Abstract:
A device for projecting liquid as jets or droplets from multiple nozzles, the device comprising:
       a plurality of transducers oriented substantially parallel to one another and each having an inner face and an outer face opposite said inner face, the transducers being arranged in a substantially planar array;   a plurality of nozzles to project liquid therefrom;   liquid supply means for supplying a liquid to the nozzles;   each nozzle is associated with an adjacent respective transducer which is excitable to cause movement of the adjacent associated nozzle in a direction substantially aligned with the nozzle axis, to project liquid therefrom;   the liquid supply means supplies liquid to an inner end of said nozzle;   means for selectively exciting transducers as required, thereby to project liquid as jets or droplets from the respective outer face by movement of the liquid through the nozzle in response to the movement of the nozzle;   wherein one or more pressure absorbing regions are disposed at a predetermined distance from said nozzles, in a direction perpendicular to the substantially planar array of transducers.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is the National Stage of International Application No. PCT/GB2007/050627, filed Oct. 12, 2007. 
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not Applicable 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a liquid projection apparatus in the form of what is known as a ‘face-shooter’ array. 
     2. Description of the Related Art Including Information Disclosed Under 37 CFR 1.97 and 1.98 
     In our previous application WO 93/10910 we describe a device for projecting droplets from a nozzle that is excited to project liquid therefrom. 
     In our previous application WO99/54140 we describe a device and method for projecting liquid as jets or droplets from multiple nozzles formed in a material layer. The nozzles are formed in a transducer that incorporates a finger with liquid being supplied to an inner end of the nozzles. By continuously stimulating excitation of the finger motion at a certain frequency, the nozzle will eject a continuous droplet stream from an outer end of the nozzle. 
     Previous devices of the type described above tend to suffer from fluidic crosstalk. Fluidic crosstalk can be defined as being the amount that an ejection event is changed (typically a change in the velocity or volume of an ejected drop) by the presence of an ejection event from another nozzle or group of nozzles. 
     An aim of the present invention is to reduce fluidic crosstalk. 
     BRIEF SUMMARY OF THE INVENTION 
     According to the present invention, there is provided a device for projecting liquid as jets or droplets from multiple nozzles, the device comprising: 
     a plurality of transducers oriented substantially parallel to one another and each having an inner face and an outer face opposite said inner face, the transducers being arranged in a substantially planar array; 
     a plurality of nozzles to project liquid therefrom; 
     liquid supply means for supplying a liquid to the nozzles; 
     each nozzle is associated with an adjacent respective transducer which is excitable to cause movement of the adjacent associated nozzle in a direction substantially aligned with the nozzle axis, to project liquid therefrom; 
     the liquid supply means supplies liquid to an inner end of said nozzle; 
     means for selectively exciting transducers as required, thereby to project liquid as jets or droplets from the respective outer face by movement of the liquid through the nozzle in response to the movement of the nozzle; 
     wherein one or more pressure absorbing regions are disposed at a predetermined distance from said nozzles, in a direction perpendicular to the substantially planar array of transducers. 
     The pressure absorbing region, or regions, will reduce both the amplitude of pressure fluctuation induced in the fluid behind the transducers and the region over which that pressure fluctuation is significant. This helps prevent the amount that an ejection event is changed (i.e. a change in the velocity or volume of an ejected drop) by the presence of an ejection event from another nozzle or group of nozzles. 
     The pressure absorbing region acts to absorb the pressure generated when a nozzle is ejecting fluid, so that this pressure is not transmitted to other nozzles, where it will influence the properties of a drop ejected from that other nozzle. This helps to reduce the fluidic crosstalk between the nozzles. 
     The one or more pressure absorbing regions may comprise one of a compliant membrane, a foam or a liquid air interface. 
     The pressure absorbing region may comprise a single region extending parallel to the substantially planar array. 
     The one or more pressure absorbing regions may be spaced from the inner face of the transducers at a distance that is less than or equal to the minimum dimension of the area of the substantially planar array, normal to the direction of nozzle motion which, in use, is moving substantially in phase. 
     Rigid surfaces may be provided between adjacent pressure absorbing regions. 
     The one or more pressure absorbing regions may be formed in an array and each pressure absorbing region may be associated with one of the plurality of transducers. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S) 
       Examples of the invention will now be described with reference to the accompanying drawings, in which: 
         FIG. 1  illustrates a cross-section of a device illustrating, in simplified form, the principle of operation whilst the material layer applies an impulse to the fluid; 
         FIG. 2  illustrates a cross-section of a device illustrating, in simplified form, the principle of operation after the material layer has applied an impulse to the fluid; 
         FIG. 3  illustrates a plan view of a first device; 
         FIG. 4  shows experimental data of the motion of a device following a 10 microsecond pulse applied at time=0; 
         FIG. 5  illustrates a graph of an experimental frequency response function of the first device; 
         FIG. 6   a, b, c, d  illustrate plan views of four further examples; 
         FIG. 7  is a cross-section of the device, illustrating a rigid surface provided at the rear of the transducers; 
         FIG. 8   a  is a cross-section of the device, illustrating a patterned surface provided at the rear of the transducers; 
         FIG. 8   b  is a cross-section of the device, illustrating a surface with rigid and compliant surfaces provided at the rear of the transducers; 
         FIG. 9   a  is a cut-away isometric view of the device, illustrating rigid walls provided between adjacent transducers in combination with a rigid backplane; 
         FIG. 9   b  is a cut-away isometric view of the device, illustrating rigid walls provided between adjacent transducers; 
         FIG. 9   c  is a plan view of the device, illustrating rigid walls provided between adjacent transducers; 
         FIGS. 10   a - d  illustrate examples in plan view, of variation in slot width between transducers; 
         FIG. 11  illustrates the effect of altering the slot width between transducers; 
         FIG. 12  is a cross-section of the device, illustrating a compliant surface provided at the rear of the transducers; 
         FIG. 13   a  is a plan view of the device, illustrating a compliant surface provided at the rear of the transducers; 
         FIG. 13   b  is a cross-section view of  FIG. 13   a;    
         FIG. 14  shows the maximum velocity of the material layer due to the different resonant modes as a function of the length of the piezoelectric actuator. 
         FIG. 15  illustrates drive signals applied to the actuator; 
         FIG. 16   a - e  illustrates the effect of different drive signals on the motion of the material layer; 
         FIG. 17  illustrates a plan view of an example. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  shows a nozzle-bearing plate  1  formed in a material layer, containing a nozzle  13 . An impulse applied to the fluid by the material layer shown at  4  induces positive pressure excursions in liquid  2  resulting in emergent liquid  3  through nozzle  13  in a direction shown at  98 .  FIG. 2  shows an emergent droplet  5  caused by the effects shown in  FIG. 1 . This, together with the ability of devices to provide pressure excursions of time duration in the region of one micro-second to one milli-second, advantageously allows liquid projection at very high frequencies. 
     One example embodiment, which has been reduced to practice, of a single transducer of the overall array device, is shown in plan view in  FIG. 3 . This illustrates a transducer incorporating a ‘beam’ or ‘finger’  6 , with, for example, one piezoelectric element  7  formed of PZT per nozzle  13 . Nozzle  13  penetrates through material layer  100 . This construction can provide a nozzle  13  mounted at the motional anti-node of the transducer, giving a symmetric pressure distribution in the sub-region of the nozzle. The transducer is distinctly formed, in this case, by the introduction of slots  10  into material layer  100 , and by mounting the piezoelectric element  7  and material layer  100  assembly on a substrate  101  with a hole  102 . 
     In this example as an operating liquid projection device, material layer  100  is electroformed Nickel of 60 microns thickness and bearing a nozzle of exit diameter 20 microns. The slots  10  were formed by electroforming and are of width 40 microns; the slot length is 6 mm, and the distance between the centres of adjacent slots  10  is 254 microns. The piezoelectric components  7  have width 214 microns, and are formed of piezoelectric ceramic  5 H sourced from CTS providing high piezoelectric constants and mechanical strength. The electrode material applied to said piezoelectric components  7  was sputtered Nickel gold of thickness in the range 2-5 microns. In this example the piezoelectric material was mounted between the material layer  100  and the substrate  101 . The material layer  100  was bonded to the piezoelectric material  7  and the piezoelectric material  7  was bonded to the substrate  101  using Epotek 353 supplied by Promatech. Electrical connections were made to the piezoelectric material  7  via the material layer  100  and the substrate  101 . 
     By stimulating excitation with only one or a discrete number of such cycles the device ejects droplets ‘on demand’ i.e. responsive to that short droplet-projection pulse or pulse train, and ceasing after that pulse train ceases. The device described above was operated with a drive voltage of 100V peak to peak and with a base frequency of 46.6 kHz. This device yielded a maximum ‘on-demand’ ejection frequency of 10 kHz. With other devices of this general form, on-demand ejection has been observed with a drive voltage of 40V peak-to-peak. The electrical signals required to drive the device can be derived from a number of means such as an array of discrete device drivers or from an ASIC. 
     This liquid projection apparatus whose fabrication was described above was mounted onto a manifold to provide liquid supply means and in proximity to printing media to form a system suitable for ink-jet printing. Using water-based ink, at a supply bias pressure from 0 to 30 mbar below atmospheric pressure, the device was demonstrated operating in drop on demand mode. It was found experimentally that no sealant was needed in order to prevent egress of fluid from the slots. 
     The experimental measurement of the motion of the device of  FIG. 3  following a 10 microsecond pulse is shown in  FIG. 4 . The motion is dominated by one mode with a characteristic frequency of 46.6 kHz. 
       FIG. 5  shows the result of experimental measurement of the electrical impedance using a HP 4194 impedance spectrometer. The frequency sweep runs from 10 kHz to 200 kHz, and shows that the only resonance in this range is the peak centred at 46.6 kHz. It also shows the absence of unwanted vibrational modes near to the desired operating frequency. 
     In alternative constructions for the example of  FIG. 3 , unimorph (single layer) and bimorph (double layer) or multi-layer geometries may be employed for the excitation means shown at  7 . The thickness of the region of material layer material  100  near the ends of the slots, and the dimensions of the excitation means material  7  are chosen to control the resonant frequency of the device. 
     Being substantially isolated by slots  10  and by the substrate  101 , arrays of such transducers allow substantially independent control of drop ejection from an array liquid projection device such as an ink-jet printhead. 
       FIGS. 6   a ,  6   b ,  6   c  and  6   d  illustrate optional constructions wherein multiple nozzle-bearing transducers  9  are formed within the material layer  100 , their lateral extent being defined by the slots  10 . Each such transducer bears a nozzle  13  through layer  100 .  FIGS. 6   a ,  6   b ,  6   c  and  6   d  differ in that they illustrate a variety of permutations of excitation means configuration  14 , as shown. 
     The “characteristic dimension of the material layer” is defined as the smallest dimension of a region of the material layer, which is normal to the direction of nozzle motion, which is moving substantially in phase. 
     In an example of the device type such as those illustrated in  FIG. 5 , the characteristic dimension of the material layer is the width of the moving portion of the material layer  100 , 214 μm. The dimensions of the common region behind the material layer  100  is 25 mm depth of fluid behind the material layer  100 , 2.8 mm in a direction in the plane of the material  100  and substantially parallel to the slots  10 , and 36.6 mm in a direction in the plane of the material layer  100  and substantially perpendicular to the slots  10 . This device exhibits ejection for a range of fluid viscosities from 0.5 cp to 300 cp. 
     A rigid surface  20  may be provided substantially parallel to the moving material layer  100  and at a distance D behind the inner face of the moving material layer as shown in  FIG. 7 . For a given motion of the material layer the impulse applied by the material layer to the fluid is increased by the presence of a rigid surface  20 . 
     As noted above, pressure is generated in the fluid through the impulse of the moving material layer. By increasing the impulse applied to the fluid, for a given motion of the material layer, the rate of fluid flow through the nozzle  13  is increased. Therefore, increasing the impulse applied to the fluid by the material layer for a given motion of the material layer reduces the motion of the material layer that is required in order to eject liquid droplets. 
     In order to increase the impulse applied to the fluid by the material layer, the distance D should be comparable to or smaller than the characteristic dimension of the material layer, L. 
     Without the rigid surface  20 , or with a rigid surface  20  at a distance D from the material layer where D&gt;&gt;L, for example D ten times greater than L, the pressure behind the material layer is proportional to the characteristic dimension L of the material layer. When a rigid surface  20  is placed at a distance D from the material layer where D is much less than L, for example D equal to half L or less, then the pressure generated by motion of the material layer is proportional to L 2 /D. At intermediate distances the pressure generated by the same motion of the material layer will vary with L in a manner between L and L 2 /D. 
     In a second example, the rigid surface  20  is patterned as shown in  FIG. 8   a . This allows the impulse applied to the fluid by the material layer to be increased behind each nozzle for a given motion of the material layer, thereby reducing the motion of the material layer required for ejection. In addition, this example is advantageous because the gaps in the rigid backplane reduce fluidic crosstalk between the nozzles  13 . 
     Crosstalk can be defined as being the amount that an ejection event is changed (typically a change in the velocity or volume of an ejected drop) by the presence of an ejection event from a neighbouring nozzle. Consider two adjacent independently actuated regions of material layer each with a nozzle  13 , material layer region A and material layer region B. If material layer region B is driven in isolation with fixed drive conditions, pressure is generated behind material layer region B to cause ejection. If both material layer regions A and B are simultaneously driven to cause ejection, then the pressure under both material layer regions A and B will be changed slightly by the motion of the adjacent material layer region compared to that when they are driven in isolation. This small pressure change behind each material layer region results in a change in the drop volume and/or drop velocity of the drop ejected by each material layer region compared to that when it is driven alone. This change is the crosstalk between material layer region A and material layer region B. The crosstalk will thus be reduced if the ratio of the pressure generated behind material layer region B due to the motion of material layer region B to the additional pressure generated behind material layer region B due to the motion of material layer region A is increased. Placing a rigid surface behind each material layer region A and B increases the pressure behind material layer region B due to the motion of material layer region B. The pressure behind region B is increased by a larger ratio than the increase in the additional pressure behind material layer region B that results from the motion of material layer region A. This is a result of the additional pressure generated being dissipated in the gaps between the rigid surfaces. Thus placing a rigid surface behind each material layer region reduces the fluidic crosstalk. 
     In a third example shown in  FIG. 8   b , compliant surfaces  31  are provided between the sections  32  of patterned rigid surface  20 . The patterned sections of rigid surface  20  act to increase the pressure behind a nozzle  13 , thereby reducing the motion of the transducer  9  required for ejection, and the compliant surfaces  31  act to reduce crosstalk. 
     Rigid side walls  21  can also be placed, between the transducers, extending along the length of the transducer, as illustrated in  FIG. 9   a . The walls also act to reduce fluidic crosstalk between nozzles as they reduce the amount of pressure that is transmitted from the fluid beneath an actuated nozzle  13  to the region of fluid behind a neighbouring nozzle  13 . The walls may be of limited length, as shown in  FIG. 9   b  and in plan view in  FIG. 9   c , the length of the walls being always preferably greater than the distance between the walls, and more preferably greater than two times the distance between the walls. The walls  21  do not have to be connected to the rigid surface  20 , although they are shown connected in  FIG. 9   a.    
     The rigid side walls  21  may also be placed without the rigid surface  20  as shown in  FIG. 9   b . In this case the height of the walls is preferably greater than the distance between the walls and more preferably greater than two times the distance between the walls. 
     In order not to introduce mechanical crosstalk between adjacent transducers, the rigid walls are isolated from the material layer, i.e. they are not mechanically engaged with the material layer. 
     The rigid surface  20  and side walls  21  do not form a chamber that contains the ink, as the ink is still free to flow in the direction that is not bounded by any walls or surfaces. For example, in  FIG. 9   a , the ink is constrained in a vertical direction and a horizontal direction with the page, but the ink is not constrained in a direction out of the page. 
     The width of the slot  10  between adjacent transducers  9  can be varied along the length of the transducer as shown in  FIGS. 10   a - d . In the particular examples shown in  FIG. 10   a - d , the width of the slot  10  between two adjacent transducers  9  is greater at a distance away from the nozzle  13  than the width of the slot adjacent the nozzle. 
     By increasing the slot width in some regions along the length of the slot  10 , spatial crosstalk is reduced between the transducers. It is desirable to reduce crosstalk so that the motion of one nozzle-bearing transducer  9 , when excited to eject liquid from its associated nozzle  13 , does not cause substantial pressure fluctuations in liquid that is adjacent to nozzle-bearing regions of other transducers. The definition of crosstalk is discussed in relation to  FIG. 8 . 
     The pressure that is transmitted, by a moving material layer region to the fluid behind a neighbouring material layer region, is reduced by the action of the air liquid interface in the slot, which acts as a pressure absorbing surface. By increasing the width of the slot  10  between two neighbouring material layer regions, the amount of pressure absorbed by the air liquid interface is increased. The pressure absorbing surface could also be a surface that has a low bending stiffness and low inertia and is therefore able to respond during the time scale with which the pressure in the fluid is created and removed, thus absorbing some of the pressure. For instance, the slot could be covered with a compliant membrane. 
     In the examples shown in  FIGS. 6   a - d  where the width of the moving material layer region is much smaller than the length of the transducer, the pressure under a material layer region, which neighbours a driven moving material layer region, depends on the width of the finger (L) and the width of the slot(s) as shown in  FIG. 11 . Spatial crosstalk is minimised when the ratio of the pressure at the neighbouring nozzle to the pressure at the driven nozzle is as low as possible (P neighbour /P nozzle ). As can be seen in  FIG. 11 , it is therefore desirable that the ratio of s/L is a large as possible. 
     It is not so advantageous simply to increase the width of the slot along the whole length of the transducer as this will also narrow the finger width. A narrow finger means that the motion required for ejection is increased. Therefore, the slots are widened at a distance away from the nozzle as illustrated in  FIG. 10   a - d  in order to reduce the nearest neighbour crosstalk and significantly reduce the next nearest neighbour crosstalk while not significantly increasing the motion required for ejection. 
     As illustrated in  FIG. 12 , a compliant surface  30 , substantially parallel to the nozzle-bearing plate  1 , can be provided at a distance D from the transducers  9 . This surface will reduce both the pressure induced in the fluid  2  behind the transducers and the region over which that pressure is significant, if the distance D is comparable to or less than the minimum dimension of the area of material layer that is moving substantially in phase. The area of the material layer that is moving substantially in phase is illustrated by a horizontal arrow in  FIG. 12 . In this Figure, three transducers are moving substantially in phase. 
     The amount of pressure that is transmitted through the fluid behind the transducers  9  is reduced because the compliant surface  30  acts as a pressure absorbing surface. 
     A compliant surface is defined as a surface that will move in response to the pressure induced in the fluid on a timescale sufficiently short that it significantly reduces the pressure in the fluid next to the compliant surface compared to the pressure at that point when the compliant surface is replaced with a bulk region of fluid. The compliant surface  30  could be a compliant membrane, with air behind it, or it could be a soft foam, or it could be a liquid air interface. 
     One example of a compliant surface as part of an ejecting device is shown in  FIGS. 13   a  and  13   b . This illustrates a compliant surface composed of an interface between air and fluid. The interface is supported by a fine mesh  103  (for example a steel mesh) that is placed behind the array of fingers  6 . 
     In this example the device is similar in construction to that shown in  FIG. 2  except that it also includes a mesh  103  that is clamped onto the back of the substrate  101 . The fluid is fed into the hole in substrate  101  between the material layer  100  and the mesh. The distance between the mesh  103  and the material layer  100  is 400 micrometers. 
     In a further example shown in  FIG. 8   b , patterned compliant surfaces  31  are provided behind the nozzle-bearing plate  1 . Between the compliant surfaces  31 , behind the centres of the regions of the transducers  9  that can be independently moved, are provided rigid surfaces  32 . The rigid surfaces  32  act to increase the pressure behind a nozzle  13 , thereby reducing the amplitude of the transducer  9  required for ejection, and the compliant surfaces  31  act to reduce crosstalk. 
     The frequency at which drop on demand ejection can be made from a device is limited by the time it takes for the motion of the ejection system to decay to a level where it does not significantly affect the next ejection. If a device is made so that its motion is primarily mono-modal following a single voltage change, the motion can be built up and then cancelled by applying voltage changes at suitable times. Thus a lower voltage can be used to achieve a desired amplitude of motion and this motion can be stopped allowing the drop on demand frequency to be increased. If the device is not mono-modal and so energy is transferred into other modes then, in general, it is not possible to construct a signal that will successfully cancel the motion of the device in a small number of cycles of the dominant mode. 
     The device can be described as mono-modal when, following a single voltage change, the maximum velocity of the material layer due to the first order mode is significantly larger than the maximum velocity of the material layer due to higher order modes. Preferably the initial velocity of the device due to the first order mode is more than twice the velocity due to higher order modes. More preferably it is greater than four times the velocity due to higher order modes. This can be achieved by selecting a suitable ratio between the length of the piezoelectric actuator and the transducer length. 
     For example consider the device shown in  FIG. 2  with a 60 micron thick electroformed material layer and 100 microns thick bulk cut piezoelectric actuator.  FIG. 14  shows the maximum velocity of the material layer due to each of the first, second, and third order modes as a function of the fractional length of the piezoelectric actuator as a proportion of the length of moving material layer, following a single voltage change for devices with resonant frequency of 50 kHz. This shows clearly that the ratio between the velocity from the first order mode and the velocity from the higher order modes is a maximum at around a piezoelectric actuator length fraction of 0.4. For the particular materials used, this length of the moving piezoelectric actuator in this device is 1.2 mm and the transducer length is 2.8 mm. In practice it may be desirable to vary the dimensions slightly from this ideal according to which particular higher order modes affect the motion of the material layer most strongly immediately beside the nozzle. 
     In order to drive such a device, rising and falling voltages are applied that reinforce the motion and thus reduce the voltage that is required to achieve a given amplitude. These voltage changes can be used to produce motion that cause one, two or many drops to be ejected. Following the ejection of the last drop that is required, the motion of the device can be stopped or significantly reduced by applying one, two or more voltage changes that are timed so as to cancel the motion of the device. This is desirable for two reasons. Firstly the frequency at which drop on demand ejection can be made from a device can be increased, as active motion cancellation can be achieved more rapidly than allowing the motion to decay to a level where it does not significantly affect the next ejection. Secondly if the motion of the device is not significantly reduced by applying a suitable signal then the ensuing motion may cause undesired drops to be ejected. 
     One example of such a drive scheme is shown in  FIG. 15 . The drive scheme consists of two pulses of equal voltage. The first voltage rise  40  and the first voltage drop  41  enhance the motion of the transducer  9  and the second voltage rise  42  and the second voltage drop  43  are designed to cancel that motion. 
     Because the device is mono-modal, the further voltage changes  42  and  43  can be applied to cancel the motion of the device. Such active cancellation of the motion reduces or removes motion of the material layer in substantially less time than would be the case if the motion is simply allowed to decay. This significantly reduces the delay time before a further series of voltage changes can be applied to initiate the next ejection event. With this drive scheme the drop on demand ejection frequency can be increased to up to a half of the resonant frequency of the device for ejection where the motion of the transducer is cancelled prior to initiating the motion required to eject the next droplet. 
       FIGS. 16   a - e  illustrate the effect of changing the timings between the four voltage changes. The material layer has a resonant frequency and associated period p and this is shown by line  400  in  FIG. 16  for illustration only. 
     In a preferred embodiment, a first falling voltage change  44   b  is timed to be a time p/2 after the first rising voltage change  44   a  so that the motion from these two voltage changes is reinforced. The motion of the material layer will be stopped if the following two conditions are met. The first condition is that the midpoint in time between the second rising voltage change  44   c  and the second falling voltage change  44   d  is 1.5 periods of the movement of the material layer after the midpoint in time between the first rising voltage change  44   a  and the first falling voltage change  44   b . The second condition is that the second falling voltage change  44   d  is placed at a suitable time after the second rising voltage change  44   c . In the theoretical case of a device with insignificant damping, the second falling voltage change  44   d  should be placed at a time p/2 after the second rising voltage change  44   c  in order to cancel the motion, as in the case of a device with insignificant damping, the motion of the material layer will continue with no decay of motion until the third and fourth voltage changes, This is illustrated in  FIG. 16   a  by line  44   e  showing the motion of an undamped device, where the motion is cancelled when the second rising and falling voltage changes are applied. 
     In a device where damping is significant, the time between the second rising voltage change  44   c  and the second falling voltage change  44   d  needs to be altered in order to cancel the motion of the material layer. In particular, the gap between the second rising voltage change  44   c  and the second falling voltage change  44   d  must be increased or decreased to detune these edges to compensate for the amplitude already lost owing to the damping of the material layer. 
     The damping causes a reduction in amplitude with time, and whilst in order to induce the maximum motion to the material layer the first rising voltage change will occur at time t=0 and the first falling edge should still occur at t=p/2, in the same way as an undamped device, the second rising voltage change and second falling voltage change are at t&gt;3p/2 and t&lt;2p respectively or at t&lt;3p/2 and t&gt;2p respectively to compensate for the fact that the induced motion has been reduced by the damping. The case where the second rising voltage change and second falling voltage change are at t&gt;3p/2 and t&lt;2p respectively is illustrated in  FIG. 16   a  by first rising voltage change  45   a , first falling voltage change  45   b , second rising voltage change  45   c  and second falling voltage change  45   d . These voltage changes result in a response from the material layer shown in line  45   e.    
     It is also possible to reduce the amplitude of motion of the material layer by increasing or decreasing the time between the first two voltage changes  40  and  41 .  FIG. 16   b  illustrates the affect of changing the timings of the first rising and first falling voltage changes.  FIG. 16   b  illustrates a device where the damping is insignificant, i.e. a theoretical device. 
     In  FIG. 16   b , the theoretical motion of an undamped device is shown in line  44   e  which is produced by voltage changes  44   a ,  44   b ,  44   c  and  44   d , as described with reference to  FIG. 16   a . When the voltage changes  44   a ,  44   b ,  44   c  and  44   d  are applied at the times shown in  FIGS. 16   a  and  16   b  as described above, a maximum amplitude of motion of the material layer will be achieved. In order to reduce the motion of the material layer to say 50% of the maximum amplitude, after applying a first rising voltage change  46   a , a first falling voltage change  46   b  is placed after the first rising voltage change at a time less than half the resonant period p of the material layer (i.e. the time between voltage changes  46   a  and  46   b  is less than the time between voltage changes  44   a  and  44   b ). As can be seen from  FIG. 16   b , this results in motion of the material layer shown in line  46   e  which has a smaller amplitude than that shown in line  44   e . To achieve a 50% reduction in amplitude of the material layer, the first falling voltage change occurs at approximately one sixth of a resonant frequency period after the first rising edge. 
     The motion of the material layer represented by line  46   e  can be cancelled as described above, by applying a second rising voltage change  46   c  and a second falling voltage change  46   d . The second rising voltage change occurs at one and a half resonant periods after the first voltage change  46   a , and the second falling voltage change  46   d  occurs at the same time interval after the second rising voltage change  46   c  as the time period between the first rising  46   a  and falling  46   b  voltage changes. 
       FIG. 16   a  illustrated the how the timings of the voltage changes are arranged to cancel the motion of the material layer for a damped and an undamped device.  FIG. 16   b  illustrated how, for an undamped device, the amplitude of motion of the material layer can be reduced by varying the timings of the voltage changes.  FIG. 16   c  illustrates a combination of  FIGS. 16   a  and  16   b.    
       FIG. 16   c  shows the voltage changes and response of the material layer for an undamped device at maximum amplitude. It also shows voltage changes  47   a ,  47   b ,  47   c  and  47   d  that are required to achieve reduced motion  47   e  in a damped device. 
     First rising voltage change  47   a  and first falling voltage change  47   b  occur at the same time as voltage changes  46   a  and  46   b . In other words, whether the device is damped or not has no bearing on when the first rising and falling voltage changes are applied to achieve a reduction in amplitude of the material layer. 
     To cancel the motion shown by line  47   e , a second rising voltage change  47   c  occurs at a time t&gt;3p/2 and a second falling voltage change  47   d  occurs at t&lt;2p to compensate for the fact that the induced motion has been reduced by the damping, as described in relation to  FIG. 16   a . The midpoint between the second rising edge and the second falling edge occurs one and a half periods after the midpoint between the first rising edge and the first falling edge. 
     Longer sequences of reinforcing and cancelling edges can be used to eject a number of droplets at resonant frequency prior to stopping the motion. An example of such a drive scheme is shown in  FIG. 16   d . In this example six voltage changes  48   a  to  48   f  are used to generate three oscillations. The motion of the damped device to the voltage changes is shown in line  48   i . These oscillations increase in amplitude so producing three drops of increasing velocity which will thus coalesce in flight. Then two voltage changes  48   g  and  48   h  are used to cancel the motion. In the previous examples the cancelling edges were less than p/2 apart, however the motion can also be cancelled by placing the cancelling edges more than p/2 apart. In this case  48   g  and  h  occur at &lt;7p/2 and &gt;8p/2. If the damping of the fingers was increased or the pulse timing was altered this drive scheme, with a correctly adjusted cancelling pulse, could be used to generate three drops with the same velocity. A second example is shown in  FIG. 16   e . In this example six voltage changes are used to eject 6 drops and then two voltage changes are used to cancel the motion. In this example more drops are produced using the same number of voltage changes as that used in the example shown in  FIG. 16   d.    
     The residual motion of the material layer after the cancellation pulses is a combination of any other modes of the device, the error in how accurately the decay constant is known and the error in how accurately the resonant frequency of the device is known. The amount of residual motion is less sensitive to errors in how accurately the frequency is known when the damping coefficient is larger. Thus in order to reduce this sensitivity the damping coefficient could be raised. This could be achieved in a number of ways for example: (i) bonding a lossy material to one surface of the actuator or material layer; (ii) making the material layer out of a lossy material; and (iii) placing a rigid surface close to, but not in contact with, a portion of the ink side of the material layer or actuator, there by creating a small gap which is lossy as fluid is forced in and out of the gap by the motion of the material layer. 
       FIG. 17  shows three neighbouring independently actuated regions of material layer  100   a ,  100   b  and  100   c . The material layer regions  100   a ,  100   b  and  100   c  are driven with different motion, to project liquid from their respective nozzles  13   a ,  13   b  and  13   c , depending on whether adjacent nozzles are ejecting liquid at the same time. As explained above, the driving of one finger that is excited to project liquid from its associated nozzle will cause pressure fluctuations in the liquid behind its neighbouring nozzles, and therefore the ejected droplet&#39;s properties are functions of both the motion of the material layer surrounding the ejecting nozzle and that surrounding the neighbouring nozzles. 
     The motion with which finger  13   b  moves, if nozzle  13   b  is ejecting liquid at the same time as nozzle  13   a , will not need to be as great as the motion required if nozzle  13   b  is ejecting alone. 
     The increase in pressure under a region of material layer as a result of the pressure generated under a neighbouring material layer region is shown in  FIG. 11  as a function of the slot width (s) expressed as a fraction of the finger width (L). 
     It is desirable to ensure that the properties of the drop ejected from a nozzle  13  such as drop volume and velocity are independent of whether or not drops are ejected by neighbouring nozzles. This is achieved by adjusting the motion of the material layer surrounding the ejecting nozzle in such a way so as to compensate for the motion of the material layer surrounding neighbouring nozzles. 
     In order to compensate for the pressure produced by the motion of neighbouring regions of material layer, the motion of a finger is reduced when neighbouring fingers are also ejecting. This can be achieved either by changing the voltage of the drive scheme or by changing the degree to which the driving voltage changes reinforce the material layer motion. In both cases, compensation can be applied either using pre-determined variations in the drive scheme, or using feedback from a sensor. 
     Each of the examples described above could usefully confer benefit in all application fields including, but not restricted to: an inkjet printer, an office printer, to image a printing plate to function as an offset master, to print onto packaging, to directly mark food stuffs, to mark paper for example to generate receipts and coupons, to mark labels and decals, to mark glass, to mark ceramics, to mark metals and alloys, to mark plastics, to mark textiles, to mark or deposit material onto integrated circuits, to mark or deposit material onto printed circuit boards, to deposit pharmaceuticals or biologically active material either directly onto human or animal or onto a substrate, to deposit functional material to form part of an electric circuit, for example to alter or generate an RFID tag, an aerial or a display.