WO2024259493A1

WO2024259493A1 - Fabrication of 3d objects

Info

Publication number: WO2024259493A1
Application number: PCT/AU2024/050654
Authority: WO
Inventors: Callum Peter VIDLER; Michael Everett HALWES; David John Collins
Original assignee: University of Melbourne
Current assignee: University of Melbourne
Priority date: 2023-06-22
Filing date: 2024-06-21
Publication date: 2024-12-26
Anticipated expiration: 2025-12-22

Abstract

The present invention provides a method of forming a 3D object, the method comprising: providing a photo-curable resin, providing a print head for transmitting curing radiation to the photo-curable resin, the print head having a cavity containing gas, introducing the print 5 head into the resin to form a submerged gas-resin interface between the gas and the resin, wherein said gas-resin interface is constrained to the print head and defines a printing surface, projecting curing radiation on the submerged gas-resin interface to promote curing of the resin at the printing surface, and promoting relative movement between the gas-resin interface and the resin to produce the 3D object. The method may also include a step of 10 transmitting acoustic waves to the submerged gas-resin interface.

Description

FABRICATION OF 3D OBJECTS

FIELD OF THE INVENTION

The invention relates generally to methods and systems for forming 3D objects, and more particularly to methods and systems for forming 3D objects using photo-curable resins.

BACKGROUND OF THE INVENTION

Additive manufacturing is a rapidly expanding multidisciplinary field providing tools for the production of arbitrary 3D objects of with complex geometry. Advances in the field extend to applications such as rapid prototyping, medical devices, aerospace components, microfabrication strategies, and even artificial organs. Among additive manufacturing approaches, optical printing of photo-curable resins, including two-photon polymerization, projection micro stereo-lithography, and volumetric printing, have garnered significant attention due to their excellent spatial resolution and material versatility.

Conventional optical printing, such as stereo-lithography, typically involves the application of light to induce local layer-by-layer polymerisation of the photo-curable resin. While those techniques can readily afford dimensionally accurate parts, the printing speed is inherently limited by the need to repeatedly reset the position of a part between printed layers. Also, those techniques do not afford printing of free-floating structures since they are limited to bottom-up printing starting from layers adhering to a print stage.

Continuous Liquid Interface Production (CLIP) is a recently proposed printing technique that affords higher printing rates by directly regulating oxygen concentration within the print volume. In CLIP, polymerising light is projected upward through an oxygen permeable window at the bottom of the resin vat (bottom-up configuration). Increased oxygen concentration in the resin layers immediately above the window prevent polymerization at the print boundary, thus enabling high-speed printing of an object that can be progressively lifted out of the resin bath. However, the need to sequentially extract the printed structure from the resin bath makes it difficult to print extremely soft materials like hydrogels, which lack self-support.

The limitations of existing layer-by-layer printing techniques have been partially overcome by the recent development of "volumetric" printing procedures, which can obtain simultaneous printing of centimetre-scale volumes of resin. Examples of volumetric printing include computed axial lithography, in which a vial containing a photo-polymer is rotated while targeted projections are exposed from azimuthal angles such that the cumulative intersection of light rays induces polymerisation within a volume of resin corresponding to the 3D object. Xolography is a further volumetric approach based on the polymerization of a spiropyran photo-switch photo-initiator. The technique requires focusing a 2D projection within a volume of resin and intersecting it with an orthogonal light sheet at two different wavelengths, where selective polymerization occurs at the intersection of these two light paths.

However, while volumetric printing affords rapid fabrication of free-floating, layer-less and soft structures, it is only effective on highly transparent resin formulations. This inherently precludes high-speed bio-printing, which is mostly performed on resins containing light scattering viable organisms (e.g. cells) that impede accurate optical focusing over extended volumes of resin.

There remains therefore an opportunity to develop techniques for the fabrication of 3D objects that address one or more limitations of existing methods.

SUMMARY OF THE INVENTION

The present invention provides a method of forming a 3D object, the method comprising: providing a photo-curable resin, providing a print head for transmitting curing radiation to the photo-curable resin, the print head having a cavity containing gas, introducing the print head into the resin to form a submerged gas-resin interface between the gas and the resin, wherein said gas-resin interface is constrained to the print head and defines a printing surface, projecting curing radiation on the submerged gas-resin interface to promote curing of the resin at the printing surface, and promoting relative movement between the gas-resin interface and the resin to produce the 3D object.

The provision of a submerged gas-resin interface constrained to the print head enables accurate spatial curing of arbitrary volumes of resin irrespective of the nature and formulation of the resin. Since the gas-resin interface defines a printing surface which is inherently constrained to a moveable print head, the method advantageously affords fast, precise, and highly customisable localisation of the printing surface anywhere within a volume of resin.

Further, the gas-resin interface provides a mechanical barrier that prevents adhesion of cured resin on the print head. As a result, the method affords precise and fast production of free- standing 3D structures, including soft structures, anywhere within the resin volume.

From the optical standpoint, the provision of the printing surface at the gas-resin interface drastically minimises optical de-focusing and aberration effects of the curing radiation, offering minimal to no refractive index change along the radiation optical path. This significantly facilitates rapid creation of arbitrary support-less structures without the need of complex optical setups.

In addition, the provision of the printing surface at the gas-resin interface renders the proposed method virtually immune from light scattering effects deriving from the use of opaque and light-scattering resins. The proposed method can therefore be implemented effectively to cure resins containing suspended particulate matter, including biological relevant entities such as living cells.

In some embodiments, the submerged gas-resin interface is provided by pressurising the gas within the cavity of the print head. Pressure within the cavity would counter hydrostatic pressure from the resin, therefore affording control and modulation of the shape and extension of the gas-resin interface.

In some embodiments, gas used to form the gas-resin interface comprises oxygen.

Oxygen can dissolve through the gas-resin interface to create an oxygen-enriched resin layer in proximity of the interface, in which polymerisation is inhibited. It is postulated that said layer can advantageously provide physical distance between the forming object and the interface, minimising mechanical interference due to surface tension effects at the interface. As a result, the polymerisation speed can be significantly increased. In some instances, high- speed printing can be attained by directly regulating the oxygen concentration within the gas. This can be particularly advantageous, for example, for the precise and fast printing of self-standing soft structures.

In some embodiments, the method comprises a step of transmitting acoustic waves to the submerged gas-resin interface.

The transmission of acoustic waves to the gas-resin interface during printing is believed to be unique in its own rights. Accordingly, the present invention may also be said to provide a method of forming a 3D object, the method comprising the steps of: providing a photo- curable resin; providing a print head for transmitting curing radiation to the photo-curable resin, the print head having a cavity containing gas; introducing the print head into the resin to form a submerged gas-resin interface between the gas and the resin, wherein said gas- resin interface is constrained to the print head and defines a printing surface; projecting curing radiation on the submerged gas-resin interface to promote curing of the resin at the printing surface; transmitting acoustic waves to the submerged gas-resin interface; and promoting relative movement between the gas-resin interface and the resin to produce the 3D object.

It was observed that the gas-resin interface can be susceptible to acoustic stimulation. By transmitting acoustic waves to the submerged gas-resin interface it is therefore possible to impart rapid modulation of the shape of the interface according to the characteristics of the acoustic waves. The rapid modulation of the shape of the interface via acoustic excitation can advantageously promote the formation of capillary waves on the interface (i.e. surface waves with a wavelength short enough that the restoring force is the resin’s surface tension), significantly enhancing resin influx around the interface. The rate and distribution of material influx can itself be modulated by controlling parameters such as the characteristics of the acoustic waves (e.g. amplitude, frequency), the print head geometry, and/or the interface curvature.

In addition, the provision of vibrational excitation at the gas-resin interface enhances resin transport across the gas-resin interface, enhancing printing speed and fidelity. Moreover, Faraday waves across the printing interface can be used to generate both fluid motion in the bulk of the resin volume, enhancing mixing, as well as generating patterning of suspended micro-objects across this interface during printing.

The proposed method is highly versatile across a broad array of materials and intricate geometries, including those that would be impossible to print using bottom-up configurations.

The method is also particularly effective for the precise curing of a range of resin materials that include soft and biologically relevant hydrogels at speeds suitable for high-viability tissue engineering, scalable manufacturing and rapid prototyping. The method of the invention is therefore suitable to achieve in-situ printing, overprinting, and bio-printing.

Distinct from volumetric approaches, the proposed method also eliminates the need for intricate feedback systems, specialized resin chemistry or complex optics while maintaining ultra-rapid printing speeds. Additionally, the method of the invention can be readily parallelized, enhancing its potential for automation. We anticipate that this approach will be invaluable for industries where high resolution, scalable throughput and biocompatible printing is imperative. The present invention provides also a system for forming a 3D object, the system comprising a print head for transmitting curing radiation to a photo-curable resin, the print head having a cavity containing gas such that, when the print head is introduced into photo-curable resin, said gas promotes formation of a gas-resin interface constrained to the print head.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will be now described with reference to the following non- limiting drawings, in which:

Figure 1 shows a schematic illustration of an example print setup for performing the method of the invention (IS image stack; IO, illumination optics; DMD, digital micro-mirror device; IL, imaging lens; PC, print head; O₂, oxygen inlet; L, 635 nm shadowgraph imaging red laser; CL, collimating lens; FL, focusing lens; CCD, charge-coupled device); the inlets show a rendered illustration of the gas-resin interface and a shadow graph image of the printed structure highlighting improved contrast,

Figure 2 shows a side view time lapse printing of a sample 3D helical stent over a period of 60s,

Figure 3 shows (a) a side profde of a sample cylindrical hollow print head with a protruding gas/resin interface generated by pressurising a gas bubble within the internal cavity of the print head, showing model extrapolation of the interface shape as a function of the gas pressure, (b) reconstructed interface displacement map from the side profile of an axisymmetric print head, and (c) comparison between a non-planar (convex) cross-sectional slice of the 3D object and a conventional traditional planar-slicing,

Figure 4 shows a sample print parameter space which can be adopted to determine practical combinations of optical power and print speed for effective printing; the inset shows an example of a rectangular test structure used to assess the parameter space, Figure 5 shows a dipped example print head printing a simple vascular tree into a glass vial containing a curable resin,

Figure 6 shows (a) standard polyethylene glycol diacrylate (PEGDA) resin against a "USAF- 1951" test pattern showing high optical transparency, (b) non-transparent alginate resin in front of the same "USAF-1951" test pattern showing low optical transparency, and (c) tricuspid valve successfully printed using the low-optical transparency resin,

Figure 7 shows (a) an illustration of the printed tricuspid geometry shown in Figure 6(c), (b) multi-part printing of multiple tricuspid valves via print-and-repeat, showing printing of three complete structures in 120 seconds, and (c) micro-computer tomography (CT) slice of the obtained tricuspid valves, showing accurate recreation of internal leaflets (scale bar 10 mm),

Figure 8 shows stitched fluorescence image of a 3D printed kidney model containing 7.2 million viable cells mL^-1 printed directly in resin contained in a 12 well plate container after 24 hours from printing showing high cell viability,

Figure 9 shows a schematic of (a) a two-step printing procedure for the printing of a soft a bucky-ball over a prior-printed harder stem, and (b) picture of the resulting PEGDA bucky- ball printed on the of a printed hexanediol diacrylate (HDDA) rod, demonstrating multi- material overprinting,

Figure 10 shows (a) multiple interface print head containing a grid of 3x3 cavities to form a corresponding array of discrete gas-resin interfaces, and (b) picture of words ‘DIP’ ("Dynamic Interface Printing", which may be used herein to identify the proposed method) with letters printed simultaneously using the multiple interface print head,

Figure 11 shows a schematic of the transmission of acoustic waves to a gas-resin interface, in which acoustic waves are introduced into the cavity of a print head, Figure 12 shows (a) a schematic of the effect of acoustic stimulation on the geometry of a submerged gas-resin interface, showing how acoustic stimulation can promote enhanced material influx through capillary driven waves, and (b) instantaneous location of the air- liquid boundary being dependent on the spatial location of the print head, internal pressure state and acoustic excitation,

Figure 13 shows different acoustic patterns (A, B, C) formed using a cylindrical print head at different cross sections of a print via acoustic excitation at different frequencies,

Figure 14 shows (a) a CAD model of mechanical components of a 3D print set-up which may be used to perform the method of the invention, including an acoustic modulation device for the transmission of acoustic waves to the gas-resin interface through the cavity of the print head, (b) a schematic view of a gas-resin interface formed at the tip of the print head under acoustic excitation, (c) illustration of the total degrees of freedom (DOF) of the printing interface location under conventional 3D printing (left) and the method described herein (right), and (d) the instantaneous interface location dependent on the sum of the locations of said degrees of freedom,

Figure 15 shows a schematic illustration of an embodiment print head assembly and acoustic air-line modulation; a, b) expanded half section view of the print head assembly; c) half section view of the air-line modulation system; d) diaphragm excitation when electrical signal is applied to the voice coil,

Figure 16 shows the process-flow diagram of the slicing algorithm illustrating steps in both the determination of convex projections and reconstruction validation via Jaccard Index

Figure 17 shows the numerical prediction of the interface release dynamics for a 15 mm diameter print head with varying circular printed structures from 4 to 14 mm in diameter, with: a) Location of the central node of the interface as a function of time for Top-Down SLA; b) Location of the central node of the interface as a function of time for Dynamic Interface Printing (DIP) without acoustic excitation; c) Location of the central node of the interface as a function of time for Dynamic Interface Printing (DIP) with acoustic excitation at a frequency of 40 Hz; d) Location of the central node of the interface as a function of time for Dynamic Interface Printing (DIP) with acoustic excitation at a frequency of 100 Hz.

Figure 18 shows numerical prediction of the average inflow fluid velocity for a 15 mm diameter print head with varying circular printed structures ranging from 4 to 14 mm in diameter, with: a) Radial magnitude of the average fluid velocity (llwll) for increasing structural diameter in top-down SLA; b) Radial magnitude of the average fluid velocity (llwll) for increasing structural diameter in DIP without acoustics; c) Radial magnitude of the average fluid velocity (llwll) for increasing structural diameter in DIP with 40 Hz acoustic driving; d) Radial magnitude of the average fluid velocity (llwll) for increasing structural diameter in DIP with 100 Hz acoustic driving; e) Peak average fluid velocity for each printing technique as a function of structural diameter, and

Figure 19 shows the numerical prediction of structural-modal interaction, with: a) Meniscus resonance mode shapes (indicated in white solid lines) over a single period at 40 Hz acoustic driving for structures with diameters of 10, 12, and 14 mm; b) Meniscus resonance mode shapes (indicated in white solid lines) over a single period at 100 Hz acoustic driving for structures with diameters of 10, 12, and 14 mm. White arrows indicate the locations of the nodal locations of the induced capillary wave.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a method of forming a 3D object. More specifically, the method of the invention is one of forming a 3D object using a photo-curable resin.

The expression "photo-curable resin" is used herein in accordance to its broadest meaning to refer to a composition containing components that cross-link upon exposure to radiation, resulting in the composition hardening. Any photo-curable resin into which a print head can be introduced to form the required gas- resin interface is suitable for use in the method of the invention. Typically, the resin would therefore be in a liquid state or semi-solid state. By "semi-solid" resin is meant herein a resin that does not hold its shape like a solid, but which may not flow like a liquid either due to its high viscosity.

Suitable examples of resins for use in the method of the invention include any photo-curable resin used in lithographic processes such as photo-lithography, two-photon lithography, electron-beam lithography, 3D direct laser writing, ion-beam lithography, and X-Ray lithography.

In some embodiments, the photo-curable resin comprises one or more of epoxy-based monomers and/or oligomers, acrylate -based monomers and/or oligomers, styrene-based monomers and/or oligomers, vinyl ether-based monomers and/or oligomers, urethane-based monomers and/or oligomers, silicone-based monomers and/or oligomers, cationic photopolymers, di -acrylates or tri -acrylates, and/or thiol -based monomers and/or oligomers. The oligomers maybe epoxides, urethanes, polyethers, or polyesters. In some embodiments, the photo-curable resin comprises norbomene- functionalised monomers and/or oligomers.

In some embodiments, the resin comprises a bio-material. The term "bio-material" is used herein in accordance to its broadest meaning to encompass materials derived from, or produced by, a biological organism (e.g. plants, animals, bacteria, fungi and other life forms). The term therefore encompasses biological entities (e.g. viable cells) as well as synthetic or natural substances suitable for direct interaction with components of a living system (e.g. saccharides, proteins, etc.).

Advantageously, when the resin comprises a bio-material, the method of the invention affords production of biologically relevant 3D structures, which may find application in the field of biomedical and tissue engineering. The bio-material itself may or may not be cross-linkable. When the bio-material is not cross- linkable (e.g. a viable cell), the resin will also include a cross-linkable component. When the bio-material is itself cross-linkable (e.g. a bio-polymer), the resin may or may not include an additional cross-linkable component.

In some embodiments, the bio-material comprises a bio-polymer. By "bio-polymer" is meant herein a polymer produced from a natural source, either chemically synthesized from a biological material or entirely biosynthesized by a living organism. Examples of suitable bio-polymers for use in the resin of the invention include thiol-based bio-polymers (e.g. bio- polymers that rely on thiol-ene click chemistry), alginate, hyaluronic acid methacrylate (HAMA), gelatin, gelatin methacryloyl (GelMA), collagen, chitosan, fibrin, elastin, silk, and dextran.

In some embodiments, the bio-polymer comprise norbomene functions. For example, the bio-polymer may comprise one or more of norbomene-functionalised alginate (Alg-NOR), norbomene-functionalised gelatin, norbomene-functionalised polyethylene glycol, and norbomene -functional hyaluronic acid.

Upon exposure to radiation, bio-polymers of the kind described herein may cross-link to form a consolidated stmcture.

In some embodiments, the bio-material comprises a bioactive agent. Examples of suitable bioactive agents in that regard include growth factors, matrix inhibitors, antibodies, cytokines, heparin, integrins, thrombins, thrombin inhibitors, proteases, anticoagulants, glycosaminoglycans, chemotherapeutic agents, antibiotic agents, cardiovascular agents, analgesics, central nervous system dmgs, hormones, enzymes, proteins, insulin, and solutes such as glucose or NaCl.

In some embodiments, the resin comprises a hydrogel precursor. By hydrogel "precursor" is meant herein a compound that upon cross-linking forms a hydrogel. In this context, the term "hydrogel" means a cross-linked network of hydrophilic polymers (natural or synthetic) that can swell in water to capture many times their original mass without dissolution. In the context of the invention, hydrogels will therefore be taken to encompass those based on natural polymers and/or synthetic polymers. As such, hydrogels in the context of the present invention include those obtained using a bio-polymer of the kind described herein, or those obtained with synthetic polymers.

Hydrogel precursors for use in the method of the invention may comprise one or more cross- linkable hydrogel macromers. By "hydrogel macromer" is meant a macromolecule that comprise a hydrophilic or water soluble region and one or more cross-linkable regions.

Hydrogel macromers may be made from a number of hydrophilic polymers. Examples in that regard include polyvinyl alcohols (PVA), polyethylene glycols (PEG), polyvinyl pyrrolidone (PVP), polyalkyl hydroxy acrylates and methacrylates (e.g. hydroxyethyl methacrylate (HEMA), hydroxybutyl methacrylate (HBMA), dimethylaminoethyl methacrylate (DMEMA)), polysaccharides (e.g. cellulose, dextran), polyacrylic acid, polyamino acids (e.g. polylysine, polyethyimine, PAMAM dendrimers), polyacrylamides (e.g. polydimethylacrylamid-co-HEMA, polydimethylacrylamid-co-HBMA, polydimethylacrylamid-co-DMEMA). Hydrogel macromers can be linear or can have a branched, hyperbranched, or dendritic structure.

In some embodiments, the resin comprises a hydrogel precursor which is a cross-linkable polysaccharide, such that upon exposure to radiation the resin provides for a polysaccharide hydrogel. Examples of polysaccharide hydrogels include hydrogels containing alginate, cellulose, and glycosaminoglycan.

In some embodiments, the resin comprises a hydrogel precursor of a bio-polymer of the kind described herein.

In some embodiments, the photo-curable resin comprises polyethylene glycol diacrylate (PEGDA), gelatin methacryloyl (GelMA), or hexanediol diacrylate (HDDA). In some embodiments, the photo-curable resin comprises viable cells suspended therein. For example, the resin may be a liquid mixture of living cells, a bio-polymer and/or hydrogel of the kind described herein, and cell nutrients. Those resins can provide for the direct production of 3D structures that allow for cell reproduction, for example to form a shape- specific target tissue.

The use of photo-curable resins containing bio-polymers, bioactive materials, and/or hydrogels of the kind described herein can therefore afford the production of 3D objects of high biological relevance.

For instance, the high degree of biocompatibility of those materials combined with their associated low immune-response affords the production of excellent host-compatible implants with arbitrary shape. Also, those materials can be effectively used for the production of custom-shaped 3D substrates for tissue growth, including organ tissue. For instance, the excellent biocompatibility of GelMA hydrogels makes them suitable as cell culture matrices that mimic native extracellular matrices (ECMs). Further, bio-polymers and hydrogels more generally present highly customisable chemistries, making it possible to encode bio-active motifs in their chemical structures for the production of function-specific 3D objects. Accordingly, the method of the invention can be particularly useful for the fabrication of 3D biomedical parts with the aim of imitating natural tissue characteristics, for example to create tissue and organ-like structures that let living cells multiply.

In some embodiment, the resin further comprises an additive. The additive may be any compound that provides or enhances one or more characteristic of the resin and/or the resulting 3D object.

In some embodiments, the photo-curable resin comprises a photo-initiator. A photo- initiators can trigger cross-linking of monomers/oligomers forming the resin upon exposure to the curing radiation. As they are known in the art, photo-initiators are compounds that upon radiation of light generate reactive species (e.g. by decomposition and/or activation of compounds present in the system) that activate polymerization of cross-linkable monomers/oligomers compounds contained in the resin.

Suitable examples of photo-initiators for use in the resin include onium salts (e.g. iodonium and sulfonium salts), organimetallic salts (e.g. a metal salt with a non-nucleophilic counter anion, such as ferrocinium salts), pyridinium salts, abstraction type photoinitiators (e.g. benzophenone, xanthones, and quinones), cleavage-type photoinitiators (e.g. benzoin ethers, acetophenones, benzoyl oximes, and acylphosphines).

In some embodiments, the photo-initiator is a combination of Tris(2,2'- bipyridyl)dichlororuthenium(II) hexahydrate and sodium persulfate (also referred to as “Ru/SPS”). Upon excitation by light, the ruthenium metal complex cleaves the O-O bond of the persulfate, and the persulfate then goes on to polymerize the desired monomer.

In some embodiment, the photo-curable resin comprises a fdler, which may be in the form of nanoparticles, microparticles, fibers, or flakes. These additives, when integrated into the resin formulation, can enhance the mechanical properties and dimensional stability of the cured resin. The addition of fillers and reinforcements provides increased strength, rigidity, and resistance to deformation, rendering the resin suitable for forming objects for use in applications requiring high durability and structural integrity.

In some embodiments, the resin comprises an additive that introduce tailored optical characteristics to the cured resin. Examples of suitable additives in that regard include dyes, pigments, or luminescent materials which impart color, translucency, or other aesthetic properties to the resin.

In some embodiments, the resin comprises a surface tension modifier. This class of modifiers can alter the surface energy and wetting properties of the resin, allowing for tuning the surface tension characteristics of the gas-resin interface.

In some embodiments, the resin comprises a thixotropic agent. Thixotropic agents can be added to the resin to modify the viscosity and flow behaviour of the resin, allowing for precise control during the printing process. By incorporating thixotropic agents, complex geometries can be fabricated with improved accuracy, ensuring the creation of high-quality objects with intricate details.

The photo-curable resin may further comprise a solvent selected from water, alcohols (e.g. isopropanol, ethanol), acetone, esters, ketones, toluene, ethyl acetate, methyl acetate, hexane, benzene, and ethanes. Provided the required gas-resin interface forms, the specific solvent may be chosen to be one that can solubilise other components of the resin without compromising the structural integrity of the cured resin. A skilled person would consider whether the use of a solvent is appropriate. For instance, a solvent may not be recommended if there is a likelihood of off-gassing, for example due to heat generated upon exposure to the curing radiation, during curing, or subsequent storage of the 3D object.

The method of the invention comprises the provision of a print head for transmitting curing radiation to the photo-curable resin. By "print head" is meant herein a component or assembly that delivers curing radiation to the photo-curable resin, such that the resin cures locally where the radiation is delivered.

In some embodiments, the print head comprises an emitter of curing radiation. Said emitter may be any component that is suitable to emit curing radiation of the kind described herein. For example, the print head may comprise an optical transmitter for emitting radiation of the kind described herein.

In some embodiments, the print head transmits curing radiation which is emitted from a radiation source external to the print head. An example of one such arrangement is shown in the schematic system depicted in Figure 1.

Particularly when the print head transmits curing radiation emitted from a radiation source external to the print head, it will be understood that the print head will be transparent to the curing radiation at least along a main optical transmission axis used to project the curing radiation on the photo-curable resin. In the schematic of Figure 1, the example print head is transparent to curing radiation projected along a vertical axis onto the photo-curable resin.

In some embodiments, the print head comprises an optical conducting component. For example, the print head may include an optical fiber for projecting curing radiation onto the photo-curable resin.

In some embodiments, the print head comprises a fibre optic to direct light, and an attachment designed to provide the required gas-resin interface at the fibre tip.

The print head may be made of any material allowing for introduction of the print head into the resin without compromising its structural integrity.

For example, the print head may be made of a material that is chemically inert toward the photo-curable resin. Suitable examples of print head materials for use in the invention include polymer materials, metals, and ceramic, for example glass.

In some embodiments, the print head is made of a polymer material. Examples of suitable polymer materials in that regard include polymers such as polyethylene, including low- density polyethylene (LDPE) and high-density polyethylene (HDPE), polypropylene (PP), polyvinyl chloride (PVC), polystyrene (PS), nylon, nylon 6, nylon 6,6, teflon (polytetrafluoroethylene), and thermoplastic polyurethanes (TPU). In some embodiments, said polymer material is a composite comprising a polymer of the kind described herein.

In some embodiments, the print head is made of metal. Examples of suitable metals in that regard include aluminium, stainless steel, and titanium.

In some embodiments, the print head is made of glass. For example, the print head may be entirely made of glass.

In some embodiments, the print head comprises one or more regions which articulate, for example in the form segments united by joints. This enables arbitrary positioning of the interface along a desired orientation, for example via the use of internal mirrors.

In some embodiments, the print head comprises an LCD panel. In those instances, the print head may be designed such that, when the print head is introduced into the resin, the gas- resin interface forms on said LCD panel, for example below said LCD panel.

In some embodiments, the print head is capable to rotate about a centre axis. In those instances, the print head may be rotated to change its fluidic flow profile and, subsequently, the shape of the gas-resin interface during printing.

The print head may have any dimension conducive to the print head functioning as intended. For example, the print head may have a largest dimension of 0.5 cm, 1 cm, 5 cm, 10 cm, or 30 cm.

In the method of the invention, the print head has a cavity containing gas and the method comprises a step of introducing the print head into the resin to form a submerged gas-resin interface between the gas and the resin.

By the expression "cavity containing gas" is meant an empty space provided within the print head which contains gas, for example air. The cavity containing gas is shaped and oriented such that when the print head is introduced into the resin, the gas in the cavity prevents resin from entering into the cavity, thereby providing the formation of a submerged gas-resin interface.

To ensure contact between the gas and the resin, it will be appreciated that the cavity of the print head would present at least one opening that, once the print head is introduced into the resin, permits contact between the gas and the resin to ensure formation of the required gas- resin interface.

In other words, the present invention may also be said to provide a method of forming a 3D object, the method comprising: providing a photo-curable resin, providing a print head for transmitting curing radiation to the photo-curable resin, the print head having an open cavity containing gas, introducing the print head into the resin to form a submerged gas-resin interface between the gas and the resin, wherein said gas-resin interface is constrained to the print head and defines a printing surface, projecting curing radiation on the submerged gas- resin interface to promote curing of the resin at the printing surface, and promoting relative movement between the gas-resin interface and the resin to produce the 3D object.

By being "submerged", the gas-resin interface is located below the surface level of the resin.

The proposed principle is analogous to that of forcing an empty glass upside-down into a volume of water. As the upside-down glass is pushed into the water, the air pocket within the empty glass prevents water from entering inside the glass, effectively counteracting the hydrostatic pressure of water and providing a submerged air-water interface at the glass opening.

Formation of the gas-resin interface may therefore be achieved by any cavity design that would be fit for that purpose.

In some embodiments, the print head comprises a cavity having one opening. In those instances, once the print head is introduced into the resin the gas contained in the cavity induces formation of the required gas-resin interface at said opening. An example of one such print head configuration is shown in Figures 1, 2, 3(a), 5, and 7. In those instances, the print head is a hollow component introduced vertically into a photo-curable resin. The component is sealed at the top end with a radiation transparent window and left open at the bottom end, to define an internal cavity with an opening at the bottom of the print head. Gas in the cavity prevents resin from entering into the cavity. In the specific examples of those Figures, the gas is pressurised to form a convex gas-resin interface protruding downward from the open cavity.

In some embodiments, the print head comprises a cavity having multiple openings. Those configurations afford the provision of multiple discrete gas-resin interfaces, for example for simultaneous curing of different volumes of resin. An example of one such configuration is shown in Figure 10. The Figure depicts a print head having a squared cross-section and an internal cavity with a 3×3 array of openings, in turn defining a 3×3 array of submerged gas- resin interfaces.

In some embodiments, the print head comprises multiple cavities and multiple openings. For example, the print head may comprise multiple cavities, each having a corresponding opening. In use, these print heads advantageously afford provision of multiple gas-resin interfaces, useful for simultaneous curing of different volumes of resin.

In the method of the invention, the gas-resin interface is constrained to the print head. Since the gas is contained in a cavity of the print head, the gas-resin interface that forms when the print head is introduced into the resin is cohesive with the print head. By the gas-resin interface being "constrained" to the print head, relative movement between the interface and the print head is restricted such that the interface and the print head move together.

The gas may be any gas that forms a gas-resin interface when in contact with the resin.

In some embodiments, the gas comprises oxygen.

Advantageously, oxygen can diffuse through the gas-resin interface to create a layer of passivated resin at the interface, where photo-curing is inhibited. During projection of curing radiation, presence of an un-curable layer of resin between the interface and the curing resin improves physical separation between the forming object and the print head. This assists to minimise chances of physical attachment between the forming object and the print head as the print head moves through the resin, enabling faster movement of the print head for faster printing.

The amount of oxygen in the gas can be controlled to tune the thickness of the layer of passivated resin at the interface, i.e. the higher the oxygen content, the thicker the layer of passivated resin. Accordingly, in some embodiments the gas comprises at least about 5%, at least about 10%, at least about 20%, at least about 50%, or at least about 75% oxygen (v/v).

In some embodiments, the gas is about 100% oxygen (v/v).

In some embodiments, the gas comprises air.

In some embodiments, the submerged gas-resin interface is provided by pressurising the gas within the cavity of the print head. The term "pressurising" will be understood to encompass the application of either positive or negative pressure to the gas, resulting in either an expansion or a contraction of the gas volume. This may be achieved by any means known to the skilled person.

In some embodiments, the print head comprises a gas inlet fluidly connected to the cavity of the print head. The gas inlet can be used to introduce gas into, and/or extract gas out of, the cavity of the print head. Since pressure of the gas in the cavity counters the hydrostatic pressure of the resin on the gas-resin interface, pressurising the gas within the cavity changes the shape and extension of the interface.

For instance, a pressure increase of the gas would expand the gas to push against the interface, which would extend outward relative to the print head. Conversely, a pressure decrease would result in a contraction of the gas volume, with consequent retraction of the interface, for example within the print head boundaries.

Pressurising the gas within the cavity of the print head advantageously ensures that the shape of the gas-resin interface can be retained during printing irrespective of the depth of the printing head within the resin. In other words, the use of pressurising gas within the printing head creates and maintains a controlled surface tension at the gas-resin interface at any resin depth, helping to retain the shape of the interface during printing and print head movement. This results in an enhancement of resin influx rates compared to conventional ‘flat’ gas- liquid interfaces, which shape is determined and modulated by the depth dependent hydrostatic pressure of the resin. Gas used to pressurise the gas in the cavity of the print head may be the same or different than the gas contained in the cavity.

The gas-resin interface may have any shape and extension that is conducive to equalising gas pressure within the cavity of the print head and the hydrostatic pressure of the resin. Changes in the gas pressure within the print head can therefore afford dynamic deformation of the gas-resin interface permitting the influx of fresh resin at the interface, thus facilitating the generation of a continuous layer-less structure.

In some embodiments, the gas-resin interface has a convex shape.

In some embodiments, the gas-resin interface has a concave shape.

In some embodiments, the gas-resin interface is substantially flat.

In this context, convexity or concavity of the interface will be understood to be relative to the gas phase. That is, a convex interface curves/projects outwards from the gas phase, while a concave interface curves/projects inward into the gas phase.

Examples of convex gas-resin interfaces are shown in Figures 3(a) and (b). The images show a convex gas-resin interface projecting outward relative to the gas phase, and outward from the print head into the resin. As shown in Figure 3(a), the shape and extension of the print head can be modulated by changing the pressure of the gas. The Figures shows a side view of an axisymmetric hollow cylindrical print head immersed in a resin. Gas within the cavity of the print head is pressurised to create a convex gas-resin interface projecting from the bottom aperture of the print head. The image shows a number of progressively extending interface boundaries that can be formed by increasing the pressure of the gas. The side profde of the interface can be extracted, and therefore predicted, in function of various values of pressure within the cavity of the print head.

By installing a camera collecting images such as that of Figure 3(a) it is possible to implement automatic control of the shape of the gas-resin interface. In those instances (see for example the CCD camera in the schematic of Figure 1), the method can be performed taking advantage of camera-based feedback to automatically modulate the shape and extension of the gas-resin interface (for example by automatically adjusting pressure of the gas within the print head). Accordingly, in some embodiments the method comprises automatic modulation of the pressure induced by pressurising gas within the print head based on image feedback of the gas-resin interface. This may be achieved, for example, by the arrangement shown in Figure 1.

The method of the invention projecting curing radiation on the submerged gas-resin interface to promote curing of the resin at the printing surface.

Any curing radiation that promotes curing of the resin may be used in the method of the invention. The choice of the specific curing radiation can depend on various factors, such as the type of resin, desired curing speed, depth of cure, and compatibility with the curing apparatus. It should be noted that the following descriptions of curing radiations are provided as examples and not intended to be limiting.

In some embodiments, the curing radiation has a wavelength between about 190 nm and about 2000 nm. For example, the curing radiation may have a wavelength in the range between about 290 nm and about 600 nm, or between about 365 nm and about 405 nm.

In some embodiments, the curing radiation is ultra violet (UV) radiation. UV radiation, typically within the range of 200 to 400 nm, can be generated using UV light-emitting diodes (LEDs), mercury vapor lamps, or other UV sources. This radiation can activate photo- initiators present in the resin and/or activate cross-linkable moieties in the resin composition, initiating a cross-linking reaction that leads to solidification of the resin within the irradiated volume.

In some embodiments, the curing radiation is visible light radiation. Visible light, with wavelengths ranging from approximately 400 to 700 nm, can penetrate deeper into the resin compared to UV radiation. Light sources such as high-intensity LED arrays or specialized lamps can emit the desired visible light spectrum. The photo-initiators and/or cross-linkable moieties present in the resin absorb the visible light and undergo a similar chemical reaction as in the case of UV radiation, leading to the curing of the resin.

In some embodiments, the curing radiation is infrared (IR) radiation. IR radiation, with wavelengths longer than those of visible light, ranging from approximately 700 nm to 1,100 nm, can effectively penetrate deeper into the resin. This deeper penetration allows for curing thick or opaque resin layers that may hinder the passage of UV or visible light. IR sources, such as IR LEDs or IR lamps, can provide the necessary radiation to initiate the curing process.

It should be appreciated that the examples of curing radiations mentioned herein are not exhaustive. Other types of radiation may also be suitable for use in the method of the invention, including for example X-ray radiation, electron beam radiation, laser radiation, or focused ion beam.

Furthermore, it is contemplated that combinations of different curing radiations may be used in specific embodiments. Sequential or simultaneous exposure to multiple wavelengths or spectral bands can be employed to optimize the curing process, enhance material properties, or achieve unique curing effects. The intensity, duration, and spatial modulation of the curing radiations can be adjusted to accommodate various resin formulations, printing requirements, or specific design considerations.

For a given resin composition, the curing radiation would be selected to deliver sufficient optical dose at the printing surface to promote local curing of the resin. For example, the curing radiation may be selected and projected to deliver an optical dose at the printing surface of between about 0.1 mW/cm² and 1.6- 10¹⁰ mW/cm².

For a given image projection, the curing resin may be projected for any exposure time conducive to effective curing of the resin. In some embodiments, the exposure time for a given projection is at least 0.1s, at least 0.5s, at least Is, at least 5 s, at least 10s, or at least 30s. In some embodiments, the exposure time for a given projection is from 0.1s to 60s.

A skilled person will appreciate that the energy density delivered to the resin and the exposure time can be tailored to specific application-related requirements.

For instance, when the resin comprises a biological entity (e.g. a viable cell), the energy density delivered at the printing surface and the exposure time for a given projection would be tailored to ensure curing of the resin while preserving cell viability. For example, the optical dose may be kept to the minimum level required to achieve curing of the resin, thereby maximising the preservation of cell viability.

In some embodiments, the curing radiation is selected and projected to deliver an energy density at the printing surface of from about 0.1 mW/cm² to about 150 mW/cm². Considering an exposure time from 0.1 to 10s, this would correspond to a total energy of 0.01 mJ/cm² to 1.5 J/cm² delivered to the printing surface.

In some embodiments, the curing radiation delivers an energy densities of from about 10 mW/cm² and about 10,000 mW/cm². Those instances are particularly suited for the formation of 3D objects made of a biologically relevant material.

For the case of non-biomedical materials, the energy delivered to the printing surface can be higher. For example, for an exposure time of 0.1 to 10s, the energy delivered at the printing surface can be from 0.01 mJ/cm² to 1.6 - 10⁸ J/cm².

The curing radiation may be projected by any means known to the skilled person, provided it reaches the gas-resin interface to promote curing of the resin.

Typically, curing radiation would be generated by a radiation source and directed to the print head, which delivers it to the gas-resin interface. Optical parameters of the emitted radiation such as direction, intensity, collimation, focus, wavelength, etc. may be controlled along the optical path of the radiation by optical components that would be known to the skilled person.

For instance, a projection system made of a radiation source, such as a digital light projector or a laser beam emitter, may be used in combination with optical components such as filters, lenses, mirrors, shutters, etc. to direct and control the emitted radiation to the print head, which delivers it to the gas-resin interface while controlling projection parameters such as intensity, duration of the exposure, and focus of the projected radiation. An example of one such optical arrangement is shown in the schematic of Figure 1.

In some embodiments, the radiation source comprises a laser scanning system to raster the relevant cross-sectional images of the 3D object onto the gas-resin. An example of one such system is a laser scanning system of the king used in two-photon polymerisation.

In those instances where the radiation emitter is integral to the print head, radiation may be emitted from within the print head and delivered directly to the gas-resin interface.

In some embodiments, the print head comprises one or more optical components for the delivery, focusing, and control of the curing radiation. Those components may comprise one or more optical lens(es), one or more mirror(s), or other optical components to shape and direct the radiation accurately.

In some embodiments, the curing radiation is projected by means of one or more optical fibres.

The curing radiation may be projected along any direction conducive to promoting curing of the resin at the printing surface. In some embodiments, the curing radiation is projected along a vertical axis. An example of one such optical arrangement is shown in the schematic of Figure 1.

In the method of the invention, the gas-resin interface defines a printing surface. By "printing surface" is meant herein a target area within the resin where curing is promoted by the curing radiation. Without wanting to be confined by theory, printing (i.e. local curing) of the resin is believed to be generated at the intersection of the gas-resin interface and the resin, which may be flat or curved. Typically, the printing surface would be taken to be substantially conform to the shape of the gas-resin interface.

Accordingly, it will be understood that the optical curing energies used in the method of the invention result in full-surface exposure, and consequently full-surface curing, of an area of the gas-resin interface, as opposed to a single curing point in space (obtained for example using a single spot-focussed laser).

In the method of the invention, local curing of the resin at the print surface can be achieved by any means known to the skilled person. For example, local selective curing of the resin at the printing surface may be achieved by providing, at the printing surface, the required optical dose to promote curing of the resin. This may be achieved, for example, by optically focusing the curing radiation at the printing surface, beyond the printing surface, or before the printing surface, relative to the optical path of the incoming radiation.

Accordingly, in some embodiments projecting curing radiation through the submerged gas- resin interface comprises focusing the curing radiation on the gas-resin interface, on the resin side of the gas-resin interface, or on the gas side of the gas-resin interface.

In some embodiments, the curing radiation comprises cross-sectional images of the 3D object.

Cross-sectional images of the 3D object may be obtained from a digital representation of the target object, which may be acquired or generated by means known to the skilled person. Those means may include computer-aided design (CAD) software, three-dimensional scanning devices, or data obtained from other 3D digital modeling techniques. The digital representation would typically comprise a stacked sequence of the cross-sectional images that stacked together form a complete 3D optical representation of the target object. By adopting a curing radiation comprising cross-sectional images of the 3D object, the method of the invention makes it possible to generate complete 3D target objects by translating the print head along a single directional axis, significantly simplifying the requirements of the printing equipment. At each subsequent translation, sequential cross- sections of the 3D object can be projected and therefore cured at the gas-resin interface, affording layer-by-layer formation of the 3D object. This is a fundamental departure from conventional 3D printing systems based on single focus-spot printing (e.g. using single spot- focussed laser for spot-curing). In those conventional systems, the print head required for printing an entire 3D objects must be moveable relative to the resin along multiple axial directions to effectively enable point-by-point curing of an entire 3D volume. Conventional printing systems in that regard may be characterised, for example, by having the print head (or the resin tank) mounted on a 3 to 6 DOF ("Degrees-Of-Freedom") robotic arm to enable movement of the focal spot across all points of a given target volume. In that regard, the method of the invention affords the adoption of significantly simplified printing systems.

In some embodiments, the cross-sectional images of the 3D object correspond to a 2D cross- section of the object. Those instances are useful for example when the gas-resin interface is flat, defining a corresponding flat printing surface.

Accordingly, in some embodiments the curing radiation comprises cross-sectional images of the 3D object, said cross-sectional images representing flat cross-sections of the 3D object that are conform to a flat gas-resin interface.

In some embodiments, the cross-sectional images of the 3D object correspond to a non-flat cross-section of the object. For instance, the cross-sectional image of the 3D object may correspond to a curved slice of the object, for example a convex or concave slice of the object. Those instances are useful for example when the gas-resin interface is non-flat, defining a corresponding non-flat printing surface, such as a convex or concave gas-resin interface defining a convex or concave printing surface, respectively. Accordingly, in some embodiments the curing radiation comprises cross-sectional images of the 3D object, said cross-sectional images representing convex cross-sections of the 3D object that are conform to a convex gas-resin interface.

In other embodiments, the curing radiation comprises cross-sectional images of the 3D object, said cross-sectional images representing concave cross-sections of the 3D object that are conform to a concave gas-resin interface.

In those instance where the gas-resin interface (and the corresponding printing surface) is non-flat (e.g. curved, such as convex or concave), it is required to project corresponding non-flat cross-sections of the target 3D object to achieve correct spatial curing of the resin in a three dimensional printing surface. That is, each projection should be confirm to the shape of the gas-resin interface, which requires accounting for both in-plane and out-of- plane structures of the 3D object during the slicing process, as the interface spans three dimensions. Consequently, the discretization of the print geometry necessitates the adoption of a non-planar approach as opposed to planar layers. This may be achieved, for example by means of customised algorithms for the determination of non-flat cross sections of the target object.

The paragraphs below will describe an example procedure for one such image transposition of non-planar slices of a target 3D obj ect in the case of an axially symmetric print head (such as that of the schematic of Figure 1) projecting curing radiation along a vertical z-direction onto a gas-resin interface having convex shape. Nevertheless, based on that information a skilled person would be readily capable to devise suitable image transposition algorithms for differently shaped print heads and gas-resin interfaces.

As shown in Figure 3(a), utilizing an axisymmetric cylindrical print head the shape of the convex layer can be extracted from the side profile of the interface for various gas pressures. Once the profile has been extracted, a 2D displacement map of the interface can be created as a function of the gas, whereby the displacement transformation matrix (r,θ,Φ) is determined (Figure 3(b)). Convex optimized projections are created by correcting the 3D voxel array using this transformation matrix, resulting in illuminated images that follow the interface curvature (Figure 3(c)).

The proposed approach can be generalized to any interface shape. In a simplified case, an assumption is made that the print head is axis-symmetric, allowing the three-dimensional shape of the interface to be approximated from a single side profile. Utilizing a high-contrast image, such as the one presented in Figure 3(a), a custom script (e.g. a MATLAB script) extracts the interface's curvature for different syringe displacement values and identifies the corresponding optimal syringe position for a given print head size. The optimal syringe position (S) is one that minimizes the average piece-wise derivative of the interface profile ((x.y)). resulting in the flattest interface shape while ensuring that the interface is fully developed (i.e. spanning the entire print head dimension).

Upon extracting the side profile, a top-down image of the interface is generated, as depicted in Figure 3(b), where the grayscale intensity represents the displacement of the interface from the print head's edge. This representation is referred to as the interface displacement map.

Utilizing the interface displacement map, the 3D voxel point cloud is displaced in the z- direction by the corresponding x-y displacement value in the displacement map, yielding a voxel point cloud that is stretched in the z-direction following the interface's profile. Once the transformed point cloud is generated, standard planar slices can be performed on the skewed point cloud, resulting in optimized slices that are subsequently used to create the desired structure.

The method of the invention can therefore integrate an image-based feedback affording automatic control of the shape and size of the gas-resin interface by modulating the gas pressure within the print head. This can be achieved, for example, by mounting a CCD camera for continuous monitoring of the gas-resin interface shape, which image data can be used by a feedback controller to act on the gas pressure within the print head in order to maintain a desired interface shape.

A more detailed description of the air-resin interface modelling for the determination of relevant cross-sectional image parameters for the curing radiation is provided in the Examples.

In the case of a multi-interface arrangement of the print head a corresponding array displacement map can be employed. For instance, in the 3×3 array obtained with the print head shown in Figure 10, the 'DIP' lettering was obtained using a 3×3 displacement map instead of a single interface map.

The method of the invention also comprises a step of promoting relative movement between the gas-resin interface and the resin to produce the 3D object.

In some embodiments, promoting relative movement between the gas-resin interface and the resin to produce the 3D object comprises moving the print head relative to the resin. For instance, the print head may be mounted on a moving structure or stage that moves relative to a static vat containing the resin. Said relative movement may advantageously be along a single axial direction during printing, providing for simplified setups relative to conventional multi -degree of freedom arrangements.

In some embodiments, promoting relative movement between the gas-resin interface and the resin to produce the 3D object comprises moving the resin relative to the print head. This may be achieved by placing a vat containing the resin on a moving stage. Said relative movement may advantageously be along a single axial direction during printing, providing for simplified setups relative to conventional multi -degree of freedom arrangements.

In some embodiments, the curing radiation is projected while promoting relative movement between the gas-resin interface and the print head. In those instances, adjacent volumes of resin can be cured with no interruption for continuous formation of the 3D object. Said relative movement may advantageously be along a single axial direction during printing, providing for simplified setups relative to conventional multi-degree of freedom arrangements.

In some embodiments, the curing radiation is not projected while promoting relative movement between the gas-resin interface and the print head. That is, curing radiation is projected when the print head is stationary to cure a first layer of resin, but not when the print head translates to a subsequent projection layer. In those instances, the 3D object may be formed sequentially (i.e. layer-by-layer) by alternating irradiation and print head placement.

In some embodiments, the relative movement between the gas-resin interface and the resin is promoted along a single axial direction during printing. Said axial direction may be a vertical (z-axis) direction. In those instances, relative movement between the gas-resin interface and the resin during printing may be promoted by moving the print head along said axial direction relative to the resin, or alternatively by moving the resin along said axial direction relative to the print-head. Once a first object is fully printed, the print head can then be translated (for example along x and y-axes) for printing of a further object.

Relative movement between the gas-resin interface and the resin may be promoted at any speed conducive to formation of the intended 3D object. For example, the interface and the resin may move relative to one another at a relative speed of at least about 0.1 μm/s, for example at least about 1 μm/s. In some embodiments, the interface and the resin move relative to one another at a relative speed of from about 0.1 μm/s to about 1 cm/s, from about 0.5 μm/s to about 1 cm/s, from about 1 μm/s to about 1 cm/s, or from about 1 μm/s to about 0.5 cm/s.

In some embodiments, relative movement between the gas-resin interface and the resin is achieved by moving the print head relative to a vat containing the resin at a speed of at least about 0.1 μm/s, for example at least about 1 μm/s. In some embodiments, the print head is moved relative to a vat containing the resin at a speed of from about 0.1 μm/s to about 1 cm/s, from about 0.5 μm/s to about 1 cm/s, from about 1 μm/s to about 1 cm/s, or from about 1 μm/s to about 0.5 cm/s. In some embodiments, said relative speeds are obtained by moving a vat containing the resin relative to the print head, which itself may be static or moving.

In a typical procedure of the method of the invention, the photo-curable resin, which is typically transparent or translucent, may be positioned in a printing chamber or vat, and the print head immersed into the resin. Gas present in the cavity of the print head would generate the required gas-resin interface. The shape and extension of the print head may be modified by pressurising the gas in the cavity, for example by means of a gas inlet provided in the print head and connected to the internal cavity. Cross-sectional image slices, for example determined using a procedure described herein, are then projected through the print head onto the gas-resin interface, for example using projection means described herein.

Each cross-section image of the target object is sequentially projected onto the gas-resin interface as the print head moves relative to the resin. As the print head moves relative to the resin, the projected light selectively exposes and solidifies resin volumes in a pattern corresponding to the shape of the projected cross-sections. This solidification process may occur layer by layer, with each projected cross-section being cured before the next layer is formed.

To facilitate accurate projection of each cross-section, the method may include an alignment and registration process. The digital representation of the target object is aligned with printing coordinates of the print head, ensuring that each projected cross-section is correctly positioned relative to the previous layers and the overall object. Alignment techniques may involve coordinate transformations, image processing algorithms, or fiducial markers placed within the printing chamber.

In some embodiments, the method comprises optimization steps to enhance the printing process. For example, projection parameters such as the intensity and duration of the projected light may be dynamically adjusted based on the properties of the photo-curable resin or specific design requirements. This optimization allows for improved curing efficiency, reduced print time, and enhanced surface quality of the printed object.

Figure 1 shows an example printing setup showing optical and mechanical components which can be used to carry out the method of the invention.

In the schematic of Figure 1, a cylindrical print head is dipped into a resin vat, which dimensions can be adapted to various sizes depending on the dimensions of the print volume and the target object. In the schematic, the print head is a hollow cylinder which is left open at the bottom and is sealed at the top with a radiation transparent glass window. The print head is therefore designed to be transparent to curing radiation projected vertically along a z-axis (represented in blue) while maintaining a gas pocket within its core when immersed in the resin. The gas pocket is exposed to the resin at the bottom of the print head, providing for the required gas-resin interface.

The print head is provided with a gas inlet that enables introduction of gas, for example air or oxygen at various concentrations, into the internal cavity. After the tip is immersed, gas (e.g. air, or O₂) can be pressurised in the internal cavity to create a curved (i.e. convex), fixed interface that defines a printing surface. Doing so produces a concave resin meniscus at the bottom end of the print head. The shape of the interface (the meniscus) can therefore be easily controlled by varying the gas pressure inside the print head.

In the schematic of Figure 1, 3D objects can be printed illuminating the gas-resin interface with desired cross-sections and continuously translating the print head out of the resin bath along the vertical z-axis. Alternatively, or in addition, the resin bath itself may be moved to add additional degrees of freedom to the system. For instance, the resin bath may be placed on a 3-axis moving stage for additional x-axis, z-axis, and/or z-axis movement. As also shown in Figure 7, the print head may additionally be translated along a horizontal direction for sequential curing of side-by-side objects.

The schematic of Figure 1 also includes a setup of an orthogonal illumination pathway (highlighted in red) which can be used to image shadowgraphs of structures forming during printing. An example of one such shadowgraph is shown in the lower inset of Figure 1.

In the method of the invention, absence of a solid interface between the print head and the forming 3D object prevents mechanical attachment of the object to the print head, whilst the surface tension maintains the interface shape, enabling structures to be produced rapidly. In addition.

Further, the method of the invention affords fast production of 3D objects. By continuously translating and projecting light, cm-scale objects can be printed in timescales on the order of 10’s of seconds. In that regard, Figure 2 shows a collection of pictures taken from the side of the resin bath during printing of a spiral stent structure using a setup correspondent to the schematic of Figure 1. The images were taken over a 60 second timeframe, and depict the continuous formation of the cm-scale structure.

The method of the invention can also advantageously afford formation of large objects. For instance, in the case of a vertically mounted print head with z-axis movement, the height of the resulting structure is governed by the focal length of the projection optics, which can permit the fabrication of cm-high structures in less than 2 minutes (e.g. 90 seconds). Further vertical translation of the print head can lead to even taller structures. There is therefore an inherent trade-off between in-plane resolution and total feature height.

Furthermore, the permeability or lack of a physical interface and contact between the print head and the forming 3D object facilitates the ability to pass objects through its surface by relying on the surface tension of the printing liquid. This technique enables the printing of objects on top of pre-existing structures or the use of these structures as support for semi free-floating constructs (Figure 9).

The multi-step printing process allows the integration of multi-material components, wherein a single material is printed and removed before adding and printing a second material onto a pre-printed structure, significantly augmenting the complexity of fabricated components (Figure 9(a-b)).

In addition to the demonstrated parallelization through sequential printing, it is feasible to engineer print heads exploiting interface control to create arbitrary configurations or multiple printing interfaces within a single print head (Figure 10(a-b)). Generating a global interface displacement map for the print head facilitates parallel printing of multiple structures, as exemplified by an array of nine individual interfaces creating three sets of the word 'DIP' (Figure 10(b)).

By the expression "acoustic wave" is meant all types of elastic waves that can propagate as a pressure variation through a transmission medium.

It was observed that the gas-resin interface can be susceptible to acoustic stimulation. By transmitting acoustic waves to the submerged gas-resin interface it is therefore possible to impart rapid modulation of the shape of the interface according to the characteristics of the acoustic waves. The rapid modulation of the shape of the interface via acoustic excitation can advantageously promote the formation of capillary waves on the interface (i.e. surface waves with a wavelength short enough that the restoring force is the resin’s surface tension), significantly enhancing resin influx around the interface (Figure 12). The rate and distribution of material influx can itself be modulated by controlling parameters such as the characteristics of the acoustic waves (e.g. amplitude, frequency), the print head geometry, and/or the interface curvature.

Accordingly, in some embodiments the method comprises transmitting acoustic waves to the gas-resin interface to induce an acoustic field on the interface in the form of Faraday waves. The application of said waves to the interface advantageously enhances resin influx during printing, resulting in faster print speeds.

Improved mass transport at the gas-resin interface obtainable under acoustic excitation advantageously affords even faster and more consistent printing relative to printing absent the acoustic excitation. This results in even higher resolution printing, as well as higher cross-section printing.

The use of acoustic wave excitation during printing of the 3D object is particularly advantageous for the fabrication of composite objects made of cured resin matrix containing suspended matter, for example in the context of bio-printing. In those instances, the enhanced resin influx at the gas-resin interface under acoustic excitation improves localisation of suspended matter (e.g. viable cells) within the print volume. This results in the fast production of 3D objects containing a high concentration of the desired suspended material. Through the use of acoustic modulation, not only can sedimentation of suspended material in the resin be practically eliminated, but an increase in encapsulation efficiency through acoustic focusing may also be achieved. This enhancement greatly augments the range of possible biological materials, whilst maintaining physiologically relevant processing parameters and cellular homogeneity.

Figure 13 shows a representation of different acoustic patterns (A, B, C) formed using a cylindrical print head at different cross sections of a print. The patterns relate to acoustic excitation at different frequencies. The images on the right hand side of Figure 13 show patterns obtained at the gas-resin interface using polystyrene microparticles suspended in the resin under acoustic excitation. The patterns are viewed through the print head at three different applied frequencies, indicating the ability to alter the number and location of concentrated micro-objects along the gas-resin interface.

Mechanical vibrations of the gas-resin interface resulting from transmission of the acoustic waves may also be used to provide local mechanical mixing of uncured resin layers adjacent to the forming object during printing. Those instances further improves the printing efficiency during fabrication of composite objects made of cured resin matrix containing suspended matter, for example in the context of bio-printing. For example, in a vertical set- up, by momentarily stopping the printing process and raising the print head a set distance above the previous layer, standing waves can be formed by the hydrodynamic interaction of the gas-resin interface and underlying structure, promoting the spatial patterning of particles or suspended materials. During this process, suspended material is driven by the acoustic radiation force formed by spatial variations in energy density. The suspended materials thus migrate to either nodes or anti-nodes of the standing waves depending on whether the acoustic contrast factor of the suspended materials relative to the surrounding fluid is positive or negative, respectively.

By transmitting acoustic waves on the submerged gas-resin interface, the method of the invention advantageously provides additional degrees of freedom of the fabrication surface, in which the superposition of the print head translation, internal pressurisation and acoustic driving signal determine the time dependent location (Figure 12(b)). This additional modality can be used to bolster fabrication rate, material processing ranges, cellular patterning or fluidic handling capabilities by providing direct control of the characteristics of the waves within the fabrication regime. Objects can therefore be created by illuminating the interface with desired cross-sections and continuously modulating the interface shape and position, where the absence of a solid interface obviates mechanical attachment, enabling structures to be rapidly produced. This approach affords reproducible formation of a wide variety of 3D centimetre -scale objects in tens of seconds. Transmission of acoustic waves to the submerged gas-resin interface may be achieved by any means known to the skilled person.

For instance, acoustic waves may be transmitted to the submerged gas-resin interface by vibrating the print head.

Acoustic waves may also be transmitted on the submerged gas-resin interface by introducing acoustic waves into the resin, for example by generating acoustic waves within the resin volume. In those instances, the acoustic waves may be made to travel through the resin to the gas-resin interface, affording the desired shape modulation of the submerged gas-resin interface.

In some embodiments, the method of the invention comprises a step of introducing acoustic waves into the cavity of the print head. In those instances, the acoustic waves can travel through the cavity of the print head as pressure waves within the gas contained in the cavity, affording shape modulation of the submerged gas-resin interface.

Acoustic waves may be generated by any means known to the skilled person. For example, acoustic waves may be transmitted to the gas-resin interface by an acoustic generator (e.g. an electroacoustic device such as a voice coil actuator, a surface acoustic wave generator, etc.) placed to emit acoustic waves that can travel to the gas-resin interface.

For instance, a suitable acoustic generator may be coupled to the cavity of the print head, such that emitted acoustic waves travel through the gas in the cavity to reach the gas-resin interface. In other configurations, an acoustic generator may be submerged within the resin, such that generated acoustic waves travel though the resin to the gas-resin interface. In further configurations, an acoustic wave generator may be coupled to the print head, such that emitted acoustic waves travel through the body of the print head to reach the submerged gas-resin interface. Alternative configurations may be readily devised by a skilled person. Figure 11 shows a schematic illustration of an example print head for performing the method through acoustic stimulation. Acoustic waves are introduced into the cavity of the print head through an opening in the print head. The print head is open at one end and enclosed with a transparent glass window to maintain a constant gas volume, while allowing optical projections to pass through. A gas-resin interface forms at the base of the print head as it is vertically submerged into the resin. The interface acts as a fabrication surface in which patterned projections are used to locally cure the resin. Acoustic manipulation of the internal print head air volume promotes enhanced material influx through capillary driven waves that travel across the interface, as shown in Figure 12 (a). Instantaneous location of the air-liquid boundary is dependent on the spatial location of the print head, internal pressure state and acoustic excitation, as shown in Figure 12(b).

Acoustic excitation of the gas-resin interface results in the formation of capillary-gravity waves and sub-surface streaming, greatly bolstering material influx into the printing volume. The ability to localise the print head itself anywhere within a resin largely removes the inherent coupling between the shape of the material container and the formation of free surface waves. Accordingly, acoustic stimulation can be performed effectively irrespective of the characteristic of the resin container. This is especially important for biological materials printed in-situ into sequential volumes such as multi-well plates, where its entirety (including all subsequently printed structures) would need to be continuously actuated, and potentially damaging delicate tissue material due to prolonged unnecessary stress to biological constituents.

The geometry of the gas-resin interface can be modulated by acting on the characteristics of the acoustic waves. For instance, for a given print head geometry and resin, the shape of the gas-resin interface, and therefore the geometry of the printing volume, can be modulated also by acting on the frequency and/or the amplitude of the acoustic waves.

By way of example, for a cylindrical print head (such as that depicted in Figures 11 and 12), it was observed that azimuthally symmetric monochromatic modes would form at low frequency acoustic waves, which progressively evolve into square symmetry at higher frequencies.

It was also observed that low amplitude modulation at frequencies synchronised with the projection framerate significantly augments mass-transport allowing for translational flow across the meniscus. Additionally, centralized jetting was observed at higher driving amplitudes, allowing for the creation and subsequent high-speed ejection of structures from the interface.

Acoustic actuation therefore significantly increases the influx of material during printing, which is further amplified by meniscus curvature due to secondary streaming effects. To demonstrate this enhancement, the transient influx of new material was captured using high speed photography with and without acoustic excitation, for various material viscosities and translational velocities. The application of acoustic modulation results in an exponential decreasing in the ‘dry’ area below the interface. By measuring the instantaneous area of the dry region prior to acoustic excitation and the duration to completely saturate the interface, the time averaged velocity of new material was found to be ~ 16 - 40 mms^-1 over the range of translational velocities under the condition used (as described in the Examples). This heuristic can be used in conjunction with the object’s topology to predict and adapt the printing speed based on the fluidic path length.

Accordingly, in some embodiments the acoustic waves have a frequency from 1Hz to 10MHz, for example from 1Hz to 20 KHz, or from 1Hz to 1000 Hz. In some embodiments, the acoustic waves have a frequency from 50 Hz to 150 Hz.

In some embodiments, the acoustic waves have an amplitude, expressed in terms of pressure amplitudes, from 0.1Pa to 1MPa, for example from 0.1Pa to 5kPa (as measured in the medium transmitting the waves, for example the gas section of the print head if the acoustic waves are generated in the gas).

In some embodiments, the acoustic waves have a frequency from 1 Hz to 100 kHz, and an amplitude in terms of pressure range from 0.1 Pa to 5kPa. It will be understood that the specific effects of acoustic stimulation on the gas-resin interface may be resin-dependent, in that the propagation dynamics of acoustic waves travelling through a resin can vary depending on the resin's density. A skilled person would be able to fine tune frequency and amplitude characteristics of the acoustic waves depending on the intended result.

Also, the specific effects of acoustic stimulation on the gas-resin interface may depend on the specific geometry of the print head. In that regard, the choice of different geometries of print head can assist in creating customary shapes of the interface under acoustic stimulation, as well as different wave patterns.

The formation of acoustic waves can be used to capture, localise and trap particles or additives suspended in the resin. Due to the interaction between the modulated wave and the underlying previous layer. This approach can be used to pattern particles or cells in specific arrangements.

The present invention provides also a system for forming a 3D object, the system comprising a print head for transmitting curing radiation to a photo-curable resin, the print head having a cavity containing gas such that, when the print head is introduced into photo-curable resin, said gas promotes formation of a gas-resin interface constrained to the print head.

The print head in the system of the invention may be a print head of the kind described herein.

In some embodiments, the system comprises a vat for containing photo-curable resin.

In a typical arrangement, the vat may be placed underneath the print head, such that the print head can be introduced into resin contained in the vat along a vertical direction. Nevertheless, any configuration allowing for the introduction of the print head into the resin to promote formation of the intended gas-resin interface will be understood to fall within the scope of the invention.

In some embodiments, the system also comprises one or more moveable stage(s) for promoting, when the print head is introduced into a photo-curable resin, relative movement between the print head and the resin. Said relative movement may be achieved, for example, by moving the print head relative to resin contained in a vat, or moving a vat containing resin relative to the print head.

In some embodiments, the print head moves only along a vertical axis (z-axis) during printing. Figure 1 shows an example system in which a print head (PC) is introduced into resin contained in a vat in an arrangement that affords vertical movement of the print head along a z-direction. In those instances, printing of multiple objects may be achieved by translating the print head over a different printing location once an initial object has been printed (as shown for example in Figure 7).

The system of the invention may further comprise a source of curing radiation, which may be curing radiation of the kind described herein. Said source of curing radiation may be integral to the print head, or independent from the print head. Accordingly, in some embodiments the print head comprises a source of curing radiation.

In some embodiments, the print head comprises an optical fibre for the transmission of curing radiation. The optical fibre may be for transmitting curing radiation form a radiation source external to the print head, or for transmitting curing radiation from a radiation source that is integral to the print head.

The cavity of the print head may have any design that is conducive to the print head operating as intended, i.e. when the print head is introduced into photo-curable resin, gas in said cavity promotes formation of a gas-resin interface constrained to the print head. For example, the print head may have an internal cavity with an opening at a bottom side of the print head, such that when the print head is introduced into photo-curable resin a gas- resin interface forms at the opening.

In some embodiments, the print head comprises a gas inlet for the introduction or extraction of gas into/from the cavity. In those instances, when the print head is introduced in the resin, gas within the cavity can be pressurised or depressurised, resulting in a modification of the shape and extension of the gas-resin interface.

In some embodiments, the print head has an internal cavity with an opening at a bottom side of the print head, such that when the print head is introduced into photo-curable resin and said cavity is filled with pressurised gas, the gas-resin interface that forms has a convex shape protruding downward from the opening.

Said opening may have any dimension conducive to formation of the submerged gas-resin interface as described herein. In some embodiments, said opening has a largest dimension of from 2 mm to 30 mm, from 2 mm to 15 mm, from 5 mm to 15 mm. In some embodiments, said opening has a maximum dimension of 10 mm, or 25 mm.

The opening may have any shape conducive to formation of the submerged gas-resin interface as described herein. In some embodiments, the opening has a circular shape, a squared shape, or a rectangular shape having a largest dimension of from 2 mm to 30 mm, from 2 mm to 15 mm, or from 5 mm to 15 mm, for example 10 mm, or 25 mm.

In some embodiment, the print head comprises an open cavity with a circular opening with a diameter of from 2 mm to 30 mm, from 2 mm to 15 mm, or from 5 mm to 15 mm, for example 10 mm or 25 mm.

An example of a print head with an open cavity having a circular opening is shown in Figures 1, 2, 3(a), 5, 7, 11, 12(a), 14(b), 15. An example of a print head having an open cavity with an array of discrete square openings (8 mm x 8 mm each) is shown in Figure 10. For simplicity axis-symmetric print heads were used to simplify the computation of the interface shape, however it is possible that any arbitrary shape of the print head is conceivable. In general print heads with cavities ranging from 30 mm to 5 mm (largest dimension) were primary utilised. For example, two print head sizes (D = 25 mm and D = 10 mm) were used.

The print head may have any shape conducive to the intended function.

In some embodiments, the print head has a tubular shape with an opening at an end and a window transparent to curing radiation at the opposite end. The tubular shape may have a circular or square cross-section. An example of a tubular print head having circular cross- section is shown in the schematic of Figure 1. An example of a tubular print head having a squared cross-section is shown in the Figure 10.

In some embodiments, the print head comprises a cavity having multiple openings. When such print head is in use, those configurations afford the provision of multiple discrete gas- resin interfaces, for example for simultaneous curing of different volumes of resin. An example of one such configuration is shown in Figure 10. The Figure depicts a print head having a squared cross-section and an internal cavity with a 3×3 array of openings, in turn defining a 3×3 array of submerged gas-resin interfaces in use.

In some embodiments, the system comprises optics components for delivery, focusing, and control of the curing radiation. Those components may comprise one or more optical lens(es), one or more mirror(s), or other optical components to shape and direct the radiation accurately. In some embodiments, the print head comprises one or more such optical components.

In some embodiments, the system further comprises control and feedback mechanisms to monitor and adjust operative parameters of the printing process. The mechanisms may include sensors, actuators, and controllers that provide real-time feedback on resin amount, radiation intensity, gas pressure in the cavity within the print head, and other relevant parameters. The control and feedback mechanism ensures the stability and accuracy of the printing process, enabling consistent and reliable fabrication of 3D objects.

For instance, the system may include an image-based feedback control system for the automatic modulation and control of the shape and dimension of the gas-resin interface. Said system may comprise a camera (see for example CCD Camera in Figure 1) that continuously monitors the profde of the interface (see also Figure 3(a)). The camera may feed profde information to a control unit. If the camera detects that the interface shape deviates from an intended configuration, the control unit can act on the gas pressure within the print head to modulate the shape of the interface to confirm to the intended one.

An example of an example assembly implementing an embodiment of the system of the invention is shown in the schematic of Figure 1, as described herein.

In some embodiments, the system comprises an acoustic wave generator for transmitting acoustic waves to the gas-resin interface.

The acoustic generator may be any device capable to transmit acoustic waves to the gas- resin interface. Examples of suitable acoustic generators in that regard include electroacoustic devices such as a voice coil actuator, a piezoelectric actuator, a magneto- strictive actuator, and a capacitive transducer. The transducer may be arranged in the form of phased arrays or modified by acoustic holograms or acoustic metamaterials.

The acoustic wave generator may be positioned in the system to effectively transmit acoustic waves to the gas-resin interface. For example, the acoustic generator may be placed in communication with the cavity in the print head, such that generated acoustic waves travel through the gas in the cavity to reach the gas-resin interface. In other configurations, the acoustic generator may be placed to transmit acoustic waves through the resin to reach the gas-resin interface, for example by being submerged within the resin. In yet further configurations, the acoustic generator may be mechanically coupled to the print head, such that acoustic waves are transmitted to the gas-resin interface as mechanical vibrations of the print head. Provided acoustic waves are transmitted to the gas-resin interface, a skilled person would be readily capable to devise alternative configurations to those described herein.

A schematic of an embodiment system of the invention including an acoustic generator is shown in Figure 14(a). Figure 14(a) shows a CAD model of mechanical components of a 3D print set-up which may be used to perform the method of the invention, including an acoustic modulation device for the transmission of acoustic waves to the gas-resin interface through the cavity of the print head.

A projection module (1) is used to generate 2D optical projections of slices of the target 3D object, which are projected vertically along the z-axis. Z-axis stage (2) is mounted to provide vertical translation movement to projection lens (3) and print head assembly (4). In the embodiment depicted in the Figure, a 12 well plate (5) is located on a multi-purpose holder (6), itself mounted on x-axis stage (7) and z-axis stage (8), for lateral movement along the horizontal plane. Pneumatic airline (9) connects an acoustic modulation device (10) to the cavity of the print head assembly (4) for transmission of acoustic waves generated by the acoustic modulation device (10) to the gas-resin interface (see also Figure 14(b)). In the embodiment of the Figure, a 50 mL syringe (11) is mounted on s-axis stage (12) and can be used to modulate pneumatic pressure within the pneumatic line (9) and the cavity in the print head assembly (4).

Figure 14(b) shows a schematic view of the corresponding gas-resin interface formed at the tip of the print head under acoustic excitation. Figure 14(c) illustrates the total degrees of freedom (DOF) of the printing interface location under conventional 3D printing (left) compared to the proposed method and system (right), and Figure 14(d) shows the instantaneous interface location dependent on the sum of the locations of said DOFs.

Alternative arrangements of the elements shown in Figure 14 may also work as intended. For instance, the projection module may be mounted to project 2D optical projections of slices of the target 3D object horizontally (similar to the arrangement shown in Figure 1). In that instance, the horizontally projected beam may be diverted along the vertical direction by way of a beam splitter. Use of a beam splitter may also afford mounting a further optical element on the opposite side of the projection module, for instance a CCD camera with horizontal focal axis for image-feedback control over the shape of the gas-resin interface. The print head may be mounted vertically, below the beam splitter to collect the vertically deflected projections and focus them on the gas-resin interface. The other components may then reflect the mounting of corresponding components described in relation to Figure 14.

In summary, we present here a rapid 3D printing technique based on the generation of a gas- resin interface. The result is an extremely flexible printing method, which can be used with already existing photochemistry, while fabricating high-resolution structures faster than that demonstrated by previously demonstrated volumetric printing methods.

Furthermore, we have shown that the process can be used to print complex structures, multi- material structures via two-step printing and overprinting by leveraging the permeability of the interface.

Furthermore, we have demonstrated that this process can be easily parallelized and is safe for bioprinting applications. We expect that the dynamic interface printing method will facilitate numerous advantages in fields where high-speed, high-resolution fabrication of three-dimensional structures is needed.

Certain embodiments of the present invention will now be described with reference to the following non-limiting Examples. EXAMPLES

EXAMPLE 1

3D printer assembly

A system in accordance to the schematic shown in Figure 1 was prepared as follows.

All components shown in the schematic were mounted on two orthogonal optical breadboards to facilitate vertical and horizontal displacement. Pattered cross-sections of a target object were projected using a high-power projection module (LRS-WQ, Visitech) with a resolution of 2560 x 1600 pixels and pixel size of 15.1 μm. The projection module is rigidly mounted to a linear stage (MOX-02-100, Optics Focus) which is affixed to the vertical component of the optical breadboard.

Direct control of the dynamic interface is done via a second linear stage (MOX-02-50, Optics Focus), which controls the displacement of a 10 mL or 50 mL syringe connected to the print head via a silicone hose for pressurisation of gas within the print head.

An additional pair of linear stages (MOX-02-100, Optics Focus) are used to position the cuvette/well plate below the print head for sequential or multi-step printing. System control was executed via a custom MATLAB graphical user interface (GUI) that enabled the management of motorized linear stages through RS232, control of the acoustic modulation device, control of the projection module parameters, and the transmission of cross-sectional images via HDMI. The shadowgraph imaging system consists of a 635 nm single mode fiber coupled laser (635nm SM FC Laser, Civil Laser) which is collimated using a lens (#32-970, Edmund Optics).

After passing through the glass cuvette, the shadowgraph is focused using the same collimating lens and imaged using a third lens (#32-483, Edmund Optics) onto the CCD of a mirrorless camera (A7 II, Sony). System control is executed via a custom MATLAB graphical user interface (GUI) that enables the management of motorized linear stages through RS232, the acquisition of shadowgraphs, and the transmission of cross-sectional images via HDMI.

For generating targeted projections, a 405 nm digital light projector with a 2560 x 1600 pixel array produces an in-plane resolution of 15.1 μm, with the maximum irradiance of the projector being 270 mW/cm² at the focal plane, where this can be modulated to lower irradiance values. The projection optics are mounted on a z-stage to translate the focal plane during the print, where further linear stages are used to position the print head in XY space to facilitate sequential printing as well as a fourth stage for direct control of the print interface via a syringe. The projection module, laser, camera and stages are controlled through a custom MATLAB -based interface.

Print head

The print head utilized in this study can be tailored to various dimensions, contingent upon the desired size of the resin container. For simplicity axis-symmetric print heads were used to simplify the computation of the interface shape, however it is possible that any arbitrary shape of the container is conceivable. In general print heads ranging from 30 mm to 5 mm were primary utilised. For example, two print head sizes (D = 25 mm and D = 10 mm) were used.

In the case of dynamic interface printing, the total size of the object in the x-y direction is limited by the projectors total field of view at the focal plane, while the total object height is limited by the focal length of the projection optics. For our setup this was approximately 70 mm. The print head was fabricated using a commercial 3D printing system (Form 3+, Formlabs) and a glass window was glued in-place to facilitate the transmission of light down its center. An internal channel was also fabricated with the print head, to enable gas exchange into the print head via the syringe system. EXAMPLE 2

Resin composition and preparation

PEGDA-based resin: various PEGDA materials were utilised ranging from 10% w/v to 100% w/v. 10g of PEGDA Mn 700 (#455008, Sigma) is dissolved into 40g of 40°C deionized water (excluding 100% w/v) and thoroughly mixed for 10 minutes. Subsequently, 0.1% w/w (e.g. 500mg) of Tartrazine (#T0388, Sigma) and 0.25% w/w (e.g. 150 mg) of lithium phenyl-2,4,6-trimethylbenzoylphosphinate (LAP, #900889, Sigma) were added to the mixture and stirred until complete dissolution.

HDDA-based resin: a solution of 500 mg of Phenylbis(2,4,6-trimethylbenzoyl)phosphine oxide (511447, Sigma) and 50 g of 1,6-Hexanediol diacrylate (#246816, Sigma) was prepared by warming the mixture to 40°C and stirring for 30 minutes. To control the resolution in the z-direction the photo-absorber Sudan I (#103624, Sigma) was added in 36 various quantities ranging from 0 - 0.04% w/w.

GelMA-based resin: GelMA was synthesized following the protocol described in Zhu, M. et al. "Gelatin methacryloyl and its hydrogels with an exceptional degree of controllability and batch-to-batch consistency", Sci Rep 9, 6863 (2019), yielding a degree of substitution of 93% (confirmed by NMR).

A 10% w/v GelMA solution was prepared by dissolving 1 g of GelMA in 10 mL of cell culture media (Freestyle 293 Expression Medium, Thermofisher) preheated to 37°C. After complete dissolution of GelMA, 100 mg of Tartrazine and 25 mg of LAP were added to the solution, which was then maintained at 37°C until complete dissolution. The mixture was sterilized by passing it through a 0.22 μm sterile filter within a biosafety cabinet and subsequently stored in a refrigerator until use.

Alginate-based resin: Norbomene-functionalized sodium alginate (AN) was synthesized based on the following procedure. 10 g of sodium alginate was dissolved in 500 ml of 0.1 M 2-(N-Morpholino)ethane-sulfonic acid buffer (#145224-94-8 Research Organics) and fixed to pH 5.0. 9.67 g of 1-Ethyl-3-(3-dimethylaminopropyl)carbodiimide·HCl, 2.90 g of N- hydroxysuccinimide, and 3.11 ml of 5 -norbomene-2 -methylamine were added. The pH was fixed at 7.5 with 1 M NaOH, and the reaction was carried out at room temperature for 20 hours. The mixture was dialysed against water for 5 days prior to lyophilisation.

The degree of norbomene functionalization was determined as 16.2% by 1H NMR. A 7% w/v AN solution was prepared by dissolving 1 g of AN in 14.29 ml of phosphate buffered saline (PBS) solution. 200 mg of Tartrazine, 20 mg of LAP, and 122.7 μl of 2,2’- (ethylenedioxy)diethanethiol were dissolved in 5.59 ml of PBS and added to the AN solution and mixed until homogenous. The pH was adjusted with 1 M NaOH until the solution was visibly opaque.

UDMA support material: A solution of 50 mg of Phenylbis(2,4,6-trimethylbenzoyl) phosphine oxide (511447, Sigma) and 5 g of Diurethane dimethacrylate (#436909, Sigma) was prepared by warming the mixture to 45°C and stirring for 30 minutes. To remove trapped air-bubbles the mixture was then transferred to a light-safe falcon tube and centrifuged at 4000 rpm for 10 minutes to remove residual air bubbles. This material was then used as the base support for the free-floating print test.

Microscopy μCT images were acquired using a Phoenix Nanotom M scanner (voxel size = 10 μm³, 90 kV tube voltage, 200μA tube current, 8 min scan time). For hydrogel samples the structures were briefly dried with tissue paper and mounted into a falcon tube for imaging. For hard materials such as HDDA, the structures were sat on top of a plastic cap to provide good contrast between the printed structure and the supporting medium. For each structure an STL surface mesh was extracted and imported into Keyshot 11 (Keyshot, Luxion) to render the final μCT representation. Scanning electron microscopy (SEM) images were acquired on a FlexSEM 1000 (Hitachi High Technologies, Japan). Printed structures on glass slides were mounted directly to the microscope stage with no further sample preparation. The samples did not have a conductive coating applied. The FlexSEM was operated in variable-pressure mode at 50 Pa, and images were acquired with a 15keV beam using the ultra-variable detector (UVD). To cover the field of view needed for the large structures the working distance was typically 40-50 mm, and multiple images were collected in a tiled manner and stitched together in post- processing.

EXAMPLE 3

The proposed method allows to create not only structures in hard acrylates such as HDDA, but also in common biomaterials such as PEGDA and GelMA. To demonstrate this, we set out to develop a print parameter space to determine the maximum achievable print speed as a function of the optical power (Figure 4). Speeds in excess of 700 μm/s were realized using a PEGDA based hydrogel material, with an optical dose of 270 mW/cm², while lower optical doses relevant for tissue engineering still facilitated high throughput printing. An example of the helical test structure printed at different power-velocity pairs can be seen in Figure 1, whereby correct pairing between the print velocity and optical dose resulted in high quality structures.

To evaluate the attainable resolution of the dynamic interface system, a series of test structures were fabricated using HDDA (methods). In order to assess the minimum in-plane feature size, a test structure comprising an array of features with defined dimensions and orientations was printed. Scanning electron microscopy (SEM) was employed to image the test structure, yielding a minimum in-plane resolution of 50 μm, which corresponds to approximately three in-plane pixels. To ascertain the system's ability to print structures with non-planar features, a gyroid lattice and Kelvin cell were fabricated and subsequently imaged using SEM and micro-computed tomography (microCT). Both structures exhibited features with dimensions below 100 μm. We propose that the proposed method offers significant advantages in the field of biomedical and tissue engineering, owing to its rapid, non-contact, and support-free fabrication capabilities. High-fidelity, low-stiffhess structures, such as a heart model (not shown) can be produced in as little as 30 seconds. The ability to alter the print head size is particularly relevant for generating biologically pertinent constructs, as working with high cell populations often necessitates the use of small volumes. To illustrate this, a small diameter (10 mm) probe was employed to print directly into a vial with a total print volume of 3 mL (Figure 5).

Furthermore, cell solutions are often opaque due to the optical scattering induced by the cell population suspended in the bio-ink. While this poses no issue for low cell populations, index matching between the material and cellular medium becomes crucial for high cell populations, particularly in the context of volumetric printing. Notably, the proposed method does not require light projection to pass through the entire volume of the resin, enabling high-resolution printing of high-cell populations or opaque resins.

A comparison between our standard PEGDA resin and an engineered opaque alginate bio- resin, which occludes the standard United States Air Force (USAF) test pattern, is presented in Figures 6(a)-(b). Despite the high optical occlusion generated by the alginate gel, the method affords accurate reproduction of the internal structure of a tricuspid valve model (Figure 6(c)).

Given that the print head can move more freely in 3D space, it is feasible to parallelize the system to sequentially create multiple structures (Figure 7). This is advantageous not only for single bath printing applications, but also for facilitating the production of multiple structures within multiple volumes (such as a well plate), which could contain various cell types, materials, or geometries. Cell printing

To assess the preliminary viability of this technique for generating cell-laden, biologically relevant constructs, a simplified kidney shaped hydrogel structure was printed using HEK 293-F cells at a density of 7.2 million cells mL-1. Human embryonic kidney (HEK) 293-F cells (Freestyle 293-F, Thermo Fisher) were used to determine the preliminary viability of the 3D printing system. Unlike other volumetric printing methods, high cell populations can be printed easily without requiring the refractive index between the cells and the printing medium to be matched.

A cell solution containing 7.2 million cells / mL was used for both the model of the kidney and the cell-viability measurements. To determine the cell viability a thin 500 μm wall was printed to minimize the effect of cell death via insufficient media diffusion which was determined via a LIVE/DEAD viability/toxicity kit (L3224, Invitrogen). Measurements were taken every day for a period of 5 days, with the viability being averaged over 4 representative regions for each day.

To create the cell loaded bio-ink, the GelMA solution was warmed to 37°C followed by the resuspension of cells into the solution. The solution was subsequently passed through a cell strainer (#0877123, Thermo Fisher) and stored in the water bath while not in use. The printing process involved pipetting approximately 3mL of the GelMA ink into a 12 well plate and lowering the print head into the well. Before each print, the motorized syringe was used to resuspend the cells by sequentially applying positive and negative pressure (analogous to pipetting the liquid up-and-down), to prevent cell setting prior to printing. Each print ran for approximately 30 seconds with a linear translation velocity of 150 μm/s.

Fluorescence microscopy was employed to image the construct over a 72-hour period (methods), revealing that the proposed method maintains high cell viability (> 85%) after 24 hours (Figure 8).

Additional functionally such as acoustically driving the interface to align cells prior to encapsulation, the superfluous need for optically transparent materials or fluid handling by using the print head as a pipetting tool, greatly opens the avenue of this system to be a highly beneficial tool for bioengineering. Currently, our system has focused on the generation of centimeter scale objects, however future iterations could extend to higher numerical aperture optics, wherein microscale structures could be created at high speeds, without the cost associated with two-photon systems.

EXAMPLE 4

Data pre-processing, printing and post-processing

3D design models of the helical stent, vascular tree, kidney model, ‘DIP’ lettering and microfluidic geometries shown in the Figures were created within Autodesk Inventor, Autodesk. Gyroid lattice, fluorite lattice and kelvin cell were created using nTopology, nTop NY. Tricuspid model, heart model and bucky-ball were download from Thingiverse.com. For each geometry the STL file was extracted and sliced using Chitubox into a stack of PNG images.

As the framerate of the HDMI signal is limited to 60fps, the layer height was chosen dependent on the print velocity i.e. zh= v^→ 60 . After slicing, the image stack was transformed by the convex slicing algorithm to produce a secondary convex-optimized image stack and the sequence was sent to the projector via a HDMI signal using Psychtoolbox-3. The print sequence starts by moving the print head to a defined distance above the print surface (or high-density material), the interface is automatically generated by displacing the syringe by a set displacement (dependent on the selected print head).

The MATLAB GUI sends a signal to turn on the LED module and the print head is displaced in the positive z-direction by the specified print velocity. The optical power of the projection module is automatically set dependent on the user-selected print velocity according to the parameter space matrix. For materials made with HDDA, the printer structures were removed from print volume and washed with isopropyl alcohol. For soft materials made from PEGDA and GelMA, the excess material was gently removed using a pipette and the structures were resuspended in deionized water to wash away remaining material. The structures were then gently detached from the bottom of the print head 93 and stored under DI water.

EXAMPLE 5

Parallel printing

In addition to the demonstrated parallelization through sequential printing, it is feasible to engineer print head exploiting interface control to create arbitrary configurations or multiple printing interfaces within a single print head (Figure 10(a)). Generating a global interface displacement map for the print head facilitates parallel printing of multiple structures, as exemplified by an array of nine individual interfaces creating three sets of the word 'DIP' (Figure 10(b)).

We have successfully demonstrated the capacity for rapid parallelization of the printing process through either employing a multi-interface print head or sequentially printing multiple structures within the same print volume or across numerous wells. We posit that these findings underscore the potential for high automation and expeditious generation of multiple structures, which may enable multiple print parameters to be explored rapidly or, in the context of multi-well plates, varying material or cell types.

EXAMPLE 6

Micro-printing

To evaluate the ability to produce intricate internal structures, two simple microfluidic structures were printed, illustrating that features as small as 500 μm can be achieved (not shown). In conjunction with overprinting, this capability could enable the fabrication of integrated microfluidic models, such as printing a microfluidic chip directly onto a prefusion device such as a syringe needle. Furthermore, the multi-step printing method could allow for the rapid incorporation of multiple cell types or materials into a single model, significantly enhancing the complexity of 3D printed tissue constructs.

EXAMPLE 7

Acoustic modulation

Synthesis of a 3D object was performed while transmitting acoustic waves onto the gasliquid interface of a submerged print head in accordance to a system as schematised in Figures 11-15.

The system configuration relied on an in-plane resolution of 15.1 μm, which is largely defined by the pixel size of a digital micromirror device (DMD) and the magnification of the imaging optics, with a DMD resolution of 2560 × 1600 pixels. The system utilises a 405 nm LED source, where the irradiance at the focal plane can be modulated from zero to -270 mW/cm². The projection illumination and optics are mounted on a z-stage to translate the print head during printing. Further stages are used to position the print head in XY space for sequential printing, as well as another stage for control of the print interface.

Additionally, acoustic control of the interface is achieved via volume manipulation of the supply line external to the system by a voice coil actuator. Acoustic modulation of the interface was also achieved via direct volume manipulation of the gas volume contained within the print head. Practically, a 3” 15W speaker driver (Techbrands, AS3034) was affixed to an enclosed 3D printed manifold containing an inlet and outlet port. The speaker was driven by a commercially available amplifier (Adafruit, MAX9744) using the supplied auxiliary port, with specified waveforms sent by the MATLAB GUI. Frequency ranges of 5 - 500 Hz were used, with fixed or transient frequency switching depending on the structure. By specifying a waveform for each degree of freedom, it was straightforward to synchronise the acoustic modulation with the remainder of the motion and pressure control. The acoustic modulation device operated as an in-line control unit, such that the inlet port was connected to the syringe system and the outlet port was connected to the print head. This facilitated pressurisation of the enclosed system and modulation about the pressurised set-point.

Acoustic waves used in the tests have a frequency from 1 Hz to 100 kHz, for example from 5 to 500 Hz, and an amplitude in terms of pressure range from 0.1 Pa to 5kPa.

The projection module, acoustic modulation device and motion control stages are controlled through a custom MATLAB-based graphical user interface.

Figure 15 shows a schematic illustration of an example print head assembly and acoustic air- line modulation; a) expanded half section view of the print head assembly; b) collapsed half section view of the print head assembly, highlighting that a sealed air-volume is formed with a transparent glass window at the top; c) half section view of the air-line modulation system, wherein a speaker diaphragm forms one side of an enclosed box; d) electrical signal applied to the voice coil causes excitation of the diaphragm which modulates the volume around a set point pressure within the air-manifold and in turn the print head.

The print head assembly includes a lens mounting adapter (13) with an optical window for mounting of a 75×50 mm glass slide (14). Print head thread adapter (16) is sealed through gaskets (15) to the glass slide (14) and the 25 mm print head (17). As shown in Figures 15(a) and (b), the print head thread adapter (14) is provided with an inlet (22) for pneumatic connection between the cavity of the print head (17) and an acoustic generator (depicted in Figures 15(c) and (d)) through an acoustically modulated airline (23). Figures 15(c) and (d) show a schematic of an example acoustic generator, including a voice coil (18), a moveable diaphragm (19) connected through suspensions (20) and gasket (15). Figure 15(d) shows a schematic of the diaphragm movement during generation of acoustic waves that travel to the cavity of the print head (17) through inlet (22). EXAMPLE 8

Gar-resin interface modelling

The shape of the interface can be approximately described by the Young-Laplace equation which relates the interface curvature to the differential pressure sustained across the boundary. In general, this can be written as the following:

Where Ap denotes the Laplace pressure, y is the surface tension and n is the vector normal to the surface. The shape of the non-dimensionalized interface can be found by substituting the general expressions for the principal curvatures of an axisymmetric surface as shown below.

The coordinate origin is taken as the contact point of the meniscus edge with the print head, with the positive z-axis being directed downward along the print head’s central axis and the r-axis parallel to the print-head’s diameter. The superscript prime denotes the derivative with respect to z, and h denotes the maximum height of the meniscus given by:

Where R_o is the radius of the theoretical spherical meniscus with volume

denotes the bond number and θ_Y is the contact angle. Therefore, the shape of the meniscus can be determined via numerical integration of the above non-linear second order ODE. The integration starts at z = 0 to the point z =h, with the initial radius and radial slope equal to the print head radius and contact angle, respectively. Additionally, the solution is constrained such that the volume of the meniscus must match the total volume of air injected into the print head. To solve this, we chose to frame the Young-Laplace equation as an initial value problem, using an implementation of the shooting method in MATLAB. The solution for this problem was defined with initial values that satisfy the following boundary constraints.

This therefore converts the above boundary value problem into a root finding solution which aims to ensure that the boundary conditions M = 0. The Young-Laplace model accurately predicts the interface curvature for an increasing internal pressure state p_i .

It is worth noting that the shape of the interface depends on the quantity p_i — pgz, where p_i denotes the pressure within the print head. As the print head is withdrawn from the bath, the value of pgz decreases linearly and therefore the value of p_i must also change linearly to maintain the same interface shape.

Convex interface formation

As the proposed method can rely on the pressurization of a cavity within a print head to produce an air-liquid meniscus, the profile of this boundary and consequently the cured region is non-planar. Traditional slicing schemes assume that the projected geometry is parallel to the construction plane and as such would result in reconstructed artefacts. To correct for this in the case of an axisymmetric print head, the three-dimensional surface can be reconstructed by revolving the Young -Laplace predicted surface about the z-axis. Let the discrete interface profile, Z(r), be the solution to the boundary value problem, with the parametric expression of the reconstructed 3D surface given by:

Voxel intersection

Unlike standard DLP printing, the projected images required for the present method arise from the intersection of a convex surface with the voxelized representation of the target geometry, resulting in a non-planar slicing scheme. The voxels which lie on this surface can be determined via a distance minimization of the surface to the voxel in the array. Let a point on the surface of the interface be defined by S_p = (x_p, y_p, Z_p) such that it satisfies the above parametric relationship, and the voxel representation of the desired model is given by [V_i, V_j, V_k], where i, j, k represent the dimensions of the voxel matrix whose i, j dimensions define the number of corresponding pixels in-plane and the maximum size of k is determined by the discretization of the object as a function of the sliced layer height. Additionally, [V_i, V_j, V_k] represents a binary 3D matrix where the presence of geometry is defined by a ‘ 1 ’ and the absence of geometry is defined by a ‘O’. Whether a voxel is located on the surface of the interface (S_p) is determined by the minimization of the Euclidian distance between that point and the closest voxel. If n voxels are present within the same Euclidian distance, then the resultant value is averaged over n samples in the following way.

Where represents the voxel coordinate and value which satisfies the above relationship.

This approach is repeated for each location on the interface in three-dimensional space, where the desired image sent to the projection module for each layer is given by:

Where denotes the voxel value and the superscript k denotes the projection in the

sequence. This relationship represents the equivalent projection of the three-dimensional voxel array onto the interface surface in two-dimensions. It’s worth noting that as the voxel array has been reduced to two dimensions via the projection, therefore we have lost some information about its original position. To preserve this, we also store the absolute original z-location of the pixels for each projection, which becomes useful later for reconstruction.

Where IZ is the matrix containing the absolute z-locations and denotes the global z-

coordinate of the pixel stored in . As the print head moves up in the positive z-direction,

the voxels intersected by the interface changes. To determine this intersection, the interface profile is translated in the z-direction corresponding to the discretization of the voxel array (layer height = L_h) in the z-direction.

Determining the intermediate interface shape

To ensure the printed object remains adhered to the resin container, the meniscus must be flattened against the bottom surface such that the maximum extent of the printed part, R max, is contained within the flat region of the meniscus. To predict the extent to which the print head must be lowered to create said flat region, a Bezier curve method for approximating the meniscus shape is used as previously described. Briefly, a MATLAB script minimizes the error of the Young-Laplace equation for a meniscus in a cylindrical capillary at a print head position corresponding to an undeformed meniscus, which is defined via the control points of a Bezier curve. The print head position is then moved downwards, and the free control points are moved radially outwards in a stepwise fashion until the height of the meniscus at R max is approximately 0, while preserving the meniscus volume. To solve for the initial meniscus shape, a dimensionless form of the Young-Laplace equation is used:

Where and is the capillary length. The above equation is solved using

the boundary conditions where x₃ is the

dimensionless form of the print head radius and 0 is the contact angle. To solve the above equation, a cubic Bezier curve is defined along with its first and second derivatives:

Where t is a parametric variable and represent the control points of the Bezier

curve. After defining the x- and y-coordinates of the control points, the kron function in MATLAB is used to calculate the x- and y-coordinates of the meniscus curve as well as the first and second derivatives. Then, are calculated using the following equations:

Afterwards, a loss term is defined corresponding to the sum of the dimensionless Young- Laplace equation divided by the sum of the y-coordinates of the meniscus curve. The undeformed meniscus shape is then calculated using the MATLAB function fmincon. Once this “steady-state” solution is found, the flattened meniscus shape is calculated by moving the control point P₃ (corresponding to the edge of the print head) down. Control points Pi and P₂ are then moved radially outward and the meniscus shape is solved again, preserving the arc length of the meniscus so that meniscus volume is maintained. This is repeated until the meniscus height at R_max is close enough to 0 as evaluated by a user-defined threshold.

Aside from remapping the 3D cartesian geometry in order to slice the volume with a curved print interface, the meniscus shape presents an additional challenge for the beginning layers of the print. If the first layer of the print were defined as that point at which the air/liquid interface were lowered into the container such that the “steady state” meniscus shape was preserved, any geometry of the desired object radially beyond the contact point C could not be cured correctly. The height of the air/liquid interface at all points between r = 0 and r = R_max (the maximum extent of the object’s base) would be too tall, and this would lead to (1) the print not adhering to the container bottom and (2) the print not correctly matching the desired geometry. Therefore, the air/liquid interface must be lowered past this initial contact point, deforming the interface to form a (pseudo) flat region.

The number of interpolation steps used is dependent on the discretization of the volume (V_k) and the layer height L_h . One challenge with applying such an approach for predicting the slicing profde within this interpolated region is that the solution is comprised of a series of overlapping surfaces wherein a voxel can be incident with more than one surface. To combat this, two approaches can be used to ensure that a single voxel and subsequently the projections that make up that voxel never result in a value that exceeds the target original value. One way to do this could be to reduce the greyscale value , such that its cumulative

dosage never exceeds . However, if the number of interpolation steps exceed 255, the

solution lacks sufficient degrees of freedom. This is further complicated by the fact that the curing propagation rate R_p scales non-linearly with intensity:

Where k_p and k_t represent the propagation and termination parameters of the material, [M] is the initial monomer concentration, Φ is the quantum yield and I_a is the absorbed intensity, which in our case is proportional to the greyscale value described in . A more convenient

approach is to exclude those voxels that have already been written by the interpolated surface from the voxel array. This approach solves both the degree of freedom constraint imposed by an 8 -bit image and the non-linear intensity threshold which governs curing onset. Therefore, the available voxels for each loop can be written as the following, where k represents the interpolation step over the domain (0, z').

Geometry reconstruction from projections To validate that the convex slicing algorithm results in the same input geometry, the generated projections are traced back through an empty target volume. For each image in the projection sequence of size k, the voxel value is determined by the quantity whose

global position in the matrix is determined by . Let V' be an empty target volume with

dimensions equal to the input geometry Therefore, any element in V is

given by the coordinate transform of the projection sequence such that:

Computing the reconstruction error (δ)

The similarity between the reconstructed volume and the input volume was computed using the Jaccard Index. For each 2D orthogonal component plane of the volume, the Jaccard Index was summed over the volume and averaged over each component axis, whereby:

The reconstruction error is thus quantified by a single value δ ∈ [0,1], which determines the similarity between the target domain and the computed domain, where a value of δ = 1 denotes a perfect match. A low value of 8 normally denotes an interface step size mismatch between the voxel representation V and the layer slice height L_h. Therefore, the slicing step size was reduced until a the Jaccard Index exceeded a threshold value

which in our case was set .

Theoretical model of optical resolution

Print resolution is determined by exposure energy density, magnification, spatial distribution of the projection optics, and the photo-polymer response, which depends on photo-initiator concentration, monomer concentration and photo-absorber concentration. To quantify the theoretical resolution of the imaging system, we employed a similar approach outlined by Behroodi et al. which predicts the final energy distribution at the projection plane as the superposition of the point-spread functions of all pixels reflected from the DMD surface via spatial convolution:

Where f(x, y) denotes the spatial function of the micromirror cross section at the projection plane. For a single pixel on the DMD, the spatial function is determined by:

Where d_x and d_y denote the dimensions of the micromirror, m is the magnification of the projection optics and g_s denotes the greyscale value [0, 255], The spatial convolution equation determines the equivalent gaussian distribution function (m₀) at the focal plane of the projection optics. The diameter of the point on the focal plane can subsequently be modelled by the Gaussian distribution, where the UV intensity of a point source at a given plane is defined by:

Where /(x,y,z) is the optical intensity of the projected light with units (J/cm²s). P is the total power of the UV light determined in units of (J /s) and ω (z) denotes the gaussian radius at a location z, whose half-width is 1/e² of the Gaussian maximum intensity I_max.

For an axisymmetric print head, the curvature of the meniscus imposes a radially symmetric change in the gaussian radius dependent on the meniscus height Z (r) . As Z (r) was initially determined from an origin located at the print head, an equivalent profile X_m(z) will be implemented such that X_m(0) = 0 and X_m(z) = maxZ(r), this ensures that the maximum meniscus deformation is coincident with the image plane when z = 0. The gaussian beam width at a location on the meniscus is therefore given by:

Where m₀ denotes the beam waist, n is the refractive index and A is the wavelength.

Therefore, the exposure energy per unit area for a finite time t and meniscus surface is:

Energy density across the meniscus

Light entering the resin through the surface of the meniscus is either absorbed or scattered by the material. These two effects determine the fraction of energy deposited into the material and therefore the polymerization thickness and penetration depth. From Beer- Lambert, the energy per unit area within the resin surface is governed by an exponential reduction in intensity based on material parameters:

Where D_p is the penetration depth at which the intensity falls to 1/e² of the surface intensity, ε_d and εi are the molar absorption coefficients of the photo-initiator and photoabsorber, respectively, D and S are the concentrations of the photo-initiator and photo-absorberand z’ defines the coordinate system into the material which is not necessarily aligned with the optical axes.

The curvature of the meniscus decomposes the incoming light at location (x, y, z) into scattered and transmitted components. At any location z on the meniscus surface the incident angle of the incoming ray of light can be defined by a₀ relative to the print head axis. In our case

however it could be feasible that 0 for some print head and optical

configurations. Similarly, the angle of the meniscus a_m and its normal at location

(x, y, z) relative to the print head axis can be determined by:

Where X_m (z) denotes the radial position of the meniscus as a function of the meniscus height z. The definition of this ray in three-dimensions coincident with a point on the surface of the meniscus (x, y, z), can be approximately described by Gaussian-beam theory. Under the assumption of an axisymmetric print head, the normal vector at this point in-two dimensions n and associated light ray u, is given by:

From Snell’s Law, the angle of the outgoing ray relative to the surface normal is given by the relative change in the refractive index of the material and the incident angle . As the angle between the incoming ray

and surface normal

is given by the dot product cos

, the outgoing angle 0₂ relative to the surface normal can be simplified to the following:

The direction of this ray represents the new coordinate system y for the Beer-Lambert solution where the rotation of the ray with respect to the local coordinate system vector

is given by:

Where the new coordinate axes for the Beer-Lambert solution are given by:

Furthermore, the proportion of light transmitted into the material is dependent on the incident angle θ₁ and the energy per unit area E(x,y,z,t). Using the Fresnel equations, the transmission coefficients for parallel and perpendicular polarizations are proportional to the cosine of the incoming and outgoing rays, such that:

Under the assumption that the incoming light is not polarized, the transmission coefficient T is given by the average of the S and P polarization states. As the Fresnel coefficients represent amplitudes, the transmitted intensity η at the ray-meniscus intersection is proportional to square of the amplitude.

The energy per unit area E is dependent on the position of the incoming ray , its coordinate

system is such that and . In general, under the assumption that the beams

ensures that

, then the vector can be shown to be:

Similarly, if

defines the normal vector at the meniscus, then the transmitted component with coordinates relative to transmissive beam, is given by:

Modelling the effective resolution, meniscus working region and interfacial focal map

The effective printing resolution can be formed by convolving the point spread function over a single pixel, wherein the theoretical point spread function in three-dimensions can be simulated by defocusing in the Fourier domain by a modulated gaussian function, where:

And,

This approach results in the 3D representation of the point spread function. Therefore, the effective pixel size was approximated over a z-range of 5 mm towards the projection lens. By assuming that the allowable pixel size can only deviate by , where denotes the

in-plane pixel size, the effective meniscus region can be plotted for varying print head sizes and material surface tensions. It’s worth noting that the entirety of the meniscus can be used as demonstrated by the convex slicing algorithm, however the spatial resolution is dependent on the curvature and its relative location away from the optical axis. To investigate the theoretical defocusing of a projected image in the plane, the standard USAF test pattern was convolved at z = 0 mm, z = 3 mm and z = 5 mm. To investigate the effective reduction in resolution across the meniscus, a checkerboard pattern was computed at numerous regions between 0 - 5 mm. By comparing the relative height of the interface at location (x,y, z) to the corresponding pixel in the defocused checkboard array, the effective defocused pixel representation was generated across the entirety of the interface.

Derivation and modelling of capillary waves on the air-liquid boundary

During printing, a thin fluid volume of uncured material is created between the meniscus and the previously cured region, the height of which depends on the oxygen inhibition zone of the material and the z-translation of the meniscus. From lubrication theory, a thin fluid volume or film can be described under the assumption that the fluid depth is much shallower than the fluid’s extent. Under this assumption, the full Navier-Stokes equations can be simplified:

As the velocity at small length-scales is small compared to the viscous forces, the initial terms on the left hand-side are negligible as they are proportional to

. This approximation reduces the momentum equation to Furthermore,

as the thickness of the film is assumed to be small, the velocity perpendicular to the plane is negligible. For the case of an axisymmetric print head, the coordinate system is such that x denotes the vector in the radial direction, z denotes the vector normal to the meniscus, and y denotes the vector tangent to the radial direction, resulting in the following reduced momentum equations.

For athin-film under incompressible flow, the increase in volumetric flow rate in the positive x-direction is given by:

This must be balanced by the decrease in volumetric flow in the z-direction . By

assuming a non-slip condition at the previous printed interface and finite shear across the boundary, the horizonal velocity profile is given by:

Equating the volumetric flow rate yields,

In our case, the volume of air within the print head is acoustically driven, causing a variation of pressure and shear force along the surface of the meniscus which is proportional to the local air pressure and velocity. The pressure in a sound wave is given by

. where the velocity is in-phase with the pressure

where A and B depend on factors such as the compressibility of the air and amplitude of the wave. The pressure within the fluid can now be described by the following:

Inserting this into the above equation for the shear force and applying the assumption of small perturbations in the interface height h = h₀ + ε, the equation can be linearized as shown below:

If B is negligible, then the meniscus would only be affected by the pressure from the acoustic driver, and not the shear from the driver. Under this assumption, the above equation can be solved analytically and simplified to the following:

The homogenous solution to the above equation is of the form

where the constant s describes the relaxation of the disturbance given by . The

particular solution should also be of the form .

Therefore, substituting this in gives the particular solution of,

The time dependent solution to a small perturbation in the interface height E, can be determined by adding together the homogeneous and particular solutions resulting in an equation that describes the full solution of meniscus perturbation under acoustic sound waves,

This equation describes the time dependent solution to the interface height as a function of the acoustically driven perturbations of the interface, whereby the produced waves are added to waves caused by previous perturbations that decay exponentially in time. It’s worth noting that this solution can only accurately be applied for low frequency acoustic perturbations (like those used in this work), as the initial terms in the momentum equation have been assumed to be negligible. Under high frequency acoustic driving, the fluid element would need to change position much faster than what is captured by this model, in this instance the components and would be non-zero. Inserting this back into the equation for the

velocity in the x-direction, yields:

In the above equation, the constants describe the amplitudes of previous evolutions

of the wave, k is the wave number, K is the dimensionless wavenumber which is normalized against the capillary length is the driving frequency, y is the surface tension, p is the

density and A_p is the driving amplitude. Note that this approximate model of the interface dynamics does not take into account the streaming effects generated by the meniscus curvature nor the squeeze flow due to the translation of the air-liquid interface in the z- direction. The result from the image based de-wetting analysis indicates that the influx rate of material under acoustic stimulation is approximately an order of magnitude higher than under lubrication-driven flow. Therefore, we can approximate the material influx rate based on acoustics alone as a conservative estimate. Furthermore, to account for the curvature of the interface, the constant fluid depth h₀ is replaced by h(x) which describes the height of the meniscus as a function of the print head’s diameter.

Scaling laws for acoustically driven flows

To understand how fluid transport is affected by different material parameters, we can assume the interface height in an idealized case is given by

where q denotes the wavenumber and describes the amplitude of the wave. Under this

approximation, the pressure within the fluid is given by the atmospheric pressure, gravitational effects and capillary affects. For lubrication theory to hold, the relative height change of the interface is small compared to its depth, therefore the curvature of the interface can be approximated by The pressure difference between the crest and the

trough scales with in the capillary case and with pgΦ in the gravity-driven case. We

can therefore describe the ratio of gravitational to capillary effects as

whereby denotes a system where gravity dominates and

denotes a system where capillary effects dominate. Using this relationship, in conjunction with the generalized equation for velocity in the x-direction, we can derive a scaling relationship for the velocity U dependent on material parameters. By using a length scale of λ in the x-direction and h₀ in the z-direction, it can be shown that:

Where the wavelength λ is found by solving the dispersion relation for capillary waves, which relates the wave frequency (m) to the wavenumber (k) and is given by:

Effect of interface curvature on streaming flows

When acoustically driving the meniscus profile under low amplitude oscillations for increasing internal pressure states, we observed a dramatic increase in fluid flow below the interface when compared to a pseudo-level interface. We postulate that this enhanced fluid transport is driven by two key factors related to the meniscus curvature and an increase in available mass volume. Firstly, the streaming velocity below the meniscus can be written as a function of the parallel streaming velocity,

Where denotes the primary flow parallel to the meniscus, denotes the tangential vector

to the meniscus and describes the surface elevation of the static meniscus, whose solution

is given by the Y oung-Laplace equation. The value for the tangential velocity at the meniscus surface, is obtained through linear interpolation of the meniscus wave along the meniscus

at

Where k_n describes the eigen-wavenumber and the coefficient

where a₀ is the forcing acceleration, s is the interface symmetry and m is

the mode number in the y-direction. Substituting in the equation for the meniscus

streaming velocity can be written as:

Where and denote the horizontal and vertical unit vectors. Therefore, u_s is intrinsically

dependent on the interface profile

, which produces a periodic streaming profile anchored about the two nodal positions in the case where the meniscus profile is symmetric. The resulting streaming magnitude is therefore dependent on the Fourier spectrum of the static meniscus profile, wherein the flow profile is shaped by the entire wave spectrum rather than a single monochromatic wave. Therefore, for a given frequency and amplitude, the curvature defines a velocity excitation mode, whose magnitude changes dependent on the interface shape. In addition to the meniscus curvature, we also hypothesize that for an increasing meniscus profile beyond the extent of the print head the available material influx scales with:

Where K denotes the maximum extent of the interface from the print head edge. The value of Q will increase up until the point that Beyond this point the interface

keeps increasing in volume laterally, however the value of K does not substantially increase. We hypothesize that this lateral volume expansion is due to manufacturing inaccuracies in the print head, which result in lateral translation and rotation of the contact line producing slightly wider and obtuse meniscus than the diameter of the print head. This over pressurization results in three key changes that effect the efficacy of the interface to induce streaming. Firstly, as the volume of the meniscus increases, we obtain an effective amplitude reduction due to the increase in internal volume. Furthermore, the contact line rotation produces a positive bulged region, which limits material influx due to flow separation and destructive flow interactions. Finally, the ‘stiffness’ of the bubble in the x-direction decreases in comparison to the z-direction, resulting in both vertical and horizonal driving modes, reducing the effective efficiency.

Interface wetting model

The print rate in the method described herein may be primarily dependent on two key processing parameters, the responsiveness of the material to light and the rate at which new material can enter the printing interface. For the former, the polymerization kinetics are driven by the intensity of light, monomer concentration, oxygen inhibition region, photo absorber concentration and photo-initiator concentration. For the latter, the rate of material influx is driven primarily by the velocity of the interface in the z-direction and the frequency and amplitude of acoustic driving. However, an important criterion to meet is to ensure that, independent of the part geometry, the interface is completely saturated with new material. To predict this infill time for a given geometry we employ a computational approach based on the distance transform of the voxel array²¹, where the presence of geometry is defined as a ‘1’ and the absence of geometry is defined by ‘0’. We can, therefore, treat the ‘0’ regions in the voxel array as resin sources, which define the fluidic path length. For each voxel in the array the distance between a white pixel and the closest source is given by,

Therefore, the time to until the voxel is completely filled with new material is

approximately,

Where t represents the infill time is the magnitude of the distance between the voxel

and the closest source and represents a correction factor which depends on the

geometry and volume of the available source material. Additionally, two constraints are applied to the solution which depend on the object geometry and interface shape. The

first is that for a given voxel the search region for the closest source point cannot

exceed k, as k defines the printing surface. Source regions greater than k contain no material as they exist above the air-liquid meniscus. Secondly, a source point is only valid if the vector between the source and the voxel does not intersect the geometry. This is to

ensure that a minimum solution is not found which is blocked by neighbouring geometry. This approach is quite similar to voxel ray tracing, which is often used in computer graphics for modelling light transport. For example, let be the vector formed between and

whose distance is given by The origin of the vector be located at

the source , with a direction vector . therefore any point along the vector

its position is given by.

Let the bounding box of the voxel array, be given by and

- To determine if the ray intersects the voxel, we compute

the intersection points with the planes defining the voxel's surfaces. For each voxel face we compute the entrance and exit points of the ray:

The ray intersects the voxel if and only if the intervals for each axis overlap.

The intersection occurs if the maximum value among all values is less than or equal

to the minimum value among all t_exit values. If an intersection is found, its position can be calculated by using the value of t over the interval in which the intersection occurred.

Print speed prediction using interface wetting model

Using the interface wetting model, the fluidic path length and wetting time can be determined for representative slice planes. By repeating this approach for all object planes and taking the maximum value for each plane, the fluidic path length D_z, interface wetting t_z time and vertical print velocity V_z (independent of curing kinetics) can be generated over the entire object. Therefore, two independent solutions for an object’s print time can be created. Firstly, a conservative approach can be applied wherein the print speed is dependent on the minimum V_z value over the entire object. Alternatively, the print speed can be dynamically increased or decreased in a geometrically dependent way based on the local V_z of that layer.

EXAMPLE 9

An example of the process flow in the use of a convex slicing algorithm is shown in Figure 16. The Figure shows the process-flow diagram of the slicing algorithm illustrating key steps in both the determination of convex projections and reconstruction validation via

Jaccard Index .

EXAMPLE 10

A simulation was used to compare and contrast conventional top-down stereo-lithography (SLA) to the method proposed herein (also referred to as "DIP", or Dynamic Interface Printing) performed using a system based on vertical z-axis lens arrangement (of the kind shown in Figures 14-15) with and without acoustic modulation of the gas-resin interface. The data shows that DIP is indeed superior to conventional top-down SLA, and enables higher throughput fabrication. To analyse the effects of the curved interface and acoustic actuation on printing speed, printing material inflow was modelled using finite element analysis (FEA) software COMSOL Multiphysics 6.1. Resin ingress across printing structure was investigated for two competing printing schemes: the DIP and the conventional top-down stereo-lithography printing approach (SLA). We employ axial symmetry of the problem by utilizing 2D axisymmetric modelling domains to drastically reduce computational effort. The print head and printed structure are treated as impermeable solids and excluded from the modelling.

The Laminar Flow module is used to model the pressure and velocity field in the printing material (PEGDA) and air subdomains. Assuming incompressible Newtonian fluids, this module utilize the Navier-Stokes equations. A non-slip boundary condition is used on all the outer walls of the domains except the free surface and the meniscus. For initial conditions, velocity components are zero and a zero reference pressure is induced at the top boundary. The air properties were set at a density of 1.204 kg/m³ and a viscosity of 18.1 pPas. The PEGDA density was 1012 kg/m³. Viscosity and surface tension data for PEGDA can be found in the literature.

PEGDA-air interface and PEGDA free surface are simulated with the Moving Mesh module. The velocity and the normal stress boundary condition on the PEGDA-air interface are set as following:

In the formulas, indices 1 and 2 denote the PEGDA and the air phases respectively,

is the unit normal, outward from the PEGDA domain, and

is the surface gradient operator. The Moving Mesh interface enables spatial displacement of the corresponding domain boundaries in response to the fluid motion. It utilizes the arbitrary Lagrangian-Eulerian (ALE) formulation where the mesh grid mapping to the material domain enables solving a deforming Lagrangian-type systems [COMSOL Multiphysics Reference Manual, Version 6.1], The Navier-Stokes equations are solved within a moving frame, fully coupled with the mesh equations. The mesh velocity normal component thus matches the normal fluid velocity on the boundary. In the case of a free surface, the expressions can be simplified accordingly.

A preliminary study is conducted to establish the shape of the PEGDA-air meniscus. To do it we use a domain which has no printed structure, and the meniscus equilibrium shape is evaluated by running a time-dependent study with stationary boundary conditions (zero boundary displacement). In the subsequent analysis, the shape of the formed meniscus defines the profile of the printed structure.

To model the transient fluid ingress during printing, a dynamic study is conducted. As an initial state, the interface is considered compressed against the printed structure, forming a uniform 50 μm thick layer of fluid. This was chosen to improve initial computational stability of the solution, especially under acoustic excitation. Selected boundaries are translated downward (along the z-axis) to replicate the displacement of the print head during the printing process. While the print head is translated upwards in the experiment, the modeling set-up is inverted and the resin container with the printed structure is displaced down instead. The displacement is performed with a delay of 0.1s necessary for the computational model stabilization. In the acoustically driven case, the upper part of the air domain is harmonically actuated at /=100 Hz in addition to the displacement. The wall velocity has an amplitude of 10 mm/s and a delay of 0. Is, necessary for model stabilization.

The computational domain mesh utilizes a hybrid grid with triangular mesh elements in the bulk of the domain, complemented with a structural grid at the fluid ingress area and near nonslip boundaries. The mesh is finely resolved at the structure tip down to dmesh=8 μm and expands to in the bulk of the domain.

The air-fluid interface aligns with the printed structure surface at the start of the simulation. The deformation of the domain propels the meniscus detachment from the structure. The displacement of the meniscus centroid C is used with the printed structure of SD=10 mm. In the timeframe 0.1-0.96s, it translates downwards, following the boundary displacement. However, the fluid ingress along the structure causes the rebound of the meniscus and subsequent recovery. The rebound dynamics was used to evaluate the computational mesh where the half-sized mesh demonstrates practically identical dynamics of the meniscus.

Figure 17 shows the spatial tracking of a point at the centre of the gas-resin interface during a layer change. During a layer change the point initially translates down (as the layer change happens) followed by a rebound as fluid flows in across the interface causing the tracked point to move back up. Insets (a-d) show corresponding point tracking for conventional top- down SLA, DIP, and DIP with 40 Hz and 100 Hz acoustic modulation of the gas-resin interface. For each simulation configuration (a-d), the size of the printed structure was varied from 4 mm to 14 mm (for a print head diameter of 15 mm). That is, the structure size was from ~ 26% of the diameter to ~93% of the diameter.

Figure 17 shows the numerical prediction of the interface release dynamics for a 15 mm diameter print head with varying circular printed structures from 4 to 14 mm in diameter. Figure 17(a) shows the location of the central node of the interface as a function of time for Top-Down SLA, 17(b) shows the location of the central node of the interface as a function of time for Dynamic Interface Printing (DIP) without acoustic excitation, 17(c) relates to the location of the central node of the interface as a function of time for Dynamic Interface Printing (DIP) with acoustic excitation at a frequency of 40 Hz, and 17(d) the location of the central node of the interface as a function of time for Dynamic Interface Printing (DIP) with acoustic excitation at a frequency of 100 Hz. For (c-d), the transparent plots denote the oscillatory interface height, with the solid lines representing the moving average across a single excitation period. This simulation shows that the proposed method (DIP) produces a faster inflow of material (due to quicker rebound of tracked point) and is less impacted by structure size relative to conventional top-down SLA.

The model was used to simulate 2D fluid velocity contour plots during a layer change. 2D plots (not shown) were provided in form of a time series of the velocity magnitude during the duration of the layer change for conventional top-down SLA and DIP without acoustics, obtained for a structure size of from 4 mm to 14 mm. The numerical prediction of the velocity magnitude for a top-down SLA and dynamic interface printing with a 15 mm diameter print head was produced. The simulations were conducted to produce (i) a time sequence velocity fields were produced for top-down SLA from the time of initial displacement (t = 100ms) to central interface release (t = 190 ms) for a 4 mm diameter printed structure, (ii) the time sequence velocity field for top-down SLA from the time of initial displacement (t = 100ms) to central interface release (t = 880 ms) for a 14 mm diameter printed structure, (iii) the time sequence velocity field for dynamic interface printing without acoustics from the time of displacement (t = 100ms) to central interface release (t = 190 ms) for a 4 mm diameter printed structure, and (iv) the time sequence velocity field for dynamic interface printing without acoustics from the time of displacement (t = 100ms) to central interface release (t = 320 ms) for a 14 mm diameter printed structure.

Each of the simulated plots illustrate that the average and maximum velocity of material flowing across the gas-resin interface is greater for DIP relative to conventional top-down SLA. The simulated data also demonstrate an intensive flow in the interface layer adjacent to the structure. The acoustic actuation was found to induce pressure variation in the air domain with an amplitude of about 20 Pa. This pressure oscillation induces capillary-gravity waves at the liquid-air interface.

Corresponding simulation plots (not shown) were also obtained for a DIP system using acoustic modulation at 40 Hz and 100 Hz. The simulation was used to produce a numerical prediction of the velocity magnitude for acoustically driven dynamic interface printing using a 15 mm diameter print head. The simulations were conducted to produce (i) the time- sequence velocity field for acoustically driven dynamic interface printing at a frequency of 40 Hz and a structural diameter of 4 mm, with time sequence spanning from the initial displacement (t = 100 ms) to the central interface release (t = 150 ms), (ii) the time-sequence velocity field for acoustically driven dynamic interface printing at a frequency of 40 Hz and a structural diameter of 14 mm. The time sequence spans from the initial displacement (t = 100 ms) to the central interface release (t = 270 ms), (iii) the time-sequence velocity field for acoustically driven dynamic interface printing at a frequency of 100 Hz and a structural diameter of 4 mm, with time sequence spanning from the initial displacement (t = 100 ms) to the central interface release (t = 150 ms), and (iv) the time-sequence velocity field for acoustically driven dynamic interface printing at a frequency of 100 Hz and a structural diameter of 14 mm, with time sequence spanning from the initial displacement (t = 100 ms) to the central interface release (t = 290 ms). The simulated data demonstrate an intensive flow in the interface layer adjacent to the structure. The acoustic actuation was found to induce pressure variation in the air domain with an amplitude of about 20 Pa. This pressure oscillation induces capillary-gravity waves at the liquid-air interface. The data demonstrates resulting fluid streaming along the acoustically actuated fluid-gas interface, ultimately accelerating the resin influx. The resin ingress in turn induces recirculating flow in adjacent gas domain. Acoustics actuation subsequently reduces the time required for complete wetting of the structure.

Figure 17 shows simulated plots of the average velocity below the interface during a layer change as a function of time, for each printing technique and object size configuration. This shows that the magnitude of velocity below the interface is higher for DIP and the grouping (spread) of velocity ranges is tighter as the object diameter increases. The second plot shows the average velocity below the interface for each structure size and printing technique. The data shows that once again DIP performs better than conventional top-down SLA under all conditions, and is less sensitive to structure size when compared to top-down SLA.

Specifically, Figure 18 presents the numerical prediction of the average inflow fluid velocity for a 15 mm diameter print head with varying circular printed structures ranging from 4 to 14 mm in diameter. Figure 18(a) relates to the radial magnitude of the average fluid velocity (llwll) for increasing structural diameter in top-down SLA, 18(b) shows the radial magnitude of the average fluid velocity (llwll) for increasing structural diameter in DIP without acoustics, 18(c) relates to the radial magnitude of the average fluid velocity (llwll) for increasing structural diameter in DIP with 40 Hz acoustic driving, 18(d) relates to the radial magnitude of the average fluid velocity (llwll) for increasing structural diameter in DIP with 100 Hz acoustic driving, and 18(e) shows the peak average fluid velocity for each printing technique as a function of structural diameter.

Simulated data of Figure 19 shows acoustic mode interaction with the underlying structure during acoustic modulation at 40Hz and 100 Hz. This shows how the interface can be used to trap material at the nodal locations. The Figure plots the oscillation modes of the acoustically actuated meniscus. This visualization demonstrates the complex interactions between meniscus shape, print head size and printed structure size which governs the oscillation intensity and eventually the fluid ingress. While this study is limited to an axisymmetric case, more complex spatial modes might be observed in 3D system. These findings underline the importance of multimodal surface actuation to ensure efficient resin influx.

Specifically, Figure 19 shows the numerical prediction of structural-modal interaction, with Figure 19(a) showing meniscus resonance mode shapes (indicated in white solid lines) over a single period at 40 Hz acoustic driving for structures with diameters of 10, 12, and 14 mm, 19(b) shows meniscus resonance mode shapes (indicated in white solid lines) over a single period at 100 Hz acoustic driving for structures with diameters of 10, 12, and 14 mm. In the Figure, the white arrows indicate the locations of the nodal locations of the induced capillary wave.

As used herein, the term “about”, in the context of numerical values, typically means +/-5% of the stated value, more typically +/-4% of the stated value, more typically +/-3% of the stated value, more typically, +/-2% of the stated value, even more typically +/-!% of the stated value, and even more typically +/- 0.5% of the stated value. Throughout this specification and the claims which follow, unless the context requires otherwise, the word ‘comprise’, and variations such as ‘comprises’ and ‘comprising’, will be understood to imply the inclusion of a stated integer or step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps.

The reference in this specification to any prior publication (or information derived from it), or to any matter which is known, is not, and should not be taken as an acknowledgment or admission or any form of suggestion that that prior publication (or information derived from it) or known matter forms part of the common general knowledge in the field of endeavour to which this specification relates.

Claims

THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS

1. A method of forming a 3D object, the method comprising: providing a photo-curable resin, providing a print head for transmitting curing radiation to the photo-curable resin, the print head having a cavity containing gas, introducing the print head into the resin to form a submerged gas-resin interface between the gas and the resin, wherein said gas-resin interface is constrained to the print head and defines a printing surface, projecting curing radiation on the submerged gas-resin interface to promote curing of the resin at the printing surface, promoting relative movement between the gas-resin interface and the resin to produce the 3D object.

2. The method of claim 1, wherein the submerged gas-resin interface is provided by pressurising gas within the cavity of the print head.

3. The method of claim 1 or 2, wherein the gas comprises oxygen.

4. The method of any one of claims 1-3, wherein the curing radiation comprises cross- sectional images of the 3D object.

5. The method of any one of claims 1-4, wherein the gas-resin interface has a convex shape.

6. The method of claim 5, wherein the curing radiation comprises cross-sectional images of the 3D object, said cross-sectional images representing convex cross-sections of the 3D object that are conform to the gas-resin interface.

7. The method of any one of claims 1-6, wherein projecting curing radiation through the submerged gas-resin interface comprises focusing the curing radiation on the gas-resin interface, or on the resin side of the gas-resin interface.

8. The method of any one of claims 1-7, wherein relative movement between the gas- resin interface and the resin is promoted by moving the print head relative to the resin.

9. The method of any one of claims 1-8, wherein the curing radiation is projected along a vertical axis.

10. The method of any one of claims 1-9, comprising changing the pressure of the gas in the cavity of the print head to modulate the extension of the gas-resin interface.

11. The method of any one of claims 1-10, wherein relative translation between the gas- resin interface and the resin is promoted by withdrawing the print head along a vertical direction.

12. The method of claim 11, wherein the print head is withdrawn at a withdrawal speed of from about Iμm/s to about 5 mm/s.

13. The method of any one of claims 1-12, wherein the curing radiation has a wavelength between about 190 nm and about 2,000 nm.

14. The method of any one of claims 1-13, wherein the curing radiation delivers an optical dose at the printing surface of between about 0.1 mW/cm² and about 1.6- 10¹⁰ mW/cm².

15. The method of any one of claims 1-14, wherein the photo-curable resin comprises an acrylate-based resin, a styrene-based resin, or a thiol-based resin.

16. The method of any one of claims 1-15, wherein the photo-curable resin comprises a hydrogel precursor.

17. The method of any one of claims 1-16, wherein the photocurable resin comprises polyethylene glycol diacrylate (PEGDA), gelatin methacryloyl (GelMA), or hexanediol diacrylate (HDDA).

18. The method of any one of claims 1-17, wherein the photo-curable resin comprises viable cells.

19. The method of any one of claims 1-18, further comprising a step of transmitting acoustic waves to the submerged gas-resin interface.

20. The method of claim 19, wherein the acoustic waves are transmitted to the submerged gas-resin interface by being introduced into the cavity of the print head, by being generated within the resin volume, or by vibrating the print head.

21. The method of claim 19 or 20, wherein the acoustic waves have a frequency from 1 Hz to 100 kHz and an amplitude in terms of pressure range from 0.1 Pa to 5kPa.

22. A system for forming a 3D object, the system comprising a print head for transmitting curing radiation to a photo-curable resin, the print head having a cavity containing gas such that, when the print head is introduced into photo-curable resin, said gas promotes formation of a gas-resin interface constrained to the print head.

23. The system of claim 22, wherein the print head is transparent to curing radiation projected vertically.

24. The system of claim 22 or 23, comprising one or more moveable stage(s) for promoting, when the print head is introduced into a photo-curable resin, relative movement between the gas-resin interface and the resin.

25. The system of any one of claims 22-24, wherein the print head is moveable along a vertical axis.

26. The system of any one of claims 22-25, further comprising a source of curing radiation.

27. The system of claim 26, wherein the print head comprises the source of curing radiation.

28. The system of any one of claims 22-27, wherein the print head has an internal cavity with an opening at a bottom side of the print head, such that when the print head is introduced into photo-curable resin and said cavity is fdled with pressurised gas, the gas-resin interface that forms has a convex shape protruding downward from the opening.

29. The system of any one of claims 22-28, wherein print head has a tubular shape with an opening at a bottom end and a radiation transparent window at a top end.

30. The system of any one of claims 22-29, wherein the print head comprises a plurality of cavities such that, when the print head is introduced into photo-curable resin, the gas promotes formation of a plurality of gas-resin interfaces constrained to the print head.

31. The system of any one of claims 22-30, further comprising an acoustic wave generator for transmitting acoustic waves to the gas-resin interface.

32. The system of claim 31, wherein said acoustic wave generator is an electroacoustic device selected from a voice coil actuator, a piezoelectric actuator, a magneto-strictive actuator, and a capacitive transducer.