Energy-dissipating nozzles and nozzle arrays for drop-on-demand printing

Abstract

To make it possible to control fluid flow and to discharge droplets having consistent properties such as shape, volume and velocity.SOLUTION: Disclosed is a nozzle for a printing system. The nozzle includes a tank which communicates with a printing material supply source. Further, the nozzle includes a constriction dissipation section communicating with the tank that may include a slender inner channel. Further, the nozzle may include a shaping tip communicating with the constriction dissipation section that may include an outlet orifice. The constriction dissipation section may include at least three inner channels which may be axially symmetric and do not communicate with each other. Also, a nozzle array for the printing system including a plurality of nozzles is disclosed. Each nozzle includes: a tank which communicates with a printing material supply source; a constriction dissipation section which communicates with the tank, is so configured as to block fluid flow, and has a slender inner channel; and a shaping tip which communicates with the constriction dissipation section, and may include an outlet orifice.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] Embodiments or implementations of this disclosure relate to energy-dissipating nozzles for drop-on-demand printing systems and methods therefor. [Background technology]

[0002] Drop-on-demand (DOD) printing systems, such as inkjet or liquid metal jet printing, achieve significant advantages over alternative technologies, two of which are the absence of additional post-processing steps and relative affordances. Unfortunately, DOD basic performance metrics (e.g., printing speed, accuracy) are, on average, more sensitive to the geometric shape of the product than other technologies. Products with complex geometric shapes manufactured with liquid metal DOD technology may require hundreds or even millions of droplets and may take longer to produce. Printed parts can also deviate from planned computer-aided designs (CAD) because errors accumulate from the nominal geometric shape per deposited droplet. Furthermore, speed and accuracy correlate with fundamental trade-offs. Printing speed is the cost of accuracy. Therefore, droplet speed, shape, and volume play important roles in print quality metrics.

[0003] In DOD (Dropout Discharge) injection systems, the focus of this fundamental trade-off lies in the injection nozzle, a device designed to control the fluid flow and eject droplets with consistent characteristics such as shape, volume, and velocity, thereby meeting the required throughput, expressed as mass ejected per unit time. The application for which the nozzle is designed drives the desired droplet characteristics. For example, in 3D printing systems, large / bulky droplets may be undesirable for the agility required to print complex geometric objects, while larger droplets may be desirable in liquid dosing applications. Throughput requirements are set to make the droplet ejection system economically attractive for the application.

[0004] Both theoretical and experimental evidence suggest that printing irregularities can occur due to the unpredictable velocity, shape, and volume of droplets produced by the nozzle, rather than the constant nominal values ​​expected by the design. Because each new droplet is generated under different initial conditions and pressure signals, these irregularities are attributable to both the dynamics of the liquid in the tank supplying the nozzle and the time it takes for the liquid in the nozzle to become stationary.

[0005] Next, the throughput and droplet characteristics requirements imply the frequency requirements at which the nozzle must consistently eject droplets. Experimental evidence shows that the launch frequency for stable fall behavior is influenced by the time it takes for the meniscus (the boundary between the fluid and atmosphere at the nozzle orifice) to settle after droplet ejection; that is, droplets should ideally be ejected when the meniscus is at rest. Droplets ejected after the meniscus has settled exhibit consistent characteristics, while ejecting droplets at a frequency faster than the reciprocal of the settling time can result in significant fall variability. Therefore, the nozzle must be designed so that the meniscus settling time after droplet ejection, also known as the relaxation time, is small enough to allow for the desired launch frequency.

[0006] A nozzle design that allows for simultaneous control of relaxation time and droplet characteristics is desirable, particularly one where the problem of controlling relaxation time can be separated from the problem of shaping droplets. What is needed is a nozzle design that simultaneously addresses the aforementioned criteria while enabling the adaptation and application of printing media and methods for designing them. [Overview of the project]

[0007] The following is a simplified overview to provide a basic understanding of some aspects of one or more embodiments of this teaching. This overview is not a broad summary and is not intended to identify the main or important elements of this teaching or to specify the scope of this disclosure. Rather, its primary purpose is simply to present one or more concepts in a simplified form as a prelude to the detailed explanations that will be presented later.

[0008] A nozzle for a printing system is disclosed. The nozzle includes a tank communicating with a source of printing material. The nozzle also includes a constricted dissipation section communicating with the tank, which may include an elongated internal channel. The nozzle also includes a shaped tip communicating with the constricted dissipation section, which may include an outlet orifice.

[0009] Certain embodiments of the disclosed nozzle may include a constricted dissipation section configured to block the fluid flow. The constricted dissipation section may be axially symmetric and may have a diameter smaller than the diameter of the tank, or alternatively, a diameter smaller than the diameter of the shaped tip. The constricted dissipation section may further include at least three internal channels that do not communicate with each other and may have substantially the same diameter.

[0010] In some embodiments, the constricted dissipation section of the nozzle may include at least two intersecting channels that are substantially perpendicular to each other. These intersecting channels may further include at least two walls that are parallel to each other. The constricted discharge section of the nozzle may include three intersecting channels arranged at substantially 45-degree angles around the axis of the constricted dissipation section.

[0011] A particular nozzle embodiment may have a constricted dissipation section that may contain a porous medium. The nozzle may further include a tapered transition section between the constricted dissipation section and the shaped tip. The exit orifice of the shaped tip may be cylindrical or comprise a narrow slit. The exit orifice may have a radius of curvature less than 10 percent of the diameter of the exit orifice. The nozzle may be configured to discharge droplets by manipulating a generation event followed by an evacuation event.

[0012] A nozzle for a printing system is also disclosed, which includes a tank communicating with a source of printing material. The nozzle may also include a constricted dissipation section communicating with the tank and configured to block the fluid flow, which may further include an elongated internal channel. The nozzle mat also includes a shaped tip communicating with the constricted dissipation section and having an outlet orifice, and the nozzle is configured to discharge droplets by manipulating a generation event followed by an evacuation event.

[0013] An array of nozzles for a printing system including multiple nozzles is also disclosed, each nozzle including a tank communicating with a source of printing material, a constricted dissipation section communicating with the tank and configured to block fluid flow and having an elongated internal channel, and a shaped tip communicating with the constricted dissipation section and possibly including an outlet orifice.

[0014] A particular embodiment may include an array of nozzles for a printing system, each nozzle comprising: a tank communicating with a source of printing material; a constricted dissipation section communicating with the tank and configured to block fluid flow, having an elongated internal channel having at least two intersecting channels substantially perpendicular to each other; and a shaped tip communicating with the constricted dissipation section, which may include an outlet orifice. [Brief explanation of the drawing]

[0015] The accompanying drawings incorporated herein and forming part thereof illustrate embodiments of this teaching. These and / or other aspects and advantages of embodiments of this disclosure will become apparent and more readily apparent from the following description of various embodiments in conjunction with the accompanying drawings.

[0016] [Figure 1] Schematic cross-sectional views illustrating exemplary additive manufacturing devices or 3D printers incorporating nozzle designs, as disclosed and according to one or more embodiments, are provided.

[0017] [Figure 2A]Illustrate a schematic cross-sectional view of a conventional nozzle design of the prior art.

[0018] [Figure 2B] Illustrate a schematic cross-sectional view of an exemplary nozzle design according to one or more of the disclosed embodiments.

[0019] [Figure 3] Illustrate a schematic cross-sectional view of a portion of a nozzle design according to one or more of the disclosed embodiments.

[0020] [Figure 4A] Illustrate some multi-sectional nozzles according to one or more of the disclosed embodiments. [Figure 4B] Illustrate some multi-sectional nozzles according to one or more of the disclosed embodiments. [Figure 4C] Illustrate some multi-sectional nozzles according to one or more of the disclosed embodiments. [Figure 4D] Illustrate some multi-sectional nozzles according to one or more of the disclosed embodiments.

[0021] [Figure 5A] Illustrate schematic cross-sectional side views of, respectively, non-restricted and restricted nozzle designs according to one or more of the disclosed embodiments. [Figure 5B] Illustrate schematic cross-sectional side views of, respectively, non-restricted and restricted nozzle designs according to one or more of the disclosed embodiments.

[0022] [Figure 6A] Illustrate schematic cross-sectional side views of simulated experiments, presented at various time instants, respectively generated using standard and restricted axisymmetric nozzle designs according to one or more of the disclosed embodiments. [Figure 6B] Illustrate schematic cross-sectional side views of simulated experiments, presented at various time instants, respectively generated using standard and restricted axisymmetric nozzle designs according to one or more of the disclosed embodiments.

[0023] [Figure 7] This is a cross-sectional side view illustrating the concept of meniscus displacement relative to the front surface of a nozzle embodiment according to one or more disclosed embodiments.

[0024] [Figure 8] Figures 6A and 6B are plots showing the simulated meniscus displacement as a function of time for the discharge of a single droplet from a narrowed, unconstructed nozzle embodiment.

[0025] [Figure 9] A basic abstract diagram of the nozzle and circuit board portion of a printer embodiment is illustrated.

[0026] [Figure 10] An example of a waveform plot representing a pressure pulse applied to the upper boundary of a nozzle, according to an embodiment of this specification, is illustrated.

[0027] [Figure 11A] This is a series of plots showing multiple droplet simulation experiments with constricted and unconstricted nozzles for three ejection frequencies according to the embodiments of this specification. The droplet volume and volume-averaged velocity are plotted against the number of droplets. [Figure 11B] This is a series of plots showing multiple droplet simulation experiments with constricted and unconstricted nozzles for three ejection frequencies according to the embodiments of this specification. The droplet volume and volume-averaged velocity are plotted against the number of droplets. [Figure 11C] This is a series of plots showing multiple droplet simulation experiments with constricted and unconstricted nozzles for three ejection frequencies according to the embodiments of this specification. The droplet volume and volume-averaged velocity are plotted against the number of droplets. [Figure 11D] This is a series of plots showing multiple droplet simulation experiments with constricted and unconstricted nozzles for three ejection frequencies according to the embodiments of this specification. The droplet volume and volume-averaged velocity are plotted against the number of droplets. [Figure 11E]This is a series of plots showing multiple droplet simulation experiments with constricted and unconstricted nozzles for three ejection frequencies according to the embodiments of this specification. The droplet volume and volume-averaged velocity are plotted against the number of droplets. [Figure 11F] This is a series of plots showing multiple droplet simulation experiments with constricted and unconstricted nozzles for three ejection frequencies according to the embodiments of this specification. The droplet volume and volume-averaged velocity are plotted against the number of droplets.

[0028] [Figure 12] This is a schematic cross-sectional view of a portion of a nozzle design according to one or more disclosed embodiments, illustrating the parameterization of a constricted axisymmetric nozzle design.

[0029] [Figure 13A] These are plots of the average velocity of the ejected droplet volume as a function of the constriction diameter, and the ejected droplet volume as a function of the constriction diameter, respectively. [Figure 13B] These are plots of the average velocity of the ejected droplet volume as a function of the constriction diameter, and the ejected droplet volume as a function of the constriction diameter, respectively.

[0030] [Figure 14] This is a spatiotemporalally scaled plot of a characteristic waveform showing its positive and negative components according to one embodiment.

[0031] [Figure 15A] Figure 14 shows a series of four plots illustrating the results of a parametric simulation experiment of the positive portion of the waveform according to one embodiment, as well as the waveform effect on droplet velocity and volume. [Figure 15B] Figure 14 shows a series of four plots illustrating the results of a parametric simulation experiment of the positive portion of the waveform according to one embodiment, as well as the waveform effect on droplet velocity and volume. [Figure 15C] Figure 14 shows a series of four plots illustrating the results of a parametric simulation experiment of the positive portion of the waveform according to one embodiment, as well as the waveform effect on droplet velocity and volume. [Figure 15D] Figure 14 shows a series of four plots illustrating the results of a parametric simulation experiment of the positive portion of the waveform according to one embodiment, as well as the waveform effect on droplet velocity and volume.

[0032] [Figure 16A] The top views of the dissipation intervals in multi-channel nozzles having four and five channels, respectively, are illustrated as examples. [Figure 16B] The top views of the dissipation intervals in multi-channel nozzles having four and five channels, respectively, are illustrated as examples.

[0033] [Figure 17] These plots show the simulated meniscus displacement as a function of time of droplet discharge from the multi-channel nozzle embodiments in Figures 16A and 16B, compared to a standard non-constricting nozzle design embodiment. [Modes for carrying out the invention]

[0034] The following descriptions of various typical embodiments are merely illustrative and are not intended to limit the Disclosure, its uses, or any other applications.

[0035] As used throughout, ranges are used as abbreviations to describe each and all values ​​within that range. Any value within a range may be selected as the endpoint of the range. Furthermore, all references cited herein are incorporated herein by reference in their entirety. In the event of any conflict between the definitions in this disclosure and the cited references, this disclosure shall take control.

[0036] In addition, all numerical values ​​are "approximately" or "about" the indicated values, taking into account the experimental errors and variations that a person skilled in the art would expect. It should be understood that all numerical values ​​and ranges disclosed herein are approximations and ranges, whether or not "approximately" is used with them. It should also be understood that, when used herein, the term "approximately" refers, along with a numerical value, to a value that may be ±0.01% (including boundary values), ±0.1% (including boundary values), ±0.5% (including boundary values), ±1% (including boundary values), ±2% (including boundary values), ±3% (including boundary values), ±5% (including boundary values), ±10% (including boundary values), or ±15% (including boundary values) of that numerical value. It should be further understood that when a numerical range is disclosed herein, any numerical values ​​that fall within that range are also specifically disclosed.

[0037] As used herein, the term “or” is an inclusive operator and is equivalent to the term “and / or” unless the context explicitly indicates otherwise. The term “based on” is not exclusive and allows for the basis of additional factors not mentioned unless the context explicitly indicates otherwise. In this specification, “at least one of A, B, and C” includes embodiments including A, B, or C, multiple examples of A, B, or C, or combinations such as A / B, A / C, B / C, A / B / B / B / C, A / B / C, etc. In addition, throughout this specification, the meanings of “a,” “an,” and “the” include multiple references. The meaning of “in” includes “in” and “on.”

[0038] Hereinafter, an exemplary embodiment of this teaching will be given detailed reference, and this embodiment is shown in the accompanying drawings. Wherever possible, the same reference numerals will be used throughout the drawings to refer to the same, similar, or identical parts.

[0039] This disclosure covers additive manufacturing devices or 3D printers and methods thereof. In particular, this disclosure covers target heating systems and methods thereof for 3D printers. Forming structures with molten metal droplets is a complex thermofluid process involving remelting, coalescence, cooling, and solidification. Voids and cold laps (lack of melting) are caused by insufficient remelting and inadequate metallurgical bonding at inappropriate temperatures at the interface formed between the molten metal droplet and the previously deposited material or substrate (e.g., the droplet). The interface temperature is mainly determined by the droplet temperature and surface temperature of the previously deposited material or substrate. Obtaining and maintaining accurate part geometry and z-height is also adversely affected by the same factors. Interface temperatures that are too low result in the formation of voids and cold laps from insufficient remelting and coalescence. If the interface temperature is too high, the new droplet flows away from the surface of the previously deposited material before solidification, which results in shape defects and z-height errors in the part geometry. The interface temperature can be affected by the initial droplet temperature, the surface temperature of the constructed part, the construction plate temperature, the droplet frequency, and the part's z-height. While this can be controlled to some extent by optimizing process parameters, the thermal processes involved can be excessively slow due to changes and mechanics that occur during part printing, which can result in unacceptable interface temperatures. As further described herein, a target heating system may or may be configured to modify the interface temperature and / or temperature gradient of the substrate and / or the area proximal to the substrate in order to control the grain size, growth, and / or structure of the metal forming the article prepared by the 3D printer in order to address the aforementioned problems. For example, a target heating system may or may be configured to modify the interface temperature and / or temperature gradient of the molten pool in order to control the grain size, growth, and / or structure of the metal forming the article, thereby improving construction strength, adhesion, porosity, and / or surface finish, and preventing cracks and fractures within the article.

[0040] Figure 1 illustrates a schematic cross-sectional view of an exemplary drop-on-demand (DOD) printer device or 3D printer 100 incorporating a target heating system 102, according to one or more embodiments. The 3D printer 100 may be a liquid metal jet printing system such as a magnetohydrodynamic (MHD) printer. However, it should be understood that any drop-on-demand (DOD) printing device may utilize the components and methods disclosed herein. The 3D printer 100 may include a print head 104, a stage 106, a computing system 108, a target heating system 102, or any combination thereof. The computing system 108 may be operable and / or communicatively coupled to any one or more components of the 3D printer 100. The computing system 108 may be able to operate, modulate, instruct, receive data, etc. from any one or more components of the 3D printer 100, or may be configured to do so. The print head 104 may include a body 110, which may also be referred to herein as a pump chamber, one or more heating elements (one of which is indicated by 112), one or more metal coils 114, or any combination operably coupled to one another. As illustrated herein, the heating element 112 may be at least partially positioned around the body 110, and the metal coils 114 may be at least partially positioned around the body 110 and / or the heating element 112. As used herein, the substrate 116 may refer to the surface of the stage 106, previously deposited printing material or metal (e.g., metal droplets), an article 118 made from the 3D printer 100 or a part thereof, a platen 128 such as a heating platen or construction plate positioned on the stage 106, and / or each of its respective surfaces. As illustrated herein, the substrate 116 may be positioned above or above the stage 106 and below the body 110. The body 110 may have an inner surface 120 defining its internal volume 122. The main body 110 may define a nozzle 124 located at a first end of the main body 110. The main body 110 of the print head 104 may also define two or more nozzles 124 that may operate in conjunction with each other or, alternatively, independently of each other.

[0041] In the exemplary operation of the 3D printer 100, continuing with reference to Figure 1, the construction material (e.g., metal) from the source 126 can be directed into the internal volume 122 of the body 110. A heating element 112 can at least partially melt the construction material contained within the internal volume 122 of the body 110. For example, the construction material may be a solid, such as a solid metal, and the heating element 112 can heat the body 110, thereby heating the construction material from a solid to a liquid (e.g., molten metal). A metal coil 114 can be coupled to a power source (not shown) capable of facilitating the deposition of construction material onto the substrate 116, or configured to do so. For example, the metal coil 114 and the power source coupled thereto may be capable of generating a magnetic field, or may be configured to generate one, which can generate an electromotive force within the body 110, thereby generating an induced current in the molten metal placed within the body 110. The magnetic field and induced current in the molten metal can generate a radially inward force on the liquid metal, known as the Lorentz force, which generates pressure in the nozzle 124. The pressure in the nozzle 124 can cause molten metal to be discharged from the nozzle 124 toward the substrate 116 and / or stage 106 in the form of one or more droplets, thereby forming at least a portion of the article 118.

[0042] In at least one embodiment, the construction material is one or more metals and / or alloys thereof, or may include them. Illustrative construction materials may include, but are not limited to, aluminum, aluminum alloys, brass, bronze, chromium, cobalt-chromium alloys, copper, copper alloys, iron alloys (Invar), nickel, nickel alloys (Inconel), nickel-titanium alloys (Nitinol), stainless steel, tin, titanium, titanium alloys, gold, silver, molybdenum, tungsten, or alloys thereof, or any combination thereof. It should be understood that droplet and substrate temperatures will differ with respect to different metals.

[0043] In another embodiment, the construction material may be one or more polymer materials or polymers, or composites thereof. The polymer may be a functional polymer, or may include a functional polymer. Illustrative functional polymers include, but are not limited to, heat-resistant polymers, conductive polymers, piezoelectric polymers, photosensitive polymers, or any combination thereof. The polymer may also be, but are not limited to, polyolefin polymers, acrylic polymers, polyurethane polymers, ether polymers, polyester polymers, polyamide polymers, formaldehyde polymers, silicone polymers, or any combination thereof. For example, polymers include poly(etheretherketone) (PEEK), TORLON®, polyamide-imide, polyethylene (PE), polyvinyl fluoride (PVF), polyvinyl chloride (PVC), polyvinylidene fluoride (PVDF), polyvinylidene chloride (PVDC), polychlorotrifluoroethylene (PCTFE), polytetrafluoroethylene (PTFE), polypropylene (PP), poly(1-butene), poly(4-methylpentene), polystyrene, polyvinylpyridine, polybutadiene, polyisoprene, polychloroprene, styrene-acrylonitrile copolymer, acrylonitrile-butadiene-styrene terpolymer, ethylene-methacrylate copolymer, Examples include, but are not limited to, styrene-butadiene rubber, tetrafluoroethylene copolymers, polyacrylates, polymethacrylates, polyacrylamides, polyvinyl acetate, polyvinyl alcohol, polyvinyl butyral, polyvinyl ethers, polyvinylpyrrolidone, polyvinylcarbazole, polyurethanes, polyacetals, polyethylene glycol, polypropylene glycol, epoxy resins, polyphenylene oxide, polyethylene terephthalate, polybutylene terephthalate, polyhydroxymethylcyclohexyl terephthalate, cellulose esters, polycarbonates, polyamides, polyimides, any copolymers thereof, or any combination thereof.In at least one embodiment, the polymer is an elastomer, a synthetic rubber, or any combination thereof, or may include these. Illustrative elastomer materials and synthetic rubbers may include, but are not limited to, VITON®, nitriles, polybutadiene, acrylonitrile, polyisoprene, neoprene, butyl rubber, chloroprene, polysiloxane, styrene-butadiene rubber, hydrin rubber, silicone rubber, ethylene-propylene-diene polymer, any copolymer thereof, or any combination thereof.

[0044] In exemplary embodiments, the polymer may include acrylonitrile butadiene styrene (ABS), polycarbonate (PC), polylactic acid (PLA), high-density polyethylene (HDPE), polyphenylsulfone (PPSU), poly(meth)acrylate, polyetherimide (PEI), polyetheretherketone (PEEK), high-impact polystyrene (HIPS), thermoplastic polyurethane (TPU), polyamide (nylon), composites thereof, or combinations thereof.

[0045] In at least one embodiment, the 3D printer 100 may include a monitoring system 130 that is capable of controlling and / or monitoring one or more components or parts of the 3D printer 100, the formation of an article 118, one or more parts of a substrate 116, one or more proximal areas of the substrate 116, and / or droplet deposition. For example, the monitoring system 130 may include one or more illuminators (not shown) that can measure droplet, build component, build plate, and substrate temperatures, build component shape and z-height, droplet size and velocity, etc., or any combination thereof, or are configured to do so. Illustrative illuminators may include, but are not limited to, lasers, LEDs, various types of lamps, fiber optic light sources, or combinations thereof. In another example, the monitoring system 130 may include one or more sensors (not shown) that can measure, or are configured to measure, the temperature of one or more components or parts of the 3D printer 100. Illustrative sensors may include, but are not limited to, thermometers, thermistors, imaging cameras, photodiodes, or combinations thereof. The monitoring system 130 may also be, or may be configured to, provide feedback or communicate with the computing system 108.

[0046] In at least one embodiment, any one or more components of the 3D printer 100 may move independently of each other. For example, any one or more of the print head 104, the stage 106, and the platen 128 coupled thereto, the target heating system 102, the monitoring system 130, or any combination thereof may move independently of any one or more of the other components of the 3D printer 100 along the x, y, and / or z axes. In another embodiment, any two or more components of the 3D printer 100 may be coupled to each other and therefore may move relative to each other. For example, the print head 104 and the target heating system 102 may be coupled to each other via mounts (not shown) such that the movement or translation of the print head 104 along the x, y, and / or z axes results in the corresponding movement of the target heating system 102 along the x, y, and / or z axes, respectively. Similarly, the target heating system 102 and the stage 106 may be coupled to each other via mounts (not shown) such that movement of the target heating system 102 along the x, y, and / or z axes results in corresponding movement of the stage 106 along the x, y, and / or z axes, respectively.

[0047] In certain embodiments, various construction materials may influence specific design considerations based on the printing material properties and composition, particularly at the injection temperature. Molten metal and / or molten polymer-based printing materials may have different viscosities and surface tensions at the influencing injection temperature, influencing nozzle design and other printing system parameters such as next-shot settings, current settings, other parameters affecting the force applied to the molten or liquid printing material, and other parameters affecting the force applied to the molten or liquid printing material to create pressure at the nozzle 124. Similarly, aqueous materials may require further design considerations to create pressure at the nozzle 124 suitable for printing in various drop-on-demand and drop-discharge configurations. Nozzle design for pulsed droplet ejection systems

[0048] In certain embodiments of DOD (Digital-to-Dose) injection systems or DOD printers, nozzles are designed to control fluid flow and eject droplets with consistent characteristics (shape / volume / velocity) to meet required throughput (mass ejection per unit time). The application for which the nozzle is designed drives the desired droplet characteristics. For example, in 3D printing systems, large / bulky droplets may be undesirable due to the agility required to print complex geometric objects, while larger droplets are preferable in liquid dosing applications. Throughput requirements are set to make the droplet ejection system economically attractive for the application.

[0049] Those skilled in the art know that printing irregularities can occur due to the unpredictable velocity, shape, and volume of droplets produced by the nozzle, rather than the constant nominal values ​​expected by the design. These irregularities can be attributed to the force required within the nozzle to expel the printing material, both in terms of the dynamics of the liquid in the tank supplied to the nozzle and the time it takes for the liquid within the nozzle to come to a standstill, because both attributes alter the initial conditions and pressure signals when each new droplet is produced.

[0050] In certain embodiments, system inputs related to throughput and droplet characteristics can ultimately determine the available frequencies at which the nozzle must eject consistent droplets. The launch frequency required for stable fall behavior may be further influenced by the meniscus, or the boundary between the fluid and atmosphere in the nozzle orifice, for settling after droplet ejection, thus determining that the fall should ideally be ejected when the meniscus is at rest. Droplets ejected after the meniscus has come to rest exhibit more consistent characteristics, while ejecting droplets at a frequency faster than the reciprocal of the settling time can result in significant fall variability. Therefore, the nozzle must be designed such that the meniscus settling time after droplet ejection labels the subsequent relaxation time and is small enough to enable the desired launch frequency. Methods for designing the nozzle to simultaneously control the relaxation time and droplet characteristics during ejection are advantageous in certain embodiments. An optimized nozzle can be designed by separating the problem of controlling the relaxation time from the problem of shaping the droplets within the ejector nozzle.

[0051] Figure 2A illustrates a schematic cross-sectional view of a conventional nozzle design of the prior art. The general structure of the nozzle 200 includes a tank 202 and a tip 204. Figure 2B illustrates a schematic cross-sectional view of an exemplary nozzle design according to one or more embodiments disclosed. In an exemplary embodiment, the nozzle 206 consists of three consecutive sections: an upper tank section 208 in which a liquid material is stored; a dissipation section 210 designed to allow a desired maximum frequency from which droplets can be discharged; and a shaping section 212, also called a shaping tip, capable of discharging droplets having consistent characteristics with respect to shape and size. Certain embodiments of the printer described herein may have a collection of one or more such nozzles 206 arranged and configured to discharge droplets simultaneously, thereby combining the discharged droplets to form a single droplet. In embodiments described herein, a method for designing a dissipation section 210 that can dissipate energy based on blocking the fluid flow through the dissipation section may be used by determining a combination of shaping the geometric shape of a nozzle having a constricted passage to the fluid flow and introducing a porous obstruction to the fluid flow or a combination thereof. In embodiments described herein, the dissipation section may be an axisymmetric portion of the nozzle between the tank and the shaped tip or shaped section.

[0052] In the embodiment shown in Figure 2B, the exemplary nozzle has a tank communicating with a dissipation section and a shaping section communicating with the shaping section. The function of the dissipation section of the nozzle is to dissipate fluid energy, increase momentum loss, then increase the meniscus damping rate, and therefore decrease the relaxation time. The relaxation time τ is defined as the time it takes for the deformation of the meniscus of the liquid printing material on the front plane of the nozzle to return to a stationary state after the drop of the printing material has been ejected. The relaxation time t is an exponentially decreasing variable, in this case the time required for the amplitude of the damped oscillation to decrease from its initial value to 1 / e or 0.368 (where e is the base of the natural logarithm). This value can be considered a consistent index for measuring the time it takes for the meniscus on the nozzle surface to return to static equilibrium. The shaping section is designed to produce teardrop-shaped droplets with a predetermined volume and center of gravity velocity, compared to elongated droplets, which are simpler to produce. The coordinated design of the two sections allows for simultaneous control of the velocity of the center of gravity of each droplet and the number of droplets formed per pulse. A pulse can be understood as a pressure signal above the upper end of the nozzle, intended to eject one or more droplets from the nozzle. Design of dissipation sections

[0053] In certain embodiments, a dissipation section with a constant cross-section may be considered for the purpose of establishing design parameters, although a constant cross-section is not required. The relaxation time τ is proportional to a constant cross-sectional area of ​​the dissipation section. Therefore, τ can be set by appropriately selecting geometric parameters that define the cross-sectional area in the dissipation section. The relaxation time is independent of the length of the dissipation section, and therefore the dissipation section should be long enough to be manufacturable and rigid. When the nozzle is operating in a steady state, the amount of fluid that travels through the dissipation section and reaches the shaping section must be equal to at least the mass of the discharged droplets. In certain embodiments, some additional fluid may also flow, and then flow back into a pump or reservoir communicating with the tank portion of the nozzle. In certain embodiments, the parameters selected for the design of the dissipation section are selected to control the relaxation time of the meniscus at the nozzle outlet orifice.

[0054] In certain embodiments, it is desirable to discharge a single droplet that does not split into satellite droplets. To avoid this, the velocity within the droplet should not differ from the velocity of the droplet's center of gravity. The kinetic energy that the droplet carries is approximately proportional to the droplet's mass over time, where the velocity of the center of gravity is squared. If the fluid moves through the dissipation section faster than the expected velocity of the droplet, the excess kinetic energy it carries should be dissipated after the droplet is discharged. The greater the fluid velocity through the dissipation section, the greater the energy that needs to be dissipated, which increases the energy cost of operating the nozzle, increases the time it takes for the meniscus damping oscillations to reach an acceptable level, and therefore lowers the operating frequency. Thus, the fluid velocity through the dissipation section must be much greater than the desired velocity of the center of gravity of the discharged droplet. Furthermore, in steady-state operation, the fluid already in the shaping section should have a velocity near zero at the start of each pulse and should be accelerated to the desired velocity of the discharged droplet. If the fluid velocity through the dissipation section is too high, the pressure increase and viscous forces in the shaping section are not sufficient to accelerate the fluid within it, which can result in multiple droplets being discharged, or droplets that become very elongated with a small diameter immediately after discharge. At the same time, the fluid moving through the shaping section must have a velocity high enough to expand the meniscus and thus generate kinetic energy; therefore, the fluid velocity through the dissipation section must necessarily be greater than the desired velocity of the droplet's center of gravity. Considering the qualitative relationship between fluid velocities in the dissipation section, the meniscus settling time and droplet velocity can be controlled by utilizing the classical ideas of fluid dynamics to design the dissipation section, i.e., by blocking the fluid flow, thereby controlling the pressure drop and velocity change. In the embodiments described herein, blocking can be achieved by preventing or hindering fluid motion by incorporating a permeable medium within the dissipation section, as seen in a Venturi nozzle and / or alternatively.

[0055] Figure 3 illustrates schematic cross-sectional views of a portion of a nozzle design according to one or more disclosed embodiments. The exit portion of the dissipation section 302 leads to the exit orifice 304 of the shaping section, which has a radius of curvature ρ, 306 that affects the nozzle design. In certain embodiments, the length and dimensions of the transition zone between the dissipation section and the shaping section also affect the dissipation of energy in the fluid printing material moving through the nozzle. In certain embodiments, the cross-sectional area of ​​the dissipation section 302 reduces the cross-sectional area of ​​the exit orifice 304. The radius of curvature ρ, 306 of the exit orifice 304 defines the meniscus dynamics, which will be described in more detail later.

[0056] Figures 4A to 4D illustrate several multi-section nozzles according to one or more embodiments disclosed. Figure 4A shows an axially symmetric nozzle embodiment having a constricted channel dissipation section. The dissipation section is designed as a constriction in relation to the diameter of the tank and the diameter of the shaping section. Given the requirement that the ejected fluid printing material must be decelerated after leaving the dissipation section, conservation of mass indicates that the dissipation section must open to increase the cross-sectional area within the shaping section. When a pressure pulse is applied to the printing material at the top of the tank, the liquid in the dissipation section achieves a very large momentum compared to the velocity target. As a result, the liquid in the shaping section is subjected to pressure. If the velocity is too high, and the cross-sectional area between the dissipation section and the shaping section is small, the droplet ejected from the nozzle dissipates very greatly in its initial velocity field. Thus, particles in such droplets move at different velocities that are too high and too low compared to the target value. Droplets in this manner are likely to have unacceptable shapes and may break before reaching the substrate. To address these undesirable effects and maximize droplet uniformity, the liquid in the shaping section being discharged must be equally accelerated from the extrusion from the dissipation section. One way to achieve this is to increase the cross-sectional area, i.e., the area connecting the two sections. An additional advantage of increasing this cross-sectional area is that the undesirable high speeds generated in the dissipation section can be slowed down. Although constricted nozzles are known to those skilled in the art, it is advantageous to use a constricted dissipation section in combination with a corresponding shaping section in DOD printing applications to control the meniscus vibration and droplet characteristics described herein. Figure 4A illustrates an axisymmetric constricted nozzle 400 having a tank 402 having a given diameter 404 as shown. The tank 402 is a reservoir or container for liquid or molten printing material not shown in this figure. The tank 402 is in fluid communication with a dissipation section 406, shown as a cylinder in this embodiment. This cylindrical dissipation section 406 defines a diameter 408, which is smaller than the shown diameter 404 of the tank 402. The cylindrical dissipation section 406 has a length of l D410 is further defined. The printing material is supplied from tank 402 to cylindrical dissipation section 406 by gravity, positive pressure, or other means known to those skilled in the art. The cylindrical dissipation section 406 is in fluid communication with shaping section 412. Shaping section 412 also defines a diameter 414, which is shown to have a larger diameter 414 compared to the diameter 408 of cylindrical dissipation section 406. Shaping section 412 has a length l S 416 is further defined. This provides a nozzle 400 having a geometrically constricted dissipation section 406 compared to the tank 402 and the shaping section 412. It is understood that the meniscus of printing material ejected by such a nozzle settles faster in a constricted nozzle compared to a non-constricted nozzle.

[0057] Figure 4B shows a nozzle embodiment having a “showerhead” channel dissipation section. This may also be referred to as a dissipation channel having at least two or more internal channels. An exemplary embodiment of the showerhead channel nozzle 420 defines a tank 422 having a given diameter 424, as shown. The tank 422 is a reservoir or container for a liquid or molten printing material, which is not shown in this figure. The tank 422 is in fluid communication with the dissipation section 426, which in this embodiment is shown as a cylinder overall. The dissipation section 426 contains three individual internal elongated cylindrical channels. In this embodiment, three internal channels 426A, 426B, and 426C are illustrated, but alternative embodiments may contain only two internal channels, or even ten internal channels, and may be determined in some cases by the nozzle design requirements defined by the dimensions and balance between system parameters. Each internal cylindrical channel 426A, 426B, 426C is shown as having a channel diameter d (not shown here) that is smaller than the overall diameter of the entire dissipation section 428, with a diameter 428 that is smaller than the indicated diameter 424 of the tank 422. CIt has 428. Although the three internal channels 426A, 426B, and 426C shown in this embodiment are shown to have the same diameter, alternative embodiments of the nozzle may have different diameters depending on the system requirements. The dissipation section 426 has a length l D 430 is further defined. The printing material is supplied from the tank 422 to the dissipation section 426 by gravity, positive pressure, or other means known to those skilled in the art. The dissipation section 426, in particular the three internal channels 426A, 426B, and 426C, are in fluid communication with the shaping section 432. Note that the three internal channels are not in direct communication with each other, but they are in communication with the tank 422 of the nozzle 420 in Figure 4B and with the shaping section 432, respectively. The shaping section 432 also has a channel diameter d, compared to the overall diameter of the dissipation section 426, whether each of the three internal channels 428 of 426A, 426B, and 426C is individually or combined with the dissipation section 426. C Diameter 434 is defined, which is shown to be a similar diameter 434 that is larger than 428. The shaping section 432 has a length l S 434 is further defined. This provides a nozzle 420 having a geometrically constricted dissipation section 426 compared to the tank 422 and shaping section 432, regardless of the diameter of the nozzle 420 itself. Such obstruction of fluid flow flows as a dissipation section having a constricted channel with a cumulative cross-sectional area comparable to other nozzle embodiments described herein, distributing the dissipation section and providing a more uniform extrusion of the fluid already in the shaping section, and thus the meniscus. This can facilitate the discharge of a single droplet from the nozzle, which has greater flexibility in selecting the pressure signal. Since all channels in the nozzle 420 have a circular cross-section, the relaxation time increases or decreases with the sum of the areas of the internal channels 426A, 426B, and 426C.

[0058] Figure 4C shows an embodiment of a nozzle having a “cross-channel” dissipation section. This may also be referred to as a dissipation channel having multiple axisymmetric parallel plate channels. This embodiment of the cross-channel nozzle 436 defines a tank 438 having a given diameter 440, as shown. The tank 438 is a reservoir or container for a liquid or molten printing material, which is not shown in this figure. The tank 438 is in fluid communication with a dissipation section 442, which in this embodiment is shown collectively as a cylinder. The dissipation section 442 includes a first set of parallel plates 444A, a second set of parallel plates 444B, a third set of parallel plates 444C, and a fourth set of parallel plates 444D. Each of the four sets of parallel plates 444A, 444B, 444C, and 444D is interconnected along the length of the dissipation section 442, thus forming four interconnected channels. This “cross-channel” constricted dissipation section has two intersecting channels that are substantially perpendicular to each other, and the two intersecting channels have two walls that are parallel to each other. An alternative embodiment may have three or more intersecting channels, arranged at substantially 45-degree angles around the axis of the constricted dissipation section. In this embodiment, four sets of parallel plates 444A, 444B, 444C, and 444D are shown, spaced uniformly at 90-degree angles to each other around the central axis of the non-dissipation section 442, but an alternative embodiment may include only two internal channels or as many as ten internal channels, and may be determined in some cases by the nozzle design requirements defined by the dimensions and balance between system parameters. Furthermore, the alternative embodiment may be spaced apart around the central axis from about 10 degrees to about 345 degrees to each other, and does not need to be evenly spaced. Each internal channel, defined by the four sets of parallel plates 444A, 444B, 444C, and 444D, has a distance between each of the sets of parallel plates not shown herein that is smaller than the indicated diameter 440 of the tank 438, as well as a distance smaller than the overall diameter of the overall dissipation section 442 (not shown herein).In this embodiment, the four sets of parallel plates 444A, 444B, 444C, and 444D are shown to have the same distance between each of the parallel plates constituting the set; however, alternative embodiments of the nozzle may have different distances between each set of plates depending on the system requirements. The dissipation section 442 further defines a length 1D 446. The printing material is supplied from the tank 438 to the dissipation section 442 via gravity, positive pressure, or other means known to those skilled in the art. The dissipation section 442 and, in particular, the four sets of parallel plates 444A, 444B, 444C, and 444D are in fluid communication with the shaping section 448. Note that the four sets of parallel plates 444A, 444B, 444C, and 444D are also in direct communication with each other, and the tank 438 of the nozzle 436 in Figure 4C is also in direct communication with the shaping section 448. The shaping section 448 also defines a diameter not shown here, which is still larger than the distance between each set of the four parallel plates 444A, 444B, 444C, and 444D of the dissipation section 426, compared to the overall diameter of the indeterminate section. The shaping section 448 further defines a length lS450. This provides a nozzle 436 having a geometrically narrowed dissipation section 442 compared to the tank 438 and the shaping section 448, regardless of the diameter of the nozzle 436 itself. In one embodiment of the nozzle 436, the dissipation section 426 blocks the fluid motion through the cross-shaped channel. Since the fluid through this section is similar to the flow between parallel plates, the relaxation time increases or decreases as the square of the cross thickness. By adding more arms or sets of inner walls or plates parallel to the interconnected channels forming the intersection, for example, the total area of ​​the cross-channel in the mismatched section 426 can be increased without changing the relaxation time, allowing the fluid to be pushed out more uniformly and reducing the velocity at which the fluid must traverse the dissipation section 426, thus creating a more robust and energy-efficient nozzle. In some embodiments, the area of ​​the cross-channel in the dissipation section 426 may be assumed to be smaller than the area of ​​the outlet orifice in the shaping section 448. In certain embodiments, the dissipation section of a cross-channel nozzle may have six interconnected channels, eight interconnected channels, or more.Although no theoretical limits are known for interconnected channels, the resulting total cross-sectional area must not exceed that of the shaped section in order to maintain the constricted dissipative section.

[0059] Figure 4D shows a nozzle embodiment having a barrier medium dissipation section. An exemplary embodiment of the barrier medium nozzle 452 defines a tank 454 having a given diameter 456, as shown. The tank 454 is a reservoir or container for a liquid or molten printing material, not shown in this figure. The tank 454 is in fluid communication with a dissipation section 458, which in this embodiment is shown as a cylinder overall. The dissipation section 458 contains a barrier medium 460 that narrows the fluid flow through the dissipation section 458 by having a plurality of random paths or channels through it. The paths through the barrier medium 460 can be interconnected along the length of the dissipation section 458. Options for the barrier medium or other porous media may include foams such as polymer foams, ceramics, or metallic foams such as titanium foam, depending on the temperature and properties of the printing medium. Furthermore, alternative embodiments may have various permeability or porosity values ​​depending on the system requirements. The dissipation section 458 has a length l D Further defining 462. The printing material is supplied from tank 454 to dissipation section 458 by gravity, positive pressure, or other means known to those skilled in the art. The dissipation section 458 and in particular the barrier medium 460 are in fluid communication with the shaping section 464. Note that the internal channels formed by the barrier medium 460 may also be in direct fluid communication with each other, and may also be in direct fluid communication with the tank 454 of nozzle 452 in Figure 4D and the shaping section 464. The shaping section 464 also defines a diameter not shown here, which is larger than the theoretical diameter of any combined channels in the barrier medium 460 in the indeterminate section 426 and similar in diameter to the diameter of the dissipation section 458. The shaping section 464 has a length l S466 is further defined. This provides a nozzle 452 having a geometrically narrowed dissipation section 458 compared to the tank 454 and shaping section 464, regardless of the diameter of the nozzle 452 itself. Unlike the geometric obstructions shown in Figures 4A to 4C, the nozzle with an obstructing medium shown in Figure 4D illustrates a nozzle that can provide energy dissipation by controlling the permeability characteristics of the medium.

[0060] Figures 5A and 5B illustrate schematic cross-sectional side views of non-constricted and constricted nozzle designs, respectively, according to one or more embodiments disclosed. Figures 5A and 5B illustrate the distinction between a standard constricted nozzle 500 in Figure 5A and a constricted nozzle 502 having a dissipation section 510 designed as a constricted section in Figure 5B. The constricted nozzle 500 in Figure 5A consists of a tank section 504 and a shaping section 506. In a non-constricted nozzle 500, the meniscus settling time and droplet characteristics cannot be independently controlled. Figure 5B also defines a tank section 508, a constricted dissipation section 510, and a shaping section 512, illustrating a more generalized embodiment of the exemplary embodiments described herein. To illustrate and verify the effect of constriction on relaxation time and droplet shape under these various conditions, high-fidelity simulation experiments solving the fluid governing equations can be performed using the open-source software OpenFOAM2, available at the following URL: https: / / www.openfoam.com. Exemplary simulations are described in the examples, and standard and constricted axisymmetric designs are shown in Figures 6A and 6B.

[0061] Figures 6A and 6B illustrate schematic cross-sectional side views of simulated experiments generated using standard and constricted axisymmetric nozzle designs, respectively, presented at various temporal moments according to one or more disclosed embodiments. Figure 6A shows a series of snapshots from an OpenFOAM2 droplet simulation test generated using a standard or constricted channel nozzle. The sequence of images shown represents snapshots of the droplet in the simulation test, taken at time (t) t=0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 milliseconds. Figure 6B shows a series of snapshots from an OpenFOAM2 droplet simulation test generated using an axisymmetric or constricted channel nozzle. The sequence of images shown represents snapshots of the droplet in the simulation test, taken at time (t) t=0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 milliseconds.

[0062] Figure 7 is a cross-sectional side view illustrating the concept of meniscus displacement relative to the front surface of an embodiment of a nozzle according to one or more embodiments disclosed herein. The nozzle 700 has a general structure similar to that of other embodiments described herein and includes an outlet portion of a dissipation section 702 that leads to an outlet orifice 704 of the shaping section of the nozzle 700. The nozzle 700 is filled with printing material 706 that can be ejected from the nozzle 700 when the nozzle 700 is included in a nozzle array, printhead assembly, or printing system. The front surface plane of the nozzle 708 is shown as a reference point for the position of the printing material 706 within the nozzle 700 in an ideal stationary state. During a printing operation, as the printing material is ejected from the nozzle and the droplets separate, the position of the meniscus displacement 710 is shown. This boundary and position of the meniscus displacement 710 still indicates an oscillating interface boundary as the printing material 706 within the nozzle settles after droplet separation. The time associated with this meniscus displacement and settling defines the relaxation time and is related to the specific nozzle design.

[0063] FIG. 8 is a plot showing the simulated meniscus displacement as a function of time for the ejection of one droplet from the non-constricted and non-constructed nozzle embodiments of FIGS. 6A and 6B. The non-constricted nozzle and constricted nozzle curves both illustrate the meniscus displacement and associated oscillations of the meniscus when it settles in the plane of the front of the nozzle, as shown and described with respect to FIG. 7. The plot of FIG. 8 shows the meniscus displacement as a function of time for the non-constricted nozzle and the constricted nozzle. The plot of FIG. 8 also illustrates an exponentially decaying fit to each curve of the non-constricted nozzle and the constricted design nozzle that defines a relaxation time τ for both the non-constricted nozzle and the constricted nozzle. This plot clearly shows a reduction in the relaxation time due to the constricted dissipation region in the constricted nozzle design as compared to the non-constricted nozzle design. Also observable is a reduction in the magnitude of the oscillations in the constricted dissipation region in the constricted nozzle design as compared to the non-constricted nozzle design. Design the shaping section

[0064] In certain embodiments, the required relaxation time of the nozzle design is defined by Aδ / S of the dissipation region. Here, A is the cross-sectional area of the dissipation region channel, δ is the characteristic length of the fluid boundary layer within the dissipation region, and S is the perimeter of the dissipation region cross-section. Since the value of δ is always less than or equal to the minimum characteristic dimension of the cross-section, its upper limit is also defined by the geometry. The required volume of the droplet and its velocity define the cross-sectional area of the exit orifice of the shaping section of the nozzle. The volume of the droplet is approximately proportional to R 3 Here, R is the radius of the exit orifice within the shaping section. Thus, if the velocity of the center of gravity of the droplet is V, then the velocity within the dissipation region must be approximately equal to VπR 2 / A. A is selected by choosing the appropriate S for the cross-section of the dissipation region such that VπR 2Since it can be selected to be close to this, it is possible to design the nozzle so that this velocity is very close to that of the center of gravity. For example, in one embodiment with a nozzle design as shown in Figure 4C, in a nozzle embodiment having a cross-channel dissipation section, if the additional set of parallel plates is increased to 4 to 6 sets of parallel plates, A increases, but A / S remains nearly constant. This velocity then defines the intensity of the pressure signal used when ejecting printing material from a nozzle designed as described herein.

[0065] Regarding the shape of the exit orifice in a particular embodiment, several possible shapes can be considered, such as an elliptical orifice or a narrow slit, but a circular orifice may be known to those skilled in the art as generally ideal for obtaining a single droplet per pulse. Therefore, the following discussion is based on a circular exit orifice. In a particular embodiment, the diameter of the exit orifice in the shaping section indicates the volume and shape of the droplet discharged from the nozzle. In the case of very small diameters, the nozzle needs to produce elongated droplets to achieve a given mass, and such droplets are discharged before reaching that mass. A similar argument holds for larger diameters, in that a larger diameter nozzle requires a waveform with a longer extrusion time, which may result in elongated droplets of an unacceptable shape. Therefore, a mechanism is needed to prevent the meniscus edge of the droplet from moving beyond the plane in front of the exit orifice. In some embodiments, this can be implemented using a sharp edge, sharp surface irregularity, or modification of the contact angle characteristics of the printing material. The radius of curvature ρ at the exit orifice defines the meniscus dynamics, as shown and explained with respect to Figure 3. If this radius of curvature ρ is very small relative to the radius of the exit orifice, the meniscus is primarily pinned to the edge of the exit orifice. If the radius of curvature ρ occupies a significant portion (e.g., 10%) of the radius of the exit hole, the meniscus moves the curvature of the exit orifice up and down as it oscillates after the droplet is discharged from the nozzle. Thus, in certain embodiments, the radius of curvature ρ can be less than 10 percent of the radius of the exit orifice, in terms of controlling the behavior of the meniscus at the exit orifice.

[0066] In certain embodiments of nozzle design, the length of the shaping section influences several factors. If the shaping section within the nozzle is very long, there may be two types of droplet discharge: slow ones due to the pressure generated by the incoming print material fluid, and instantaneous ones if the ejection of fluid from the dissipation section into the shaping section is not sufficiently slowed or dissipated. In other embodiments, if the shaping section is of intermediate length, the shaping section design provides a way for the incoming print material fluid to increase the pressure within the shaping section, pushing the print material fluid into the shaping section to form larger droplets. For print material fluids of sufficient viscosity, the length of the outlet region may be adjusted to homogenize the fluid velocity before droplet formation. Implementing this design strategy may be impractical for aluminum, the material of interest in DOD 3D printing applications. As previously mentioned, the nozzle outlet orifice can provide a stable equilibrium of the meniscus, especially if the fluid contact angle is in contact with the nozzle and wet. Furthermore, if the cross-sectional area of ​​the dissipation section is smaller than the cross-sectional area of ​​the outlet orifice, the outlet of the dissipation section can provide a second stable equilibrium with a smaller potential energy. Thus, the length of the shaping section can provide a potential energy barrier to prevent the meniscus from moving from the outlet orifice to the outlet of the dissipation section during the discharge operation. This balance between the design of the shaping section and the design of the dissipation section to minimize the nozzle relaxation time τ may be utilized and leveraged in the nozzle design to prevent the formation of vortices and recirculation spots within the nozzle when the fluid is sufficiently viscous. This is not the case for aluminum or water. Water or alloy materials used in metal printing are very low in viscosity and are therefore prone to complex phenomena occurring at the intersection of the dissipation section and the shaping section when pressure pulses are applied. One phenomenon is a quadratic vector field or vortex that generates a desired vertical motion and causes rotation. Another phenomenon observed is that, due to its low viscosity, the meniscus at the nozzle surface can contract and settle at locations different from the nozzle tip after discharge, such as the intersection between the dissipation and shaping sections, or at deeper locations inside the nozzle.

[0067] The nozzle relaxation time τ increases or decreases with the dimensions of the dissipation section; the smaller the decay section, the faster the relaxation time, resulting in less turbulence in the meniscus during discharge. However, this constraint on the diameter of the dissipation section also limits the volume of the droplet. Alternative embodiments of printing systems utilizing the nozzle design principles described herein may include an array of multiple nozzles with small relaxation times, positioned close enough as the generated droplet falls, and thus the overall volume of droplet discharge can be increased by combining multiple nozzles while maintaining small relaxation times. In certain embodiments, if the amplitude of the lateral vibration of the droplet shape during fall is greater than the distance between nozzles, the droplets may merge into a single larger droplet. The parallel pressure signals of multiple nozzles can be adapted from those of a single nozzle with little or no modification. This described embodiment is analogous to an example of a nozzle with a showerhead channel dissipation section, as shown in Figure 4B, which does not have a shaping section. This is an example of parallel discharge using multiple nozzles, where the channels are positioned close enough to each other. Examples of simulated experiments

[0068] The following are embodiments submitted to further define the various types of the present disclosure. These embodiments are for illustrative purposes only and are not intended to limit the scope of the present disclosure. Multiple test cases are performed utilizing high-fidelity simulations of multifaceted nozzle designs, and the resulting nozzle ejection behavior is monitored for single and multiple droplet events. Two areas of focus are to highlight the effects of energy dissipation on print / eject throughput and to evaluate basic parametric analysis to study the sensitivity of throughput metrics to basic nozzle characteristics. Outputs of interest related to these simulations are the droplet characteristics of interest, i.e., droplet velocity, volume, and shape, and the energy dissipation metric, i.e., the relaxation time of meniscus displacement. The studies performed in the exemplary studies are limited to narrow axisymmetric channel nozzle designs and showerhead multichannel designs, as illustrated in Figures 4A and 4B, respectively.

[0069] Figure 9 illustrates a basic abstract diagram of the nozzle and substrate portion of a printer embodiment. The nozzle 900 is shown to define a tank 902 and a constricted axisymmetric section 906, and to have basic dimensions, namely, the radius 910 of the tank 902, the length 912 of the nozzle 900, the length 914 of the constricted axisymmetric section 906, and the length 916 of the gas phase atmosphere 908, which is considered to be fixed to two simulated and initialized phases, namely, a liquid phase consisting of a model liquid printing material 904 and a gas phase 908. The first phase is a liquid having properties similar to those of a molten aluminum alloy at its melting temperature as a typical printing material. The second phase is a gas having properties similar to an external atmosphere, for example, an argon atmosphere. The values ​​of the aforementioned properties used are shown in Table 1. Finally, the contact angle between the nozzle wall and the liquid / gas interface is assumed to be uniform and set to 60 degrees. [Table 1]

[0070] Figure 10 illustrates a waveform plot representing a pressure pulse applied to the upper boundary of a nozzle according to an embodiment of this specification. This input signal is a pressure pulse applied to the upper boundary of the nozzle, set 4.5 mm from the substrate. The signal has an incoming pulse waveform as shown in Figure 10. It consists of a positive pressure (extrusion) component 1002 and a negative pressure (suction) component 1004. The positive pressure component of the waveform may be called the generation event, or the positive generation portion of the waveform, and generates droplets, while the negative pressure component may also be called the discharge event, or the negative discharge portion of the waveform, and controls its separation from the orifice. The negative pressure component, which may also be called the shape of the negative pressure component, controls its separation from the orifice. To operate the nozzle and discharge droplets of a predetermined shape, volume, and velocity, a suitable temporal pressure pulse / signal is required at the interface between the tank and the dissipation section. Such a signal may consist of two clearly identifiable intervals of time, an initial push signal, followed by a pull signal, as illustrated in Figure 10. The push section compresses the fluid in the tank and pushes it through the dissipative and shaping sections of the nozzle, expanding the meniscus at the outlet orifice of the shaping section. The pull section can draw the fluid into the nozzle and decelerate it, creating a sharp fluctuation in the fluid velocity near the outlet orifice. Thus, the fluid in the expanded meniscus moves forward from the nozzle, but the fluid in the nozzle is decelerated by the tensile component of the waveform. This creates a breakup point where droplets separate near the outlet orifice. If the fluid velocity in the meniscus is sufficiently high, droplets may appear without the need for a tensile section. The meniscus then stretches to a point where a concave region with low pressure appears, and droplets break from there. The tensile section of the signal enables a degree of control over how droplets separate from the fluid in the nozzle. The velocity, volume, and number of droplets per pulse within the range can be calibrated by adjusting the intensity and duration of each part of the pressure signal.

[0071] The quantities monitored in the simulated experimental examples include observations related to the generation of a single droplet in a candidate nozzle design according to the embodiments herein. Considering the nozzle geometry and input signals, (a) a single droplet is generated and the droplet has a suitable shape (close to spherical), and (b) the droplet remains a single droplet throughout its entire trajectory (i.e., without splitting into smaller droplets). Droplet volume is similarly quantified as a substitute for droplet mass. Since the fluid of the model printing material is incompressible for this application, volume is a conserved quantity. Droplet velocity is recorded as volume-averaged velocity, which is the velocity of the center of gravity of the droplet. It is considered constant as the effect of gravity is negligible. Meniscus relaxation time is a characteristic time τ in the exponential fitting C exp(-t / τ) of the envelope of the time variation of meniscus displacement after droplet discharge, as shown in Figure 8. Relaxation time is a measure of whether excess kinetic energy of the fluid in the nozzle is consumed. The OpenFOAM platform allows you to run simulated experiments and implement Interform routines using a computational fluid dynamics (CFD) solver. This routine is a solver for two incompressible isothermal immiscible fluids that uses a numerical approximation of the fluid volume.

[0072] In the simulation experiment of a constricted axisymmetric nozzle design, a single droplet event involves a single pressure pulse applied to the top of the upper tank, thereby ejecting a single droplet. Figures 6A and 6B show snapshots of a standard and constricted nozzle design satisfying the axisymmetric hypothesis, respectively. The system response is monitored by recording the interface trajectory by plotting the maximum displacement as a function of time, as illustrated in Figure 7, thereby yielding plots similar to those shown in Figure 8. The resulting plots show free meniscus oscillations after droplet ejection is recorded for both the standard and constricted nozzle designs. In both simulation experiments, the initial spikes indicate the moments of droplet creation and destruction, followed by damped oscillations as the meniscus relaxes. Data relevant to the non-constricted design is the realization of a freely oscillating meniscus after a single droplet ejection in a standard (non-constricted) nozzle. In this particular case, the nozzle design is similar to the nozzle design shown in Figure 5A, with an outlet orifice having a diameter of 500 μm. The relaxation time τ is capped at 9.82 milliseconds. The data related to the constricted axisymmetric design in Figure 5B are from identical simulated experimental runs on a constricted nozzle with a constriction radius of 170 μm and a constriction length of 400 μm. The length of the shaping section is 100 μm, and the radius of the exit orifice is equal to 250 μm. In this case, meniscus sedimentation occurs remarkably quickly, ≤4.95 milliseconds. The ratio of relaxation times is very close to the ratio of areas, as can be expected from the formula above. Nozzle behavior at different pulse frequencies

[0073] Next, the behavior of the same constricted and unconstricted nozzles was studied by periodically repeating pressure pulses over time using different frequencies similar to those used during steady-state printing. Simulated experiments were performed in which 20 droplets were ejected at frequencies of 200 Hz, 255 Hz, and 300 Hz. Figures 11A to 11F are a series of plots showing multiple droplet simulation experiments of constricted and unconstricted nozzles for three ejection frequencies according to the embodiments herein. The droplet volume and volume-average velocity are plotted against the number of droplets. In Figures 11A, 11C, and 11E, the droplet volumes of 20 droplets are plotted for 200 Hz, 255 Hz, and 300 Hz, respectively. In Figures 11B, 11D, and 11F, the volume-average velocity of 20 droplets is plotted for 200 Hz, 255 Hz, and 300 Hz, respectively. Table 2 shows the standard deviations of volume and volume-average velocity across 20 droplets plotted in Figures 11A to 11F. Furthermore, for the non-constricted nozzle design, it was found that 85%, 45%, and 80% of the ejected droplets were destroyed before reaching the substrate at firing frequencies of 200 Hz, 255 Hz, and 300 Hz, respectively. The corresponding velocities for the constricted nozzle design were 0%, 0%, and 10% at firing frequencies of 200 Hz, 255 Hz, and 300 Hz, respectively. At all tested ejection frequencies, the results for the constricted nozzle exhibited very regular droplet-to-droplet behavior, in contrast to the more aggressive variations of the non-constricted nozzle design. [Table 2]

[0074] Figure 12 shows a schematic cross-sectional view of a portion of a nozzle design according to one or more embodiments disclosed, illustrating geometric considerations related to a constricted axisymmetric nozzle design. The nozzle 1200 design used in subsequent simulation experiments has adjustable design parameters that represent the dimensions of both the dissipation section 1202 and the shaping section 1204, which are the diameters of the constricted section, and the constriction d of the dissipation section 1202. c Diameter 1206 and shaping section 1204 exit orifice d eThe diameter is 1220. The fixed parameter for the nozzle simulation experimental design illustrated in Figure 12 is the length l of the dissipation interval 1202. D 1208 and the transition length l between the dissipative interval 1202 and the shaping interval 1204. m 1210 and the length l of the shaping section 1204 S Includes 1212. Other fixed dimensions include the exit orifice length κ01214, upper κ11216, and lower κ11218, representing the transition length of the merge section, or the transition zone connecting various sections of the nozzle. Parameter Study I: Stenosis Diameter

[0075] As mentioned above, in certain embodiments, the nozzle geometry primarily controls the droplet shape, the droplet trajectory after rupture, its volume, and velocity. The geometry can also be modified to control energy dissipation. The results of the studies shown and described with respect to Figure 12 are shown in Figures 13A and 13B. Figures 13A and 13B are plots of the average velocity of the ejected droplet volume as a function of the constriction diameter dc, and the ejected droplet volume as a function of the constriction diameter dc, respectively. As the constriction diameter decreases, the velocity and volume of the ejected mass also decrease first. Clearly, a narrower cross-sectional wall obstructs the liquid flow. Since the pressure pulse does not compensate for additional energy, less material is ejected, resulting in slower velocity. Finally, for constriction diameters dc = 0.4, 0.3, and 0.2 mm, the relaxation times are capped at 0.0083 seconds, 0.0049 seconds, and 0.0039 seconds, respectively. This is consistent with the expected relationship τ ∝ d²c. In the monotonicity diagram 13B for volume-averaged velocity, a significant change can be observed around dc / de, where dc / de is approximately 78%. The volume-averaged velocity steadily decreases with dc, and then increases sharply as dc decreases further. A jump in the discharge volume value is observed at the same value of dc. This behavior may be due to the fact that as the diameter of the constriction decreases, the velocity of the fluid inside it increases. When a fast-moving fluid enters the shaping section, the increase in fluid viscosity and pressure is not sufficient to accelerate the fluid on the region outside the shaping section. Therefore, the fluid coming from the dissipation section loses less momentum to the surrounding fluid and exits the nozzle at a faster velocity. The discharged mass is often accompanied by fluid with significantly different velocities, which can lead to droplet breakdown and sometimes satellite discharge. Parameter Study II: Input Signal

[0076] The input signal and corresponding waveform provide the energy entering the nozzle / liquid system. This primarily controls droplet velocity and volume, and consequently affects the time and positional breakup specifications. Secondly, the input signal affects droplet shape and energy dissipation in nozzle design simulation experiments. In printing devices, waveforms such as those shown in Figure 10 are the output of hardware circuits that control the signal intensity and the duration of the negative portion. If the nozzle geometry is fixed, the shape of the pressure signal can be defined and adjusted to obtain droplets with desired characteristics. One way to explore the sensitivity of droplet characteristics to the pressure signal is to fix the realized waveform as a reference and, instead, introduce a scaling parameter to the hardware-based controller that affects its intensity and duration. Figure 14 is a spatiotemporal scaled plot of a characteristic waveform showing its positive and negative components according to one embodiment. A systematic modification of the reference pulse 1402 is simulated for several wavelength parameters shown in Figure 14 by varying the parameter Mp (magnitude of the positive generating portion of the waveform) 1404, tp (duration of the positive generating portion of the waveform) 1406 which increases or decreases the positive portion of the pulse, the analog parameter Mn (magnitude of the negative ejection portion of the waveform) 1408, and tn (duration of the negative ejection portion of the waveform) 1410 for the negative portion of the pulse. This change is represented by wavelength 1412. Regarding the geometric design of the nozzle defined by dc=0.35, de=0.4, and lD=0.05, the results of calculations for droplet characteristics with varying Mp and tp are shown in Figures 15A to 15D. Figures 15A to 15D are a series of four plots showing the results of a parametric simulation experiment of the positive portion of the waveform in Figure 14 and the waveform effect on droplet velocity and volume according to one embodiment. Figures 15A and 15B are plots of velocity vs. Mp and volume vs. Mp, respectively. Figures 15C and 15D are plots of velocity vs. tp and volume vs. tp, respectively. The effect of the extrusion portion of the pressure pulse is shown, while the tensile / suction portion of the waveform is kept constant and equal to the reference signal. The strong linear behavior of the droplet characteristics can be observed with respect to the extrusion parameter.The smooth fluctuations of both quantities illustrate the possibility of tuning the signal to adjust the volume and velocity of droplets within a certain range. However, this smooth fluctuation of volume and velocity with pulse parameters does not reflect the effect they have on droplet shape, which can vary significantly. Pressure pulses with a sufficiently large Mp, and certainly within the ranges of Figures 15A and 15B, accelerate the fluid enough to produce droplets that are too elongated and / or break after discharge. Thus, it is unlikely that a single droplet of acceptable shape will form within such a range. In contrast to changing the Mp and tp values, the values ​​of Mn and tn affect droplet properties in complex ways. Results from other parametric studies outside the scope of these studies recommend a large value for Mn, and tn has a negative impact on the dynamics. These negative impact ranges delay the flow in the nozzle and in the discharged droplets, inducing a larger kinetic energy load due to a stronger suction, which dissipates unnecessarily long periods of time.

[0077] Additional experiments were conducted using the showerhead multi-channel nozzle design shown in Figure 4B, where the dissipation section consists of at least two multiple narrow channels. As previously discussed with respect to Figure 4B, the relaxation time of this channel is equal to the sum of the cross-sectional areas of each narrow channel. An additional advantage of this multi-channel nozzle design is that by pushing the meniscus in a more distributed manner over the outlet orifice, it increases the range of velocities over which the fluid can pulse or discharge through the dissipation section without generating multiple droplets upon discharge. Figures 16A and 16B illustrate top views of the dissipation section in a multi-channel nozzle having four and five channels, respectively. Additional studies of droplet discharge were studied using the designs shown in Figures 16A and 16B. The multi-channel nozzle design 1602 in Figure 16A includes four symmetrically arranged channels 1602A, 1602B, 1602C, and 1602D, each with a diameter of 160 μm, and the multi-channel nozzle design 1604 in Figure 16B includes five symmetrically arranged channels 1604A, 1604B, 1604C, 1604D, and 1604E, each with a diameter of 120 μm. Figure 17 is a plot showing the simulated meniscus displacement as a function of time of droplet discharge from the multi-channel nozzle embodiments of Figures 16A and 16B compared to a standard non-constricted nozzle design embodiment. Figure 17 illustrates the meniscus motion in a single droplet event of the 4-channel multi-channel nozzle design in Figure 16A and the 5-channel multi-channel nozzle design in Figure 16B compared to a standard nozzle design. The results of the meniscus motion over time suggest that the 4-channel and 5-channel nozzle designs with multi-channel dissipation intervals dissipate energy considerably faster than the standard design, with upper bound estimates of 0.0098 seconds for the standard design, 0.005 seconds for the 4-channel design, and 0.003 seconds for the 5-channel nozzle.

[0078] This disclosure has been described with reference to exemplary embodiments. While a limited number of implementations have been illustrated and described, those skilled in the art will understand that modifications may be made to these implementations without departing from the principles and spirit of the embodiments for carrying out the invention described herein. This disclosure is intended to be construed as including all such modifications and changes, such as those falling within the scope of the appended claims or their equivalents.

Claims

1. A nozzle for a printing system, A tank connected to the printing material supply source, A constricted dissipation section communicating with the tank, comprising an elongated internal channel having at least two intersecting channels substantially perpendicular to each other, wherein the at least two intersecting channels are composed of at least two walls parallel to each other, A nozzle comprising a shaping tip that communicates with the aforementioned constricted dissipation section and is equipped with an outlet orifice.

2. The nozzle according to claim 1, wherein the radius of curvature of the outlet orifice is less than 10 percent of the diameter of the outlet orifice.

3. The nozzle according to claim 1, wherein the nozzle is configured to discharge droplets by manipulating a generation event followed by a discharge event.

4. An array of nozzles for a printing system, It has multiple nozzles, and each nozzle is A tank connected to the printing material supply source, A constricted dissipation section communicating with the tank, comprising an elongated internal channel having at least two intersecting channels substantially perpendicular to each other, wherein the at least two intersecting channels are composed of at least two walls parallel to each other, An array of nozzles comprising a shaped tip that communicates with the aforementioned constricted dissipation section and is equipped with an outlet orifice.

Images