Patent Publication Number: US-2023150262-A1

Title: Efficient Ink Jet Printing

Description:
CLAIM OF PRIORITY 
     This application claims priority to U.S. Patent Application Ser. No. 63/279,795, filed on Nov. 16, 2021, the contents of which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     Ink jet printing can be performed using an ink jet print head that includes multiple nozzles. Ink is introduced into the ink jet printhead and, when activated, the nozzles eject droplets of ink to form an image on a substrate. The printhead can include fluid delivery systems with actuators that operate to eject fluid from a pumping chamber of the printhead. Actuation of an actuator causes deformation of a membrane that changes a volume of a pumping chamber, which in turn causes fluid to be ejected from the fluid delivery system. 
     SUMMARY 
     We describe here a high efficiency fluid ejector and an approach to energy efficient ejection of fluid, such as ink, from a fluid ejector. The fluid ejectors described here have a single, vertical channel of uniform width and impedance, which reduces or eliminates impedance mismatch and fluid resistance along the fluid flow pathway through the fluid ejector. In addition, the geometry of the fluid ejectors described here gives the fluid ejectors a low impedance and high resonance frequency, which contributes to high energy efficiency in operation. The fluid ejectors described here also have large differences in impedance between the single channel in the fluid ejectors and the flow pathways into and out of the fluid ejectors, which reduces or eliminates leakage of energy out of the fluid ejectors. 
     In an aspect, a method for ejecting fluid from a fluid ejector includes actuating a piezoelectric actuator to cause deformation of a membrane defining a wall at a first end of an elongated channel of the fluid ejector, the deformation of the membrane causing ejection of a droplet of fluid from a nozzle disposed at a second end of the channel. The elongated channel fluidically connects a first channel to the nozzle, the first channel disposed at the first end of the elongated channel, and wherein an impedance of the first channel is at least ten times greater than an impedance of the elongated channel. Deformation of the membrane induces fluid flow along the elongated channel, and wherein at least 60% of the fluid flow induced by the deformation of the membrane is in a direction extending from the first end of the elongated channel to the second end of the elongated channel. 
     Embodiments can include one or any combination of two or more of the following features. 
     At least 80% or at least 90% of the fluid flow induced by the actuation is in the direction extending from the first end of the elongated channel to the second end of the elongated channel. 
     The impedance of the first channel is at least twenty times greater or at least fifty times greater than the impedance of the elongated channel. 
     The method includes ejecting a droplet of fluid from the nozzle responsive to actuation of the piezoelectric actuator. The method includes flowing fluid that is not ejected from the nozzle into a second channel disposed at the second end of the elongated channel. An impedance of the second channel is at least ten times greater than an impedance of the elongated channel. The method includes, after ejection of a droplet from the nozzle, drawing fluid into the elongated channel from the first channel, second channel, or both. 
     The elongated channel has a uniform width along the length of the elongated channel. 
     The elongated channel has a uniform impedance along the length of the elongated channel. 
     A cross sectional area of the inlet channel is less than a cross sectional area of the elongated channel. 
     The extent of a clear area of the membrane is greater than or equal to a width of the elongated channel. For instance, the extent of the clear area of the membrane is between 0 and 30% greater than the width of the elongated channel. 
     In an aspect, a fluid ejection apparatus includes a first channel; a nozzle; an elongated channel fluidically connecting the first channel to the nozzle, wherein the first channel is disposed at the first end of the elongated channel and the nozzle is disposed at the second end of the elongated channel; and an actuator. The actuator includes a membrane defining a wall at a first end of the elongated channel; and a piezoelectric element positioned to apply an actuation force to fluid in the elongated channel, the membrane being disposed between the piezoelectric element and an interior of the elongated channel. An impedance of the first channel is at least ten times greater than an impedance of the elongated channel. During operation of the fluid ejection apparatus, deformation of the membrane induces fluid flow along the elongated channel such that at least 60% of the fluid flow induced by the deformation of the membrane is in a direction extending from the first end of the elongated channel to the second end of the elongated channel. 
     Embodiments can include one or any combination of two or more of the following features. 
     The impedance of the inlet channel is at least twenty times greater or at least fifty times greater than the impedance of the elongated channel. 
     A width of the elongated channel is substantially uniform along the entire length of the elongated channel. 
     The fluid ejection apparatus includes a second channel disposed at the second end of the elongated channel. An impedance of the second channel is at least ten times greater than the impedance of the elongated channel. 
     The piezoelectric actuator is centered about an axis of the elongated channel. 
     The membrane has a thickness of between 0.1 μm and 20 μm, e.g., between 2 μm and 8 μm. 
     The membrane extends across an entire width of the elongated channel. 
     A cross sectional area of the inlet channel is less than a cross sectional area of the elongated channel. 
     The extent of a clear area of the membrane is greater than or equal to a width of the elongated channel. For instance, the extent of the clear area of the membrane is between 0 and 30% greater than the width of the elongated channel. 
     In an aspect, a printhead includes an array of fluid ejectors according to the previous aspect. 
     The array can include a parallelogram shaped array of fluid ejectors. 
     The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features and advantages will be apparent from the description and drawings, and from the claims. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a diagram of a fluid ejector. 
         FIG.  2    is a diagram of a high efficiency fluid ejector. 
         FIG.  3    is a diagram of an array of fluid ejectors. 
         FIGS.  4 A and  4 B  are side view and top view diagrams of a high efficiency fluid ejector. 
         FIGS.  5 - 7    are diagrams of high efficiency fluid ejectors. 
         FIG.  8    is a flow chart. 
     
    
    
     DETAILED DESCRIPTION 
     We describe here a high efficiency fluid ejector and an approach to energy efficient ejection of fluid, such as ink, from a fluid ejector. The fluid ejectors described here have a single channel of uniform width and impedance, which reduces or eliminates impedance mismatch and fluid resistance along the fluid flow pathway through the fluid ejector. In addition, the geometry of the fluid ejectors described here gives the fluid ejectors a low impedance and high resonance frequency, which contributes to high energy efficiency in operation. The fluid ejectors described here also have large differences in impedance between the single channel in the fluid ejectors and the one or more flow pathways into and out of the fluid ejectors, which reduces or eliminates leakage of energy out of the fluid ejectors. 
     Referring to  FIG.  1   , a fluid ejector  100  of an ink jet printer includes fluid flow pathways formed in a substrate through which fluid can flow and be ejected from a nozzle  104  of the fluid ejector. The nozzle  104  is fluidically connected to a pumping chamber  106  via a descender  108 . The width w d  of the descender  108  is less than the width w p  of the pumping chamber  106 . The descender  108  is shown as having regions of different width; in some examples, the descender has uniform width along the entire length of the descender. One or more channels  110   a ,  110   b  fluidically connect the fluid ejector  100  to corresponding manifolds  112   a ,  112   b  (collectively referred to as channels  110  and manifolds  112 ). At the nozzle end of the descender  108 , one or more channels  114   a ,  114   b  fluidically connect the fluid ejector  100  to corresponding manifolds  116   a ,  116   b  (collectively referred to as channels  114  and manifolds  116 ). Each manifold  112 ,  116  is connected to multiple fluid ejectors  100 . Although a total of four channels  110 ,  114  are shown in  FIG.  1   , the fluid ejector can be supplied with fluid through fewer than four or more than four channels. 
     The fluid ejector  100  includes an actuator  118 , such as a piezoelectric actuator. The actuator  118  includes a piezoelectric element  119  and a deformable membrane  120 , such as a silicon membrane. The piezoelectric element  119  is separated from the pumping chamber  106  by the deformable membrane  120  such that the membrane  120  defines at least a portion of a top wall of the pumping chamber. The membrane  120  isolates the piezoelectric element  119  of the actuator  118  from fluid in the pumping chamber  106 . The membrane  120  can be a unitary part of the substrate  102  or can be formed of a material different from the substrate. In operation, the piezoelectric element  119  contracts parallel to the motion of the actuator  118 , and the membrane  120  works against the piezoelectric element  119 , causing the actuator  118  to bend. 
     To eject a droplet of fluid from the nozzle  104 , the actuator  118  is actuated, applying an actuation pulse to fluid in the pumping chamber  106 . The actuator  118  is operated according to the resonance frequency of the fluid ejector  100 . The applied actuation pulse causes the drop to eject from the nozzle  104 . Specifically, deformation of the membrane  120  of the actuator  118  caused by a rising edge of the applied waveform increases the volume of the pumping chamber and this, in turn, causes the propagation of a low pressure wave along the elongated channel  108 . When the low pressure wave reaches the nozzle  104 , the meniscus of fluid at the nozzle  104  is pulled back. A high pressure wave, generated by from the falling edge of the applied waveform returning the pumping chamber is then propagated along the elongated channel  108 , timed such that the returning fluid flow from the negative pressure wave hits the meniscus with the high pressure wave, causing ejection of a droplet of fluid from the nozzle  104 . 
     Fluid flow in the pumping chamber  106  responsive to actuation of the actuator  118  is perpendicular to the direction of actuation of the actuator: actuation of the actuator  118  induces fluid flow both horizontally along the pumping chamber  106  and vertically down the descender  108 , as shown by the flow lines in  FIG.  1   . 
     Following fluid ejection from the nozzle  104 , the fluid ejector  100  is refilled by fluid drawn into the pumping chamber  106  and descender  108  from some or all of the channels  110 ,  114 . The fluid flow pathways through which ejector refill flow is provided is based on factors such as the impedance of each channel and the cumulative inductance from the nozzle  104  to the manifolds  112 ,  116  along the respective pathways. In some examples, the fluid ejector  100  also implements a recirculation flow, in which fluid flows into the fluid ejector through the channels  110  and out of the fluid ejector through the channels  114 . 
     In some examples, the actuator  118  is a piezoelectric actuator including drive and ground electrodes, with a piezoelectric layer positioned between the two electrodes. The drive electrode and the ground electrode are formed from a conductive material (e.g., a metal or conductive ceramic), such as copper, gold, tungsten, titanium, platinum, iridium, indium-tin-oxide (ITO), or a combination of conductive materials. The thickness of the drive and ground electrodes is e.g., about 2 μm or less, about 1 μm, about 0.5 μm, about 0.25 μm, etc. To actuate the actuator  118 , an electrical voltage is applied between the electrodes, causing a difference across the piezoelectric layer positioned therebetween. Alternatively, an electric field is applied directly to the piezoelectric layer. The voltage or applied electric field induces a polarity on the piezoelectric layer that causes the piezoelectric layer to shrink, generating a stress force that in turn generates a moment, driving bending of the membrane  120 . The deflection of the membrane  120  causes a change in volume of the pumping chamber  106 , producing a pressure pulse in the pumping chamber  106  that results in ejection of fluid from the nozzle  104 . 
     Referring to  FIGS.  2  and  3   , a high efficiency fluid ejector  200  has a configuration that mitigates at least some sources of energy loss, allowing the fluid ejector  200  to operate with high efficiency.  FIG.  2    shows a side view of a single fluid ejector  200 , and  FIG.  3    shows a top perspective view of a parallelogram-shaped array  250  of such fluid ejectors  200 . 
     In operation, fluid flows through fluid flow pathways of the fluid ejector  200  and is ejected from a nozzle  204  of the fluid ejector. Channels  210   a ,  210   b  (collectively channels  210 ) are horizontally oriented and supply fluid to the fluid ejector  200  from corresponding manifolds  252  ( FIG.  3   ), each of which is connected to multiple fluid ejectors  200 . The channels  210  are fluidically connected to the nozzle  204  by a vertically oriented, elongated channel  230 , with the channels  210  meeting the elongated channel  230  at a first end of the channel and the nozzle  204  being disposed at a second end of the channel. The channels  210  are perpendicular to the elongated channel  230 . 
     The width w c  of the elongated channel  230  is substantially constant along the entire length of the elongated channel  230  (sometimes referred to as “uniform width”). A channel that has a substantially constant width may have a slight variation in width along its length, e.g., due to manufacturing considerations. For example, a channel with substantially constant width can have a width that varies by less than 10%, less than 5%, less than 2%, or less than 1% along its length. The nozzle  204  is centered relative to the elongated channel  230 . At the nozzle end of the elongated channel  230 , channels  214   a ,  214   b  (collectively channels  214 ) fluidically connect the fluid ejector  200  to corresponding manifolds  254  ( FIG.  3   ), each of which is connected to multiple fluid ejectors  200 . The channels  214  are oriented horizontally and are perpendicular to the elongated channel  230 . 
     The fluid ejector  200  includes an actuator  218 , such as a piezoelectric actuator, e.g., as described above for the actuator  118 . The actuator  218  includes a piezoelectric element  219  and a deformable membrane  220 , such as a silicon membrane. The piezoelectric element  219  is separated from the elongated channel  230  by the deformable membrane  220  such that the membrane  220  defines at least a portion of a wall at the first end of the elongated channel  230 , isolating the piezoelectric element  219  of the actuator  218  from the fluid in the elongated channel  230 . 
     The relative sizes of the actuator  218  and the elongated channel  230  are selected such that fluid flow through the channel  230  is substantially in the same direction as the displacement of the actuator  218  (e.g., in a direction directly toward the nozzle and perpendicular to the plane of the actuator  218 ). For instance, the width w m  of the actuator  218  is equal to or greater than the width w c  of the elongated channel  230 . The sizing of the actuator  218  and elongated channel  230  are discussed further with respect to  FIGS.  4 A and  4 B . 
     To eject a droplet of fluid from the nozzle  204 , the actuator  218  is actuated, applying an actuation pulse to fluid in the elongated channel  230 . The applied actuation pulse causes fluid to flow down the elongated channel  230  and out the nozzle  204 , e.g., due to propagation of pressure waves as described above for  FIG.  1   . Following fluid ejection from the nozzle  204 , the fluid ejector  200  is refilled by fluid drawn into the elongated channel  230  from the some or all of the channels  210 ,  214 , e.g., depending on the impedance and inductance of each flow pathway. The fluid ejector  200  can also implement a recirculation flow, in which fluid flows into the fluid ejector through the channels  210  and out of the fluid ejector through the channels  214 . 
     The configuration of the high efficiency fluid ejector  200  reduces energy loss in the fluid ejector  200 , allowing more of the energy generated by deflection of the actuator  218  to contribute to ejection of a droplet from the nozzle  204 . For instance, as discussed in the following paragraphs, energy loss can be reduced by one or more of the following: reducing or eliminating impedance mismatch along the fluid flow pathway through the fluid ejector, reducing inductance of the fluid ejector, reducing resistance along the fluid flow channels, or reducing or eliminating leakage of energy into fluidic connections to the fluid ejector  200 , e.g., the inlet channels, recirculation channels, or both. 
     In the high efficiency fluid actuator  200 , the presence of the elongated channel  230  enables fluid flow in the elongated channel  230  responsive to actuation of the actuator  218  to parallel to the direction of deformation of the membrane. Fluid is drawn into the elongated channel  230  from some or all of the channels  210 ,  214 . Upon actuation of the actuator  218 , the membrane  220  deforms in the vertical direction, as shown by an arrow  250 . The deformation of the membrane  220  induces fluid flow vertically down the elongated channel  230  from the first end to the second end of the elongated channel  230 , toward the nozzle  204 , as shown by an arrow  252 . The extent of the clear area of the actuator  218  relative to the width of the elongated channel  230  contributes to the amount of vertical and horizontal flow in the fluid ejector  200 . For instance, at least 60%, at least 70%, at least 80%, at least 90%, or at least 95% of the fluid flow that is induced by actuation of the actuator  218  is in the direction extending from the first end to the second end of the elongated channel  230 . That the direction of fluid flow and the direction of membrane deformation are harmonized facilitates energy efficient operation of the fluid ejector  200 . 
     That the fluid flow pathway through the fluid ejector  200  includes only a single elongated channel  230  of uniform width connecting the inlet channels  210   a ,  210   b  to the nozzle  204  (e.g., rather than both a pumping chamber and a distinct descender) means that there is no change in impedance as the fluid flows through the fluid ejector  200 . This constant impedance also contributes to the high efficiency operation of the fluid ejector  200 . The constant impedance of the fluid flow pathway within the fluid ejector  200  (e.g., the constant impedance of the elongated channel  230 ) prevents reflection of energy at an interface with mismatched impedance, thereby allowing a larger portion of the energy generated by the actuator  218  to arrive at the nozzle  204 . By contrast, in some fluid ejectors, energy can be reflected due to an impedance mismatch at an interface between a pumping chamber and a descender (e.g., between the pumping chamber  106  and the descender  108  of the fluid ejector  100  of  FIG.  1   ), reducing the amount of energy supplied by the actuator that arrives at the nozzle. 
     In addition, the lack of a shallow pumping chamber with horizontal flow in the fluid ejector  200  reduces the inertance I of the fluid ejector as compared to an ejector with such a pumping chamber (e.g., the fluid ejector  100  with pumping chamber  106 ). The inertance, which is proportional to the length of the channel over its cross sectional area, is further reduced because of the large cross-sectional area (perpendicular to the direction of fluid flow) of the elongated channel  230 . This reduction in inertance in turn increases the resonant frequency of the fluid ejector  200 . The resonant frequency f nat  of a fluid ejector is given by the following equation; it can be seen that a reduction of inertance enables the actuator to becauses an increase in resonant frequency: 
     
       
         
           
             
               
                 f 
                 resonance 
               
               = 
               
                 
                   1 
                   
                     2 
                     ⁢ 
                     π 
                   
                 
                 * 
                 
                   1 
                   
                     
                       C 
                       * 
                       I 
                     
                   
                 
               
             
             , 
           
         
       
     
     where C is the compliance of the actuator and I is the fluidic inertance of the fluid ejector. For a fluid ejector with a smaller I, C can be bigger (e.g., the actuator can be softer) while still achieving a desired resonant frequency. Because a softer actuator requires a smaller voltage to achieve the appropriate deflection volume for a target drop size, the decrease in fluidic inertance allows an increase in actuator compliance thereby leading to a more efficient jet (e.g., the ratio of energy out to energy in) operating at a given target resonance frequency. The energy out of the fluid ejector (given as ½mv 2 ) remains the same regardless of resonant frequency. However, for the same ink and same sized actuator, the energy in (given as ½cV 2 , where c is the capacitance and V is the voltage) is lower, because the voltage can be lower given the higher resonant frequency. 
     The presence of a single elongated channel  230  also enables high efficiency operation in that the fluid flow pathway through the fluid ejector  200  is deep in the direction of fluid flow, thus presenting low resistance to the flow of fluid through the fluid ejector  200 . With low resistance in the fluid flow pathway through the fluid ejector  200 , little of the energy supplied by the actuator  218  is lost. By contrast, in some fluid ejectors, the presence of a shallow pumping chamber (e.g., the pumping chamber  106  of the fluid ejector  100  of  FIG.  1   ) generates resistance to fluid flow, thus absorbing some of the energy generated by the actuator and causing less of the generated energy to contribute to fluid flow to the nozzle. 
     The elongated channel  230  presents a low resistance to the fluid flowing through the fluid ejector  200 , also contributing to the energy efficiency of the ejector. As fluid flows along a channel, viscous loss occurs due to the interaction between the fluid and the walls of the channel, causing a loss of energy. As a channel is made wider, the resistance presented by the walls of the channel decreases, but the volume of the channel increases, which also absorbs energy. The size (e.g., width, height, or both) of the elongated channel  230  is balanced to reduce channel volume while also reducing the surface area of the walls of the channel, thereby reducing the amount of energy absorbed by fluid flow through the elongated channel  230 . The balance between resistive energy loss and volume energy absorption changes with both cross-sectional area of the elongated channel  230  and length of the elongated channel  230 . For instance, the width of the elongated channel can be between 100 μm and 300 μm and the length of the elongated channel can be between 300 μm and 1000 μm. 
     The relative sizes of the inlet channels  210   a ,  210   b , recirculation channels  214   a ,  214   b , and the elongated channel  230  contribute to the performance of the fluid ejector  200 . The ratio of cross sectional areas contributes to the amount of energy lost out the inlet channels  210   a ,  210   b  and recirculation channels  214   a ,  214   b . The inertance of the inlet channels  210   a ,  210   b  and recirculation channels  214   a ,  214   b , which is proportional to the length of the channel divided by its cross sectional area, contributes to the speed with which the fluid ejector  200  can be refilled after jetting. 
     In the fluid ejector  200 , the height h i  and depth (into the page of the figure; not shown) of the inlet channels  210   a ,  210   b  is significantly smaller than the width w c  of the elongated channel  230 . Thus, the inlet channels  210   a ,  210   b  have a cross sectional area (in the plane defined by their height and depth) that is small. Combined with their length, that small cross sectional area gives the inlet channels  210   a ,  210   b  a high inertance. In addition, the cross sectional area of the inlet channels  210   a ,  210   b  is significantly smaller than the cross sectional area of the elongated channel  230  (in the plane defined by its width and depth), meaning that the impedance of the inlet channels  210   a ,  210   b  is significantly greater than the impedance at the jet resonant frequency of the elongated channel  230 , e.g., at least ten times greater, at least 20 times greater, or at least 50 times greater. Similarly, the height h r  and depth of the recirculation channels  214   a ,  214   b  is significantly smaller than the width w c  of the elongated channel  230 . This means that the recirculation channels  214   a ,  214   b  have a high inertance and resistance, and that the impedance of the recirculation channels  214   a ,  214   b  is significantly greater than the impedance of the elongated channel  230  and nozzle at the jet resonant frequency, e.g., at least ten times greater, at least 20 times greater, or at least 50 times greater. 
     The small cross sectional area of the inlet channels  210   a ,  210   b  and recirculation channels  214   a ,  214   b  compared to the cross sectional area of the elongated channel  230 , and the resulting large difference in impedance between the inlet or recirculation channels and the elongated channel  230 , contributes to the energy efficient operation of the fluid ejector  200 . The narrow inlet and recirculation channels prevent significant leakage of energy and fluid out of the fluid ejector  200 , such that substantially all of the fluid in the fluid ejector flows down the elongated channel  230  and toward the nozzle  204 . Furthermore, the high impedance of the inlet channels  210   a ,  210   b  and recirculation channels  214   a ,  214   b  means that energy propagating in the elongated channel  230  is not lost into the inlet and recirculation channels, but rather stays in the elongated channel  230 , further facilitating high efficiency operation. 
       FIGS.  4 A and  4 B  shows a portion of a fluid ejector  400  in side view and top view to illustrate the relationship between the extent of the clear area of the actuator  218  and the width of an elongated channel  430  having a uniform width. In the example of  FIG.  4 A , the uniform width elongated channel  430  has regions II and III of slightly different width, e.g., arising from processing considerations. The extent of the actuator is marked as Region I. The clear area of the actuator  218  is the region of the actuator  218  that is not directly bonded to the substrate of the fluid ejector. 
     The extent of the actuator  218  is slightly greater than the width of the elongated channel  430  (e.g., the width of Region II), facilitating substantially vertical flow through the elongated channel  430 . In some examples, the extent of the actuator  218  is equal to the width of the elongated channel  430  (e.g., the width of Region II). Generally, the clear area of the actuator  218  is less than 30% greater than the width of the elongated channel, e.g., less than 25% greater, less than 20% greater, less than 10% greater, less than 5% greater, or less than 1% greater. 
     In the example of  FIG.  4 A , the cross sectional area of the elongated channel  430  (e.g., of the Region II area of the elongated channel  430 ) is significantly greater than the cross sectional area of inlet channels  410   a ,  410   b . This configuration also facilitates vertical flow through the elongated channel  430  and helps to reduce the reflection of energy into the inlet channels  410   a ,  410   b.    
     Referring again to  FIG.  2   , as discussed above, the reduced inertance of the fluid ejector  200  enables the compliance of the actuator  218  to be increased as compared to, e.g., the compliance of the actuator  118  of the fluid ejector  100  for a given resonance frequency. For instance, the membrane  220  of the actuator  218  can be thinner, and thus less stiff than, the membrane of the actuator  118  of the fluid ejector  100 . For instance, the membrane  220  can have a thickness of less than about 20 μm e.g., between 0.11 μm and  20  between 1 μm and 10 μm, or between 5 μm and 8 μm. In some examples, a thin, rigid membrane can be used in conjunction with an elongated channel with a small cross sectional area. 
     The fluid ejector  200  is capable of operating effectively at lower voltages than standard fluid ejectors of comparable size, e.g., running at comparable jetting frequencies and drop velocities but with a lower voltage than standard fluid ejectors. For instance, the fluid ejector  200  can operate with a drop velocity of about 4-10 m/s, e.g., about 6-8 m/s at a voltage that is lower than that of standard fluid ejectors. Moreover, the fluid ejector  200  is capable of operating at jetting speeds (e.g., frequencies) that are consistent with those of comparably sized standard fluid ejectors, indicating that high efficiency operation can be obtained without sacrificing speed. For instance, the fluid ejector  200  can perform at jetting frequencies of up to, e.g., 100 kHz, and with a pulse width of between 1.5 μs and 2.5 μs, e.g., between 1.8 μs and 2.1 μs, e.g., enabling a printing line speed of up to 2 m/s. Alternatively, the fluid ejector  200  can be smaller than a standard fluid ejector for a given set of operating parameters (e.g., voltage, drop velocity, and frequency). 
       FIGS.  5 - 7    show examples of alternative or additional configurations for high efficiency fluid ejectors. In general, a high efficiency fluid ejector has a single elongated channel of uniform width that provides a fluid flow pathway of low resistance and constant impedance to the nozzle of the fluid ejector. A high efficiency fluid ejector can have one or more inlet channels, one or more recirculation channels, or both that are narrow compared to the elongated channel, thereby presenting a high impedance that helps prevent leakage of energy out of the fluid ejector. 
     Referring to  FIG.  5   , a high efficiency fluid ejector  300  includes only a single inlet channel  210   a  fluidically connected to the nozzle  204  by the elongated channel  230 . At the nozzle end of the elongated channel  230 , the recirculation channels  214   a ,  214   b  fluidically connect the fluid ejector  300  to corresponding return manifolds. The actuator  218  is separated from the elongated channel  230  by the deformable membrane  220  such that the membrane  220  defines at least a portion of a top wall of the elongated channel  230 , isolating the actuator  218  from the fluid in the elongated channel  230 . The height and width characteristics of the inlet channel  210   a , recirculation channels  214   a ,  214   b , and elongated channel  230  are as described above for the fluid ejector  200 . 
     Referring to  FIG.  6   , a high efficiency fluid ejector  400  includes two inlet channels  210   a ,  210   b  fluidically connected to the nozzle  204  by the elongated channel  230 . At the nozzle end of the elongated channel  230 , a single recirculation channel  214   b  fluidically connects the fluid ejector  400  to corresponding return manifolds. The actuator  218  is separated from the elongated channel  230  by the deformable membrane  220  such that the membrane  220  defines at least a portion of a top wall of the elongated channel  230 , isolating the actuator  218  from the fluid in the elongated channel  230 . The height and width characteristics of the inlet channels  210   a ,  210   b , recirculation channel  214   b , and elongated channel  230  are as described above for the fluid ejector  200 . 
     Referring to  FIG.  7   , a high efficiency fluid ejector  500  includes a single inlet channel  210   a  and a single recirculation channel  214   b . The actuator  218  is separated from the elongated channel  230  by the deformable membrane  220  such that the membrane  220  defines at least a portion of a top wall of the elongated channel  230 , isolating the actuator  218  from the fluid in the elongated channel  230 . The height and width characteristics of the inlet channel  210   a , recirculation channel  214   b , and elongated channel  230  are as described above for the fluid ejector  200 . 
     Referring to  FIG.  8   , in operation of a high efficiency fluid ejector, an actuator, such as a piezoelectric actuator, is actuated ( 700 ), causing a membrane of the fluid ejector to deform ( 702 ). The membrane defines a wall at a first end of an elongated channel of the fluid ejector. The deformation of the membrane induces fluid flow, along a length of the elongated channel to a nozzle disposed at a second, opposite end of the elongated channel ( 704 ). Because of the configuration of the fluid ejector, e.g., the uniform width of the elongated channel, at least 60%, at least 70%, at least 80%, at least 90%, or at least 95% of the fluid flow induced by the deformation of the membrane is along the length of the elongated channel, in a direction extending from the first end to the second end of the elongated channel. 
     The fluid flow results in ejection of a droplet of fluid from the nozzle of the fluid ejector ( 706 ). Fluid that is not ejected from the nozzle flows into one or more recirculation channels disposed at the second end of the elongated channel ( 708 ), where it is returned via the return manifolds to a reservoir and reused for a subsequent ejection operation. Responsive to the ejection of a droplet of fluid from the nozzle, fluid is drawn into the elongated channel from one or more inlet channels disposed at the first end of the elongated channel to refill the fluid ejector ( 710 ). The impedance of each of the one or more inlet channels is greater than the impedance of the elongated channel, e.g., at least ten times, at least 20 times, or at least 50 times greater. The impedance of each of the one or more recirculation channels is greater than the impedance of the elongated channel, e.g., at least ten times, at least 20 times, or at least 50 times greater. 
     Particular embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve desirable results. As one example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain implementations, multitasking and parallel processing may be advantageous.