Surface ripple wave diffusion by non-retroreflective aperture configurations for acoustic ink printers

Abstract: The free ink surface levels (13) of acoustic ink printers (11) are controlled by cap structures (31) that have substantially non-retroreflective aperture configurations. The non-retroreflective configurations of the apertures (32,42) of these cap structures (31) cause diffusive scattering or directional deflection of the reflected surface ripple waves, thereby significantly reducing the time that is required for the oscillatory perturbations, which are caused by reflection of the surface ripple waves that are generated during the droplet ejection process, to dissipate to a negligibly low amplitude in the critical local areas of the ejection sites. This, in turn, increases the droplet ejection rates at which printers (11) having such cap structures (31) can be operated asynchronously.

Description: This invention relates to apertured cap structures for controlling the free ink surface levels of acoustic ink printers and, more particularly, to improved aperture configurations for these cap structures. US-A-5,028,937, entitled "Perforated Membranes for Liquid Control in Acoustic Ink Printing," suggests using apertured cap structures for controlling the free ink surface levels of acoustic ink printers. However, it has been found that the free ink surface level control that is provided by the apertured cap structures of the '937 patent tends to be degraded, under dynamic operating conditions, by the reflection of surface ripple waves from the sidewalls of the essentially round apertures of those cap structures. These ripple waves are generated as an inherent byproduct of the droplet ejection process, so the oscillatory free ink surface level perturbations that are caused by the reflection of the ripple waves from the aperture sidewalls threaten to impose unwanted constraints on the droplet ejection rates at which printers that utilize such cap structures can be operated reliably in an asynchronous mode (i. e.. a mode in which the ejection timing of each droplet is independent of the ejection timing of every other droplet). Therefore, in accordance with this invention, the time that is required for the amplitude of these perturbations to dissipate to a negligibly low level is reduced significantly by configuring the apertures to scatter the reflected ripple waves. As described herein, "acoustic ink printing" is a direct marking process that is carried out by modulating the radiation pressure that one or more focused acoustic beams exert against a free surface of a pool of liquid ink, whereby individual droplets of ink are ejected from the free ink surface on demand at a sufficient velocity to cause the droplets to deposit in an image configuration on a nearby recording medium. This process does not depend on the use of nozzles or small ejection orifices for controlling the formation or ejection of the individual droplets of ink, so it avoids the troublesome mechanical constraints that have caused many of the reliability and picture element ("pixel") placement accuracy problems that conventional drop-on-demand and continuous-stream ink jet printers have experienced. Several different droplet ejector mechanisms have been proposed for acoustic ink printing. For example, (1) US-A-4,308,547, entitled "Liquid Drop Emitter," provides piezoelectric shell-shaped transducers; (2) US-A-4,697,195, entitled "Nozzleless Liquid Drop Emitters," provides planar piezoelectric transducers with interdigitated electrodes (referred to as "IDTs"): (3) US-A-4,751,530, entitled "Acoustic Lens Arrays for Ink Printing," provides droplet ejectors that utilize acoustically illuminated spherical focusing lens; and (4) US-A-5,041,845, entitled "Multi-Discrete-Phase Fresnel Acoustic Lenses and Their Application to Acoustic Ink Printing," provides droplet ejectors that utilizes acoustically illuminated multi-discrete-phase Fresnel focusing lenses. Droplet ejectors having essentially diffraction-limited, f/1 lenses (either spherical lenses or multi-discrete-phase Fresnel lenses) for bringing the acoustic beam or beams to focus essentially on the free ink surface have shown substantial promise for high quality acoustic ink printing. Fresnel lenses have the practical advantage of being relatively easy and inexpensive to fabricate, but that distinction is not material to this invention. Instead, the feature of these lenses that most directly relates to this invention is that they are designed to be more or less diffraction-limited f/1 lenses, which means that their depth of the focus is only a few wavelengths λ: where λ is the wavelength in the ink of the acoustic radiation that is focused by them. In practice, λ typically is on the order of only 10 µm or so, which means that the free ink surface levels of these high quality acoustic ink printers usually have to be controlled with substantial precision. Apertured cap structures are economically attractive free ink surface level controllers for acoustic ink printing. As pointed out in the above-referenced Khuri-Yakub et al. '937 patent, an apertured cap structure utilizes the inherent surface tension of the ink to counteract the tendency of the free ink surface level to change as a function of small changes in the pressure of the ink. Thus, for example, an apertured cap structure is useful for increasing the tolerance of an acoustic ink printer to the ink pressure variations that can be caused by slight mismatches between the rates at which its ink supply is depleted and replenished. Furthermore, as taught by the '937 patent, a pressure regulator or the like can be employed for maintaining a substantially constant bias pressure on the ink whenever it is necessary or desirable to increase the precision of the surface level control that is provided by such a cap structure. The fluid dynamics of the acoustic ink printing process generate a generally circular wavefront ripple wave on the free ink surface whenever a droplet of ink is ejected. The viscosity of the ink hydrodynamically dampens this surface ripple wave as it propagates away from the ejection site. However, in printers that have multiple droplet ejectors, such as those that comprise one or more linear arrays of droplet ejectors for line printing, this hydrodynamic damping generally is insufficient to prevent the ripple waves produced by any given one of the droplet ejectors from interfering with the operation of its near neighboring droplet ejectors. Accordingly, to avoid this unwanted "crosstalk," a multi-ejector printer advantageously includes a cap structure that has a plurality of spatially distributed apertures that surround the ejection sites of respective ones of the droplet ejectors . A cap structure of this type effectively subdivides the free ink surface of the printer into a plurality of individual ponds of ink, each of which is dedicated to a different one of the droplet ejectors. Ink may flow from pond-to-pond between the ejectors and such a cap structure, but the cap structure acts as a physical barrier for inhibiting surface ripple waves from propagating from one pond to another. In operation, the acoustic beams that are emitted by the droplet ejectors of such a multi-ejector printer come to focus more or less centrally of respective ones of the apertures in the cap structure, so the aperture diameters preferably are at least approximately five times greater than (and, indeed, may be twenty or more times greater than) the waist diameters of the focused acoustic beams, thereby preventing the apertures from materially influencing the hydrodynamics of the droplet ejection process or the size of the droplets of ink that are ejected. For example, if the acoustic beams have nominal waist diameters at focus of about 10 µm, the apertures suitably have diameters of approximately 250 µm. These relatively large apertures are practical, even for printers that print pixels on centers that are spatially offset by only a small fraction of the aperture diameter, because the droplet ejectors of these higher resolution printers can be, for example, spatially distributed among multiple rows on staggered centers. As previously pointed out, prior cap structures of the foregoing type have had essentially round apertures. A round aperture configuration suggests itself because of its circular symmetry. However, it now has been found that the retroreflection of the surface ripple waves from the sidewalls of these round apertures is a limiting factor that interferes with operating acoustic ink printers having such cap structures at higher asynchronous droplet ejection rates. Consequently, an aperture configuration that significantly reduces the effect of such surface ripple waves on the acoustic ink printing process is needed to enable such cap structures to be used as free ink surface level controllers for higher speed, asynchronous acoustic ink printers. In response to the foregoing need, this invention provides an acoustic ink printer according to claim 1 of the appended claims. Particular embodiments of the invention are set out in claims 2 and 5 of the appended claims. The present invention further provides an acoustic ink printer according to claim 6 of the appended claims. Particular embodiments are set out in claims 7 to 10 of the appended claims Additional features and advantages will become apparent when the following detailed description is read in conjunction with the attached drawings, in which: Fig. 1 is a fragmentary and diagrammatic elevational view of an acoustic ink printer having an apertured cap structure constructed in accordance with the present invention; Fig. 2 is a first order graphical analysis of the relative ripple wave amplitude in the central region of a round aperture as a function of the wave propagation distance; Fig. 3 is fragmentary plan view of a cap structure with an aperture having a polygonal transverse-sectional contour for implementing this invention; Fig. 4 provides the same graphical analysis as Fig. 3 for apertures having several different odd-sided polygonal transverse-sectional contours, including the pentagonal aperture shown in Fig. 2; Fig. 5 provides the same graphical analysis as Fig. 3 for apertures having a variety of even-sided polygonal transverse-sectional contours; and Fig. 6 is a fragmentary and diagrammatic plan view of still another apertured free ink surface level controller that is constructed in accordance with the broader aspects of this invention. Turning now to the drawings, and at this point especially to Fig. 1, there is an acoustic ink printer 11 (shown only in relevant part) that has one or more droplet ejectors 12 for ejecting individual droplets of ink from the free surface 13 of a pool of liquid ink 14 on demand at a sufficient velocity to deposit the droplets 15 in an image configuration on a nearby recording medium 21. For example, the printer 12 suitably comprises a one or two dimensional array (not shown) of droplet ejectors 12 for sequentially printing successive lines of an image on the recording medium 21 while it is being advanced (by means not shown) in a process direction, as indicated by the arrow 22. As illustrated, each of the droplet ejectors 12 comprises an acoustic lens 25, which typically is an essentially diffraction-limited f/1 lens, that is formed in one face of a suitable substrate 26. This lens 25 is acoustically coupled to the free surface 13 of the ink 14, either by the ink 14 alone (as shown) or via an intermediate single or multiple layer, liquid and/or solid acoustic coupling medium (not shown). The other or opposite face of the substrate 26 is bonded to or otherwise maintained in intimate mechanical contact with a piezoelectric transducer 27. As a general rule, the substrate 26 is composed of a material (such as silicon, alumina, sapphire, fused quartz, and certain glasses) that has a much higher acoustic velocity than the ink 14, so the lens 25 typically is configured to behave as a spherical concave focusing element for the acoustic radiation that is incident upon it. In operation, the transducer 27 suitably is excited by an amplitude modulated radio frequency (rf) signal that causes it to couple an amplitude modulated, generally planar wavefront, acoustic wave into the substrate 26 for illuminating the lens 25. The lens 25 refracts the incident radiation and bring it to focus essentially on the free ink surface 13, so the radiation pressure that is exerted against the free ink surface 13 makes brief controlled excursions to a sufficiently high pressure level for ejecting individual droplets of ink 15 therefrom under the control of amplitude modulated rf signal that is applied to the transducer 27 (not shown). Typically, the transducer 27 is excited at an rf frequency of about 168MHz, and the amplitude of that rf excitation is pulsed at a pulse rate of up to about 20KHz. In keeping with the teachings of the above-referenced Khuri-Yakub '937 patent, the free ink surface 13 is capped by an apertured cap structure 31 which is supported (by means not shown) so that its inner face is maintained in intimate contact with the ink 14. As shown, the cap structure 31 has a separate aperture 32 for each of the droplet ejectors 12, so the acoustic beam that is emitted by any given one of the droplet ejectors 12 comes to focus on the free ink surface 13 more or less centrally of an aperture 32 that effectively isolates that potential ejection site from the ejection sites of the other droplet ejectors 12. As previously pointed out, each of the apertures 32 is sized to have a diameter that is much larger (i. e., at least approximately five times greater than and, in some cases, twenty times or more times larger) than the waist diameter of the focused acoustic beam, so the apertures 32 have no material affect upon the formation, size or directionality of the droplet of ink 15 that are ejected. As will be understood, the free ink surface 13 forms a meniscus 33 across each of the apertures 32 because of its surface tension. Furthermore, the capillary attraction between the ink 14 and the aperture sidewalls resists any tendency this meniscus 33 may have to shift upwardly or downwardly within the aperture 32 as a function of any slight changes in the volume of the ink 14, so the cap structure 31 effectively stabilizes the free ink surface level, at least under quiescent operating conditions. However, the free ink surface level still is dynamically instable because the droplet ejection process inherently generates surface ripple waves. This is a hydrodynamically damped instability, so the challenge is to reduce the time that is required for the perturbations to dissipate to a negligibly low amplitude. Referring to Fig. 2, conventional ray analysis techniques are useful for determining the amplitude versus time characteristics of the transient oscillatory perturbations that disturb the level of the free ink surface 13 within the critical central region of the aperture 32 immediately after a droplet of ink 15 is ejected therefrom. Fig. 2 is based on the assumptions that the aperture 32 is a round aperture having a diameter of 250µm and that its so-called "critical central region" is a concentric circular area having a diameter of 50 µm (i. e., an area that is sufficiently proximate the ejection site that perturbations occurring within it are likely to have a meaningful influence on the ejection process). The amplitude of the perturbations has been normalized to unity at the time of droplet ejection, and their amplitude has been plotted as a function of the distance the ripple wave has propagated (which is proportional to time since the propagation velocity is substantially constant). As would be expected, the surface ripple wave initially is contained within the central critical region of the aperture 32. The ripple wave then propagates outwardly to the aperture sidewalls, where it is reflected back toward the center of the aperture 32, so it re-enters the central region of the aperture 32 to complete a first roundtrip. This propagation/reflection process repeats itself, so the level of the free ink surface 13 in the central region of the aperture 32 is periodically perturbed, with the amplitude of this oscillatory perturbation decaying at a rate, as indicated by the line 35 in Fig. 2, that is determined by the exponential attenuation that the surface wave experiences as it propagates. The impact of the retroreflectivity of the generally round (i. e., circularly configured) aperture 32 on the amount of time that is required for the amplitude of these oscillatory perturbations to decay to a negligibly low level will be evident when their instantaneous amplitude, as represented by the line 35, is compared on a corresponding time scale with the asymptote 36, which represents the amplitude of the perturbations that would exist within the central region of the aperture 32 if the surface ripple wave was decomposed into wavelets uniformly distributed over the full span of the aperture 32 (the amplitude of the asymptote 36 tracks the amplitude of decay rate 35, but is only 4% as high because the critical central region of the aperture 32 has been assumed to be 4% of total transverse-sectional area of the aperture 32). Turning now to Fig. 3, in accordance with this invention, there is a non-retroreflective aperture configuration 42 that can be used to increase the rate at which droplets of ink 15 can be ejected by the droplet ejector 12 asynchronously. This particular aperture has a pentagonal transverse-sectional configuration, but any aperture having a substantially non-retroreflective transverse-sectional configuration will significantly increase the rate at which the troublesome free ink surface level oscillations dissipate to a negligibly low level (an amplitude no greater than about ± ½λ) . This includes apertures having serpentine curvilinear transverse-sectional shapes, as well as those that have polygonal configurations. The performance characteristics of several even-sided polygonal aperture configurations are analyzed in Fig. 4, where the curves 43, 44, 45, and 46 represent the perturbations that occur within the central region of the aperture 42 if it has a square, hexagonal, octogonal or decagonal transverse-sectional shape, respectively. The analysis assumes that the aperture 42 has the same total area, as well as a "critical central region" of the same shape (circular) and diameter (50 µm), as the aperture 32 (Fig. 2). As will be seen, the surface wave induced perturbations that occur within the central region of these even-sided apertures still have a strong periodicity, but their amplitude dissipates to a negligibly low level significantly faster than the perturbations that occur in the central region of aperture 32 (compare the decay rates of the curves 43 - 46 with the decay rate 35 and the asymptote 36 from Fig. 2. Fig. 5 provides a similar analysis, based on the same assumptions, for several odd-sided polygonal aperture configurations. Specifically, curves 51, 52, 53, and 55 represent the surface ripple wave induced perturbations that occur within the central region of the aperture 42 if it has a triangular, pentagonal, heptagonal or nonagonal transverse-sectional configuration, respectively. These curves show that the even numbered reflections of the surface ripple wave have no affect on the free ink surface level in the central regions of these odd-sided polygonal apertures 42. That is meaningful, especially for cases in which the perturbances created within the central region of the aperture 42 by the third and higher order reflections are of negligible amplitude (i. e., where the diffusion provided by the aperture 42 can be optimized strictly for the first reflection). Another interesting observation is that the amplitude of the perturbation that is produced within the central region of the aperture 42 by the first reflection of the surface ripple wave is lower for a pentagonal aperture configuration than for any of the other odd-sided aperture configurations that are analyzed (compare the peak amplitude of the curve 52 with the peak amplitudes of the curves 51, 53 and 54 for the relative amplitudes of the perturbances that are caused by the first reflection of the ripple wave). This suggests that a pentagonal aperture configuration may be optimal for some applications. Fig. 6 illustrates a somewhat more specialized embodiment of this invention, where the geometric center 51 of each of the apertures 52 is spatially displaced from the droplet ejection site 53 of the associated droplet ejector (i. e., the focal point of the droplet ejector) by a distance that is greater than the radius of the so-called critical region of the aperture 52. This embodiment is particularly interesting for applications in which the surface ripple wave is attenuated to a neglibily low level by the time it completes its second roundtrip because it can be implemented for those applications by means of a cap structure that has round apertures 52. Specifically, if the apertures 52 are round, their geometric eccentricity with respect to the ejection cites 53 of the respective droplet ejectors will cause the focal point for the reflected ripple waves within any given one of the apertures 52 to alternatively shift back and forth between the ejection site 53 and a location that is symmetrically opposed (with respect to the geometric center 51 of the aperture 52) to the ejection site 53 on their even and odd numbered reflections, respectively. Consequently, the notion of diffusively scattering the reflected ripple waves can be extended in accordance with the broader aspects of this invention to include the more general concept of geometrically tailoring the apertures of a cap structure of the foregoing type so that a substantial portion of the ripple wave energy that is reflected by their sidewalls is directed away from the critical regions proximate the respective droplet ejection sites, at least on the first (i. e., least attenuated) reflection of the ripple waves. As will be understood, the mean transverse dimensions of the apertures shown in Figs. 3, 4 and 5 (sometimes referred to as their "diameters") are selected to be substantially greater (at least five times greater and as much as twenty or more times greater) than the diameters of the critical regions around the droplet ejection sites. While those critical regions have been assumed to be generally circular areas, it should be noted that both the shape and the transverse dimensions of the these regions are application specific parameters that should be analytically or empirically computed when implementing this invention. In view of the foregoing it now will be evident that this invention significantly increases the droplet ejection rates at which acoustic ink printers that utilize apertured cap structures for free ink surface level control can be operated asynchronously. Moreover, it will be evident that this improved performance can be achieved at little, if any, additional cost.

Claims: An acoustic ink printer having at least one droplet ejector for ejecting individual droplets of ink of predetermined maximum diameter from a free surface of a pool of liquid ink on demand, a cap structure for holding said free surface at a predetermined level; said cap structure comprising a body having a dedicated aperture formed therethrough for each droplet ejector, thereby providing an isolated portion of said free ink surface for each droplet ejector, each aperture being sized to have a mean transverse dimension that is substantially greater than the maximum diameter of said droplets of ink, characterised in that each aperture has a sectional shape transverse to the direction of droplet ejection which is substantially non-retroreflective. The acoustic ink printer of Claim 1 wherein each droplet ejector includes means for illuminating said free ink surface with an amplitude modulated, substantially focused acoustic beam for ejecting droplets of ink therefrom on demand, and said acoustic beam is incident on said free surface generally centrally of the aperture dedicated to said droplet ejector. The acoustic ink printer of Claim 2 wherein said acoustic beam has a predetermined maximum waist diameter at focus; and the mean transverse dimension of said aperture is at least approximately five times larger than said waist diameter of said beam. The acoustic ink printer of any of Claims 1 - 3 wherein said aperture has (1) an odd-sided polygonal configuration, (2) a pentagonal configuration, (3) an even-sided polygonal configuration, or (4) a curvilinear configuration. The acoustic ink printer of Claim 4 wherein the mean transverse dimension of said aperture is on the order of twenty times larger than the waist diameter of said beam. An acoustic ink printer having at least one droplet ejector for ejecting individual droplets of ink of predetermined maximum diameter from a free surface of a pool of liquid ink on demand, a cap structure for holding said free surface at a predetermined level; said cap structure comprising a body having a dedicated aperture formed therethrough for each droplet ejector, such that said aperture isolates a portion of said free ink surface for the droplet ejector to which it is dedicated, each aperture being sized to have a mean transverse dimension that is significantly greater than said maximum diameter of said droplets, characterised in that each aperture is positioned with respect to a predetermined critical region of said aperture including the point of ejection of said droplets, for reflectively redirecting surface ripple waves originating therein away from said critical region, at least when said ripple waves are first reflected. The acoustic ink printer of Claim 6 wherein each droplet ejector includes means for illuminating said free ink surface with an amplitude modulated, substantially focused acoustic beam for ejecting droplets of ink therefrom on demand, said acoustic beam is incident on said free surface at an ejection site that is located centrally of the critical region of the aperture that is dedicated to said droplet ejector, and said critical region of said aperture is a generally circular area of predetermined radius that is centered on said ejection site, with said radius being substantially less than one half said mean transverse dimension. The acoustic ink printer of Claim 6 or 7 wherein each droplet ejector has a geometric center that is offset from the ejection site therein by a distance that is greater than said radius. The acoustic ink printer of Claim 6, 7 or 8 wherein each aperture is defined by a generally round passageway that extends through said cap structure.

Inventors: ELROD SCOTT A, HADIMIOGLU BABUR B, KHURI-YAKUB BUTRUS T, QUATE CALVIN F, RAWSON ERIC G, ELROD, SCOTT A., HADIMIOGLU, BABUR B., KHURI-YAKUB, BUTRUS T., QUATE, CALVIN F., RAWSON, ERIC G.
Applicants: XEROX CORP, XEROX CORPORATION
Application year: 1992
Main classification: B41J2
IPC codes: B41J2