generate the pumping effect and the resulting net fluid flow through the channel  500  shown by the fluid flow direction arrows. The large X at the top of nozzle  116  is intended to indicate that there is no fluid flow through the nozzle  116 . 
     In general, an inertial pumping mechanism enables a pumping effect from a fluid displacement actuator  224  in a fluidic channel  500  based on two factors. These factors are the asymmetric (i.e., off-center, or eccentric) placement of the actuator  224  in the channel  500  with respect to the length of the channel, and the asymmetric operation of the actuator  224 . As shown in  FIG. 5 , each of the two fluid displacement actuators  224  is located asymmetrically (i.e., off-center, or eccentrically) in the channel  500  with respect to the length of the channel. This asymmetric actuator placement, along with asymmetric operation of the actuator  224  (i.e., control of the timing, duration and amplitude of fluid displacements), enable the inertial pumping mechanism of the actuator  224 . 
     Referring generally to  FIGS. 5   a  and  5   b , the asymmetric location of the actuator  224  in the fluidic channel  500  creates a short side of the channel  500  that extends from the first fluid feed hole  214  to the actuator  224 , and a long side of the channel  500  that extends from the actuator  224  to the second fluid feed hole  216 . The asymmetric location of the actuator  224  within the channel  500  creates an inertial mechanism that drives fluidic diodicity (net fluid flow) within the channel  500 . A fluidic displacement from the actuator  224  generates a wave propagating within the channel  500  that pushes fluid in two opposite directions. The more massive part of the fluid contained in the longer side of the channel  500  has larger mechanical inertia at the end of a forward fluid actuator pump stroke (i.e., deflection of the actuator  224  into the channel  500  causing a compressive fluidic displacement). Therefore, this larger body of fluid reverses direction more slowly than the fluid in the shorter side of the channel  500 . The fluid in the shorter side of the channel  500  has more time to pick up the mechanical momentum during the reverse fluid actuator pump stroke (i.e., deflection of the actuator  224  back to its initial resting state or further, causing an expansive fluidic displacement). Thus, at the end of the reverse stroke the fluid in the shorter side of the channel  500  has larger mechanical momentum than the fluid in the longer side of the channel  500 . As a result, the net fluidic flow moves in the direction from the shorter side of the channel  500  to the longer side of the channel  500 , as indicated by the black direction arrows in  FIGS. 5   a  and  5   b . The net fluid flow is a consequence of the non-equal inertial properties of two fluidic elements (i.e., the short and long sides of the channel  500 ). 
     The asymmetric operation of the actuator  224  within the channel  500  is the second factor that enables the inertial pumping mechanism of the fluid displacement actuator  224 . The operation of the actuator  224  on the right side of fluid ejection device  114   a  in  FIG. 5   a  shows a shorter compressive displacement (i.e., the displacement has lesser duration with more deflection of the actuator  224  into the channel  500 ) and a longer expansive displacement (i.e., the displacement is longer in duration with less deflection of the actuator  224  out of the channel  500 ) of the actuator  224 . In one embodiment, the asymmetric operation of the actuator  224  is controlled by controller  110  through the conjugated ramp voltage waveform in graph  502 . Although similar conjugated ramp voltage waveforms are discussed throughout as controlling the asymmetric operation of actuators  224 , controlling the operation of the actuators  224  in an asymmetric manner can be achieved using other types of drive waveforms. The dotted line arrows in  FIG. 5   a  between the actuator  224  and the conjugated ramp voltage waveform in graph  502  show that the stronger compressive displacement is associated with a voltage change that is temporally short and more steeply sloped, while the smaller expansive displacement is associated with a voltage change that is temporally longer and gently sloped. The durations and amplitudes of the waveforms control the durations and magnitudes of the displacements from the actuator  224 . Thus, voltage drive waveforms having asymmetric durations and amplitudes controlled by controller  110  drive asymmetric operation of the actuator  224 . With this manner of asymmetric operation of actuator  224 , the direction of net fluid flow through the channel  500  is from the short side at the first fluid feed hole  214  toward the long side at the second fluid feed hole  216 . Note that if this same manner of asymmetric operation is implemented with respect to the actuator  224  on the left side in  FIG. 5   a , the direction of net fluid flow through the channel  500  will be reversed. 
     The actuator  224  in  FIG. 5   b  on the right side of fluid ejection device  114   a  is shown operating in an opposite manner than that shown in  FIG. 5   a . That is, the operation of the actuator  224  on the right side of  FIG. 5   b  shows a longer compressive displacement (i.e., the displacement is longer in duration with less deflection of the actuator  224  into the channel  500 ) and a shorter expansive displacement (i.e., the displacement is shorter with more deflection of the actuator  224  out of the channel  500 ) of the actuator  224 . The conjugated ramp voltage waveform in graph  502  and dotted line arrows show that the longer/weaker compressive displacement is associated with a voltage change that is temporally long and gently sloped, while the smaller expansive displacement is associated with a voltage change that is temporally shorter and steeply sloped. With this manner of asymmetric operation of actuator  224 , the direction of net fluid flow through the channel  500  is reversed from that shown in  FIG. 5   a . The direction of net fluid flow through the channel  500  is from the long side at the second fluid feed hole  216  toward the short side at the first fluid feed hole  214 . Note that if this same manner of asymmetric operation is implemented with respect to the actuator  224  on the left side in  FIG. 5   a , the direction of net fluid flow through the channel  500  will be reversed. 
       FIG. 6  shows a simplified cross-sectional view of a fluid ejection device  114   a  with fluid displacement actuators  224  operating in an alternating multi-pulse actuation mode, according to an embodiment of the disclosure. The multi-pulse actuation module  128  executing on controller  110  controls the actuators  224  in a multi-pulse actuation to activate the actuators in different compressive and expansive fluid displacement combinations. The multi-pulse actuation provides a double pumping action that results in stronger net directional fluid flow through channel  500 . 
     As shown in  FIG. 6 , the multi-pulse actuation module  128  controls the right and left actuators  224  so that they are activated in an alternating manner. For example, first the left side actuator generates a compressive fluid displacement and an expansive fluid displacement. The stronger compressive displacement and larger deflection of the left actuator is associated (by dotted arrow lines) with a voltage change in the conjugated ramp voltage waveform of graph  600  that is temporally shorter and more steeply sloped, while the expansive displacement and lesser deflection of the left actuator is associated with a voltage change that is temporally longer and more gradually sloped. As mentioned in the discussion of  FIG. 5  above, this operation of the left actuator results in net fluid flow through the channel  500  in a direction from the short side of channel  500  (with respect to the left actuator) at the second fluid feed hole  216  toward the long side at the first fluid feed hole  214 . 
     After a time delay during which the left side actuator is activated, the multi-pulse actuation module  128  activates the right side actuator to generate a compressive fluid displacement and an expansive fluid displacement. The time delay is at least long enough in duration to encompass the activation of the left actuator, but may in some embodiments be longer in duration such that activation of the right side actuator does not begin directly after activation of the left side actuator. Graph  600  shows the stronger expansive displacement of the right actuator is associated (by dotted arrow lines) with a voltage change that is temporally shorter and more steeply sloped than the compressive displacement, which is associated with a voltage change that is temporally longer and more gradually sloped. As mentioned in the discussion of  FIG. 5  above, this operation of the right side actuator results in net fluid flow through the channel  500  in a direction from the long side of channel  500  (with respect to the right actuator) at the second fluid feed hole  216  toward the short side at the first fluid feed hole  214 . The double action pumping from the left and right side actuators in a phase defined by graph  600  and the following equation result in a stronger net fluid flow through channel  500  than is available when only one actuator operates as a pump:
 
Time delay: t=d/v  
         (v: circulation flow rate/velocity; d: mean distance between left &amp; right actuators)
 
Phase delay: φ=2π t/T  
   (T: actuation period=1/(actuation frequency))       

     The multi-pulse actuation module  128  controls the right and left actuators  224  and actuation conditions (e.g., duration, amplitude, frequency) to control fluid flow through the channel  500 , and first and second fluid feed holes  214  and  216 , in either direction. While only one example is discussed, a number of different operational combinations for this multi-pulse mode are available. 
       FIG. 7  shows a simplified cross-sectional view of a fluid ejection device  114   a  with fluid displacement actuators  224  operating in an alternating multi-pulse actuation mode, according to an embodiment of the disclosure. In this embodiment, the multi-pulse actuation module  128  executing on controller  110  controls the actuators  224  in a multi-pulse actuation that activates the left and right actuators in an alternating manner that has fluid displacements that are opposite to those discussed regarding  FIG. 6 . Thus, the multi-pulse actuation provides a double pumping action that results in strong net directional fluid flow through channel  500  in the opposite direction than in the  FIG. 6  embodiment. 
     As shown in graph  700  of  FIG. 7 , the multi-pulse actuation module  128  controls the right and left actuators  224  so that they are activated in an alternating manner. However, in the  FIG. 7  embodiment, the expansive and compressive fluid displacements are reversed.  FIG. 7  shows a stronger expansive displacement and larger deflection of the left actuator associated (by dotted arrow lines) with a voltage change that is temporally shorter and more steeply sloped.  FIG. 7  shows a weaker compressive displacement and smaller deflection of the left actuator associated (by dotted arrow lines) with a voltage change that is temporally longer and gradually sloped. This operation of the left side actuator results in net fluid flow through the channel  500  in a direction from the long side of channel  500  (with respect to the left actuator) at the first fluid feed hole  214  toward the short side at the second fluid feed hole  216 . The double action pumping from the left and right side actuators in a phase defined by graph  600  and the time and phase delay equations noted above result in a stronger net fluid flow through channel  500  than is available when only one actuator operates as a pump. 
       FIG. 8  shows a simplified cross-sectional view of a fluid ejection device  114   a  with fluid displacement actuators  224  operating in a simultaneous multi-pulse actuation mode, according to an embodiment of the disclosure. In this embodiment, the multi-pulse actuation module  128  controls the right and left actuators  224  so that they are activated simultaneously (i.e., with no time delay) but with displacements that are opposite one another. That is, while the right side actuator has a short expansive fluid displacement with a larger deflection, the left side actuator has a short compressive fluid displacement with a larger deflection. Likewise, while the right side actuator has a long expansive fluid displacement with a smaller deflection, the left side actuator has a long compressive fluid displacement with a smaller deflection. As noted above, these fluid displacements create a net directional fluid flow through the channel  500  from the first fluid feed hole  214  to the second fluid feed hole  216 . 
       FIG. 9  shows a simplified cross-sectional view of a fluid ejection device  114   a  with fluid displacement actuators  224  operating in a simultaneous multi-pulse actuation mode, according to an embodiment of the disclosure. In this embodiment, the in-chamber circulation module  130  controls the right and left actuators  224  so that they are activated simultaneously and in different displacement phases. Thus, as shown in  FIG. 9 , while the left side actuator has a short duration expansive fluid displacement followed by a long duration compressive fluid displacement, the right side actuator has, respectively, a long duration compressive displacement followed by a short duration expansive displacement. After a time delay, the operation of the actuators continues with a reversal of the compressive and expansive fluid displacements as indicated in graph  900 . The operation of the actuators repeatedly alternates compressive and expansive fluid displacements in this manner, creating movement of the fluid within the channel  500  (more specifically, the chamber  212  portion of the channel  500 ) that sloshes the fluid back and forth between the left actuator and the right actuator forming a local fluid circulation loop  902  within the chamber  212 . 
       FIG. 10  shows a simplified cross-sectional view of a fluid ejection device  114   a  with fluid displacement actuators  224  operating in a simultaneous in-phase actuation mode, according to an embodiment of the disclosure. In this embodiment, the drop-eject circulation module  132  controls the right and left actuators  224  so that they are activated simultaneously and in the same compressive displacement phases. As discussed above with respect to  FIG. 3   a , this type of simultaneous, same-phase compressive displacement actuation of both left and right actuators  224  typically results in a drop ejection. This is also the case in the present embodiment of  FIG. 10 . However, in the  FIG. 10  embodiment, the amplitudes of the voltage waveforms driving the left side and right side actuators  224  are different as shown in the graph  1000 . Accordingly, there is a greater fluidic displacement created by the right side actuator than by the left side actuator. The drop-eject circulation module  132  controls the right and left actuators  224  to generate simultaneous compressive fluid displacements with enough energy to eject a fluid drop through nozzle  116 . In addition, the extra compressive fluid displacement from the right side actuator generates a net directional fluid flow in the channel  500  from the first fluid feed hole  214  toward the second fluid feed hole  216 . In another embodiment (not shown), the left side actuator can be driven with a larger voltage waveform than the right side actuator, creating additional compressive fluid displacement from the left side actuator that generates a net directional fluid flow in the channel  500  from the second fluid feed hole  216  toward the first fluid feed hole  214 . 
       FIG. 11  shows a flowchart of an example method  1100  of circulating fluid in a fluid ejection device  114  (e.g., a printhead), according to an embodiment of the disclosure. Method  1100  is associated with the embodiments discussed herein with respect to  FIGS. 1-10 . Method  1100  begins at block  1102  with generating compressive and expansive fluid displacements of different durations from a first actuator  224  while generating no fluid displacements from a second actuator  224 . The first actuator is located asymmetrically within a fluidic channel  500  between a first fluid feed hole  214  and a nozzle  116 , and the second actuator is located asymmetrically within the channel between the nozzle and a second fluid feed hole  216 . 
     In one implementation, generating compressive and expansive fluid displacements includes generating compressive fluid displacements of a first duration and generating expansive fluid displacements of a second duration different from the first duration. In one implementation, the first duration is shorter than the second duration and the fluid displacements cause fluid to flow through the channel in a first direction. In one implementation, the first duration is longer than the second duration and the fluid displacements cause fluid to flow through the channel in a second direction. In one implementation, generating compressive and expansive fluid displacements of different durations includes executing a machine-readable software module that causes a controller to control voltage waveforms driving activation of the first actuator. 
     In one implementation, generating compressive fluid displacements includes flexing the first actuator into the channel such that area within the channel is reduced. In one implementation, generating expansive fluid displacements includes flexing the first actuator out of the channel such that area within the channel is increased. 
     The method  1100  continues at block  1104  with generating compressive and expansive fluid displacements of different durations from the second actuator while generating no fluid displacements from the first actuator. 
     At block  1106  of method  1100 , there is alternating activation of the first and second actuators to generate compressive and expansive fluid displacements from both actuators. In one implementation alternating activation includes activating the first actuator while not activating the second actuator. The implementation includes executing a time delay while activating the first actuator, where the time delay lasts at least as long as the activating of the first actuator. After the time delay expires, the method includes activating the second actuator. In one implementation, during activation of the second actuator, activation of the first actuator is delayed by the time delay. After activation of the second actuator, the first actuator is activated. 
       FIG. 12  shows a flowchart of another example method  1200  of circulating fluid in a fluid ejection device  114  (e.g., a printhead), according to an embodiment of the disclosure. Method  1200  is associated with the embodiments discussed herein with respect to  FIGS. 1-10 . Method  1200  begins at block  1202  with generating simultaneously activating a first and second actuator to generate compressive and expansive fluid displacements, where the first and second actuators alternate between compressive and expansive fluid displacements such that they do not generate compressive or expansive fluid displacements at the same time. 
     In one implementation, the first actuator is located asymmetrically within a fluidic channel  500  between a first fluid feed hole  214  and a nozzle  116 , and the second actuator is located asymmetrically within the channel between the nozzle  116  and a second fluid feed hole  216 . In one implementation the nozzle  116  and a chamber  212  are located between the actuators, and the simultaneous activation creates a fluidic flow back and forth between the actuators. 
     At block  1204  of method  1200 , the first and second actuators are activated to generate concurrent compressive fluid displacements having different compressive displacement magnitudes to eject a fluid drop from the nozzle and create a net directional fluid flow through the channel.