Large scale 3D extrusion printing

Abstract

A method for moving a material includes: causing a first fluid to flow axially, the first fluid being characterized by inertial forces dominating viscous forces; causing a second fluid to flow axially, the first fluid and the second fluid being miscible with each other and having an interface region between the first fluid and the second fluid; allowing a reaction to create reaction products in the interface region, the reaction products mitigating turbulent mixing between the first fluid and the second fluid.

Description

[0001] Related application citation

[0002] This application relates to and claims priority to U.S. Application No. 62 / 987,584, filed March 10, 2020, entitled “Large Scale 3D Extrusion Printing,” the entire contents and disclosure of which are incorporated herein by reference. For the purposes of the United States, this application claims the benefit of 35 USC 119 relating to U.S. Application No. 62 / 987,584, filed March 10, 2020, entitled “Large Scale 3D Extrusion Printing.” Technical Field

[0003] This invention relates to 3D extrusion printing of structures. Specific embodiments provide a method and apparatus for 3D extrusion printing of hydrogel tubing, which can be used in the medical field or various other fields. Background Technology

[0004] Hydrogels are versatile materials that typically exhibit high biocompatibility due to their high water content, low toxicity, and antifouling properties. Their relatively low cost, ease of use, and inherent biodegradability have encouraged their use in small-scale applications such as wound healing, cell transplantation, and delivery of bioactive agents. However, the use of hydrogels in large-scale medical applications is limited by structural inhomogeneities during gelation and the poor mechanical strength of hydrogel structures resulting from the deposition process in conventional 3D bioprinting. One particularly interesting, but not limiting, application of large-scale hydrogel structures is in medical procedures involving the delivery of blood outside the human body, as the antifouling properties of natural polymer hydrogels may limit the interaction between blood and the material.

[0005] Extracorporeal circulation is a medical intervention in which blood is transported from a patient's body through plastic tubing (extracorporeal circulation, ECC) and can then be used for other procedures such as hemodialysis, extracorporeal membrane oxygenation (ECMO), and extracorporeal circulation surgery. Currently, the most commonly used materials for ECCs are silicone, polyvinyl chloride (PVC), and polyurethane (PU); however, despite their widespread use, blood has been shown to interact with the surfaces of these synthetic tubings, leading to protein and platelet deposition, which can result in clot formation and inflammatory responses when the blood is reintroduced into the patient. The inflammatory state in patients can increase with subsequent dialysis treatment, leading to chronic inflammation. Due to this tendency for clot formation and inflammatory responses, these patients are often treated with high doses of potentially harmful medications (such as anticoagulants) to compensate for the limitations of ECC materials. Surface modification of conventional plastic ECC tubing to make the material more biocompatible is a promising approach. However, to date, the availability of cost-effective, truly antithrombotic surface coatings has hindered the commercial application of this surface modification technology. To enable the medical community to utilize the biocompatibility and biodegradability of hydrogels at the ECC scale, there is a general need for devices and methods that can robustly and scalably create strong hydrogel structures (such as ECC tubes) with tunable dimensions.

[0006] Some complex hydrogel structures have been constructed by depositing continuous filaments from a 3D bioprinter. These hydrogel filaments have a maximum outer diameter of D. o Printed with a printhead of approximately 400 μm, the hydrogels form at a rate of about 4–10 mm per second (see Yong He et al., Research on the printability of hydrogels in 3D bioprinting. Scientific Reports, 6:29977EP–, July 2016). In terms of hydrodynamic stability, this relatively slow printing speed and relatively small printhead diameter ensure Reynolds numbers (Re) on the order of Re ~1 – see equation (11) below. This slow deposition process and the resulting material integrity generally hinder the applicability of these hydrogel structures in practical applications. Furthermore, some of these hydrogel structures are unsuitable for practical use due to poor mechanical strength, limited dehydration, and limited long-term performance.

[0007] The foregoing examples and related limitations of the related art are intended for illustrative purposes and not for exclusivity. Further limitations of the related art will become apparent to those skilled in the art upon reading the specification and studying the accompanying drawings. Summary of the Invention

[0008] The following embodiments and aspects thereof are described and illustrated in conjunction with systems, tools, and methods intended to be exemplary and illustrative rather than limiting. In various embodiments, one or more of the aforementioned problems have been mitigated or eliminated, while other embodiments involve other improvements.

[0009] One aspect of the invention provides a method for 3D extrusion printing a structure (such as a pipe) by stratifying two fluids flowing in a pipe, wherein the composition of the fluids has been selected such that it causes localized changes in rheological properties at the interface between the liquids, allowing the flow rates that would otherwise result in mixing to stably produce a material such as a pipe.

[0010] The layering of liquids at their interfaces through gelation rapidly produces tough and environmentally friendly hydrogel tubing with excellent blood compatibility. Natural polymers (such as alginate) are particularly suitable for in-situ layering because they react with salt solutions (e.g., those containing polyvalent cations such as Ca). 2+ When in contact with salt solutions (such as salts), they gel relatively quickly.

[0011] One aspect of the present invention provides a method for large-scale 3D extrusion printing of biocompatible materials for sculpting.

[0012] Various aspects of the present invention provide methods and apparatus for producing hydrogel tubing (e.g., blood-compatible hydrogel tubing), comprising the flow of a generalized miscible, layered fluid, wherein at least one fluid initially flows under inertial conditions, and wherein chemical components are incorporated into local rheological properties—for example, wherein the chemical composition of reactants and gelation reactions result in localized changes in the rheological properties of the moving material. This incorporation has enabled the scaling up of the size and speed of currently known 3D coaxial extrusion bioprinters to produce hydrogel tubing (e.g., biocompatible hydrogel tubing) at speeds greater than 3 cm / s, which is significantly greater than the speeds of currently known 3D coaxial extrusion bioprinters.

[0013] The hydrogel products produced through various aspects of the present invention are potential alternatives to many plastics (in contrast to currently known extruded biomaterials, which exhibit poor mechanical strength and dehydration properties).

[0014] Materials that can both enhance the strength of the printed structure and provide a hydrophobic coating to limit dehydration can be added to the flow.

[0015] Regarding the extrusion of tubing (e.g., medical tubing), the dimensions in some embodiments suitable for medical use (e.g., in ECC applications) can be in the range of 3.2-12.7 mm inner diameter and can be used for several hours in ECC applications before being disposed of.

[0016] With the combination of biodegradable materials providing hydrophobic coatings, the methods and apparatus according to various aspects of the present invention can rapidly produce tubing with mechanical properties comparable to conventional plastics, as well as enhanced single-use and blood compatibility compared to conventional plastics.

[0017] Fiber materials can be used to reinforce hydrogel pipes formed by the methods and devices described herein.

[0018] One aspect of the present invention provides a method for moving materials to create reaction products. The method includes: flowing a first fluid axially, the first fluid being characterized in that inertial forces dominate the viscous forces of the first fluid; flowing a second fluid axially, the first fluid and the second fluid being miscible with each other and having an interface region between the first fluid and the second fluid; allowing a reaction to create reaction products in the interface region, the reaction products mitigating turbulent mixing between the first fluid and the second fluid.

[0019] The first fluid and the second fluid may have a contact area at the upstream end of the interface region, and the first fluid and the second fluid are in contact with each other at the contact area.

[0020] The inertial force of the first fluid can be greater than the viscous force of the first fluid, such that the Reynolds number of the first fluid at the axial position corresponding to the upstream range of the interface region is greater than 100.

[0021] The inertial force of the first fluid can be greater than the viscous force of the first fluid, such that the Reynolds number of the first fluid at the axial position corresponding to the upstream range of the interface region is greater than 500.

[0022] The second fluid is characterized in that inertial force dominates the viscous force of the second fluid. The inertial force of the second fluid can be greater than the viscous force of the second fluid, such that the Reynolds number of the second fluid at the axial position corresponding to the upstream range of the interface region is greater than 100. The inertial force of the second fluid can be greater than the viscous force of the second fluid, such that the Reynolds number of the second fluid at the axial position corresponding to the upstream range of the interface region is greater than 500.

[0023] The flow of one or more of the first fluid and the second fluid can be turbulent flow.

[0024] The characteristics of the reaction in the interface area can be expressed when the Damcole value is less than 10. 9 The characteristics of the reaction in this interface region can be seen in the Damcohl value of 10-10. 6 The reaction characteristics in this interface region can be described by the Damcoulette value in the range of 100-10. 5 Within the range.

[0025] The reaction products can flow axially, wherein the local Reynolds number of the reaction products in the interface region can be less than 100. The reaction products can flow axially, wherein the local Reynolds number of the reaction products in the interface region can be less than 20.

[0026] The method may include modifying one or more of the first fluid inlet velocity and the second fluid inlet velocity to control the cross-sectional dimensions (e.g., diameter) of the reaction products.

[0027] In this interfacial region, the rate of change of rheological properties associated with the reaction can be greater than the advection rates of the first and second fluids. In this interfacial region, the reaction may lead to a localized rheological property change, wherein the ratio of local viscous force to local inertial force in the interfacial region is less than about 1.25. In this interfacial region, the reaction may lead to a localized rheological property change, wherein the viscous force in the interfacial region is less than the inertial force in the interfacial region.

[0028] The first fluid can be a solution of the first reactant, and the second fluid can be a solution of the second reactant. The first reactant can be a polyvalent cation, the second reactant can be an alginate, and the reaction product can be a hydrogel. The concentration ratio of the first reactant to the second reactant can be less than or equal to 4. The concentration ratio of the first reactant to the second reactant can be greater than or equal to 0.5.

[0029] The first fluid flow may have a rectangular shape in a cross-section spanning the axial direction. The second fluid flow may also have a rectangular shape in a cross-section spanning the axial direction.

[0030] Another aspect of the invention provides a method for moving materials to create reaction products. The method includes: flowing a first fluid axially; flowing a second fluid axially, the first fluid and the second fluid having an interface region; wherein the first fluid has a Reynolds number greater than 500 at an axial position corresponding to the upstream extent of the interface region; and allowing a reaction to occur between the first fluid and the second fluid in the interface region, whereby the reaction products have a local Reynolds number less than 100 in the interface region.

[0031] The first fluid and the second fluid may have a contact area at the upstream end of the interface region, and the first fluid and the second fluid may come into contact with each other at the contact area.

[0032] The first fluid and the second fluid are miscible with each other.

[0033] The Reynolds number of the first fluid at the axial position corresponding to the upstream range of the interface region can be greater than 1000.

[0034] The Reynolds number of the second fluid at the axial position corresponding to the upstream range of the interface region can be greater than 500. The Reynolds number of the second fluid at the axial position corresponding to the upstream range of the interface region can be greater than 1000.

[0035] The local Reynolds number of the reaction products in the interfacial region can be less than 10.

[0036] The characteristics of the reaction in the interface area can be seen in the Damcoulette value of 10-10. 6 The reaction characteristics in this interface region can be described by the Damcoulette value in the range of 100-10. 5 Within the range.

[0037] The flow of one or more of the first fluid and the second fluid can be turbulent flow.

[0038] The method may include modifying one or more of the first fluid inlet velocity and the second fluid inlet velocity to control the cross-sectional dimensions (e.g., diameter) of the reaction products.

[0039] In this interface region, the rate of change of rheological properties associated with the reaction can be greater than the advection rate between the first fluid and the second fluid. In this interface region, the reaction may lead to a localized rheological property change, wherein the ratio of local viscous force to positional inertial force in the interface region is less than about 1.25. In this interface region, the reaction may lead to a localized rheological property change, wherein the viscous force in the interface region is less than the inertial force in the interface region.

[0040] The first fluid can be a solution of the first reactant, and the second fluid can be a solution of the second reactant. The first reactant can be a polyvalent cation, the second reactant can be an alginate, and the reaction product can be a hydrogel. The concentration ratio of the first reactant to the second reactant can be less than or equal to 4. The concentration ratio of the first reactant to the second reactant can be greater than or equal to 0.5.

[0041] The first fluid flow may have a rectangular shape in a cross-section spanning the axial direction. The second fluid flow may also have a rectangular shape in a cross-section spanning the axial direction.

[0042] Another aspect of the present invention provides a method for moving a material. The method includes: providing a first fluid flowing axially; providing a second fluid flowing axially, the first fluid and the second fluid being miscible and having an interface region therebetween; allowing a reaction to occur in the interface region, thereby creating locally non-mixing conditions through the reaction, thereby reducing mixing between the first fluid and the second fluid.

[0043] Allowing a reaction in the interface region may include generating a reaction product in the interface region that reduces mixing between the first fluid and the second fluid. Allowing a reaction in the interface region may include providing a state change of at least one of the first fluid and the second fluid in the interface region that reduces mixing between the first fluid and the second fluid.

[0044] Another aspect of the present invention provides a method for moving a material along an axial direction. The method includes: providing a first miscible fluid flowing along an axial direction; providing a second miscible fluid flowing along an axial direction, the first fluid and the second fluid having an interface region; and providing the properties or composition of the first miscible fluid to react with the second miscible fluid in the interface region, thereby reducing the local Reynolds number in the interface region to below 100; wherein the Reynolds number of the first fluid and the second fluid at an axial position corresponding to the upstream extent of the interface region is greater than 500.

[0045] Another aspect of the present invention provides a method for moving a material. The method includes: flowing a first fluid axially; flowing a second fluid axially, the first fluid and the second fluid having an interface region between them, and the first fluid and the second fluid flowing under miscible conditions; and reacting the first fluid and the second fluid to create local immiscibility of the first fluid and the second fluid in the interface region.

[0046] Another aspect of the present invention provides a method for moving a material. The method includes: causing a first fluid to flow axially; causing a second fluid to flow axially, the first fluid and the second fluid having an interface region between them; causing the first fluid and the second fluid to react in the interface region, thereby generating a local Reynolds number of less than 100 in the interface region; wherein the Reynolds number of the first fluid and the second fluid at an axial position corresponding to the upstream extent of the interface region is greater than 500.

[0047] Another aspect of the present invention provides a method for moving a material. The method includes: causing a first fluid to flow axially; causing a second fluid to flow axially, the first fluid and the second fluid having an interface region; and allowing a reaction to occur between the first fluid and the second fluid in the interface region; wherein the first fluid and the second fluid have a Reynolds number greater than 500 at an axial position corresponding to the upstream extent of the interface region; causing the first fluid and the second fluid to react produces a local Reynolds number less than 100 in the interface region; and the reaction between the first fluid and the second fluid has a value between 10⁻¹⁰ and 10⁻¹⁰. 6 The Damköhler value within the range.

[0048] Another aspect of the invention provides a method for generating (e.g., extrusion) a reaction product according to any of the methods described herein.

[0049] In addition to the exemplary aspects and embodiments described above, other aspects and embodiments will become apparent from the accompanying drawings and from studying the following detailed description. Attached Figure Description

[0050] Exemplary embodiments are illustrated in the accompanying drawings. The embodiments and drawings disclosed herein are intended to be illustrative rather than restrictive.

[0051] Figure 1A This is a schematic diagram of a method and apparatus for 3D extrusion of a structure (e.g., hydrogel tubing) formed using multiple flowing fluid inputs, according to a specific embodiment. Figure 1B-1E It shows Figure 1A The device has various possible (but not limiting) cross sections in a plane that is generally perpendicular to the flow / extrusion direction.

[0052] Figures 2A-2D It shows Figure 1A Various simulation results were obtained using a simulation version of the device with non-reactive fluids.

[0053] Figure 3A It shows about Figure 1A The stability of the device using the reaction fluid as a function of the Peckley (Pe) number and the Damköhler (Da) number in multiple simulation cases. Figure 3B Multiple Figure 3A A series of representative snapshots of the simulated concentration field. Figure 3C Expanded Figure 3A The simulation range was defined, and stability was examined as a function of Da and the velocity ratio u1 / u2 at a fixed Pe = 164 to understand... Figure 3A The simulation is sensitive to inlet conditions.

[0054] Figure 4A It shows in Figure 1A The spatiotemporal plot of the simulated use of the reactive fluid, observed at a specific cross-sectional location of the device, illustrates the dynamic unmixed conditions. Figure 4B It shows from Figure 4A A snapshot taken from a portion of the spatiotemporal graph at multiple time intervals.

[0055] Figure 5A It shows the use of Figure 1A Experimental setup of the equipment. Figure 5B , 5C 5D demonstrates the use of Figure 5A Settings and Figure 1AThe various results and conditions of the equipment illustrate the conditions corresponding to hydrodynamic stability. Figure 6 It shows the relationship with Figure 1A The experimental data related to the equipment indicate that the shear stress of the reaction products is a non-monotonic function of the reactant concentration ratio.

[0056] Figures 7A-7D It shows the use of Figure 1A The equipment consists of alginate ( Figure 7A ), with nanoscale fiber additives (especially nanofibrillated cellulose (NFC)) Figure 7B Alginate, with micron-sized fiber additives (especially rhythmically oxidized Northern Bleached Cork Kraft Paper (NBSK) cellulose fibers) Figure 7C Alginate and millimeter-scale fiber additives (especially NBSK cellulose fibers) Figure 7D Examples of air-dried hydrogel tubing made from alginate.

[0057] Figure 8A It shows the use of Figure 1A The velocity field and outer diameter D of the hydrogel tubing of the equipment o Experimental measurements (using a particle image velocimeter). Figure 8B In the context of Figure 8A Simulation under the same conditions. Figure 8C and 8D The following are examples of reactions at different reaction times: Figure 1A The cross-section of the alginate tube (reaction product) recovered by the equipment. Figure 8D The reaction time of the tube shown is... Figure 8C The length. Figure 8E It shows the use of Figure 1A The hydraulic performance of the hydrogel tubing extruded by the equipment for the flow rate (Q) range.

[0058] Figure 9A This is a schematic diagram of an apparatus for 3D extrusion of a structure (e.g., a hydrogel structure) formed using multiple (e.g., 3) flowing fluid inputs, according to a specific embodiment. Figure 9B yes Figure 9A A magnified view of the flow of the equipment.

[0059] Figure 10A and 10B (Collectively referred to as Figure 10) illustrates the process for producing fiber-reinforced hydrogel tubing. Figure 9A The equipment.

[0060] Figure 11A The tangential and axial stress-strain curves of hydrogel tubing extruded using the equipment shown in Figure 10 are illustrated using a Dynamic Mechanical Analyzer (DMA). Figure 11B It shows that in such Figure 11AThe effect of alginate (0.75% (w / w) and 1.5% (w / w)) on the Young modulus of hydrogel tubes (reaction products) under the same experimental conditions and rate ratios (u3 / u2) shown. Figure 11C The effect of the velocity ratio (outer fluid to inner fluid) u3 / u2 on the distribution of fiber orientation ζ in the reaction products of the device in Figure 10 is depicted. Figure 11D The apparatus 110 shown in Figure 10 uses 1.5% (w / w) and 1% (w / w) NBSK pulp fibers (such as intermediate fluid 116) and 1% (w / w) Ca 2+ Stress-strain curves of alginate (A) tubing 120 produced by internal and external fluids with various velocity ratios u3 / u2. Figure 11E The elastic modulus of the reaction products with fiber reinforcement (shaded by diagonal lines) and without fiber reinforcement (shaded by dots) are shown at different speed ratios u3 / u2.

[0061] Figure 12A This indicates that the adsorption of pro-inflammatory complement proteins, platelet adhesion, and erythrocyte hemolysis are important markers of the biocompatibility of the material with whole blood. Figure 12B This demonstrates how the inventors tested the extruded hydrogel tubing under ECC-like conditions (using...). Figure 1A The experimental setup for the compatibility of blood with alginate as the internal fluid and CaCl2 and MgCl2 as the external fluids (equipment). Specifically, Figure 12B (i)-(ii) show the PVC pipe before and after cultivation, while Figure 12B (iii)-(iv) show the hydrogel tubing formed using device 10 before and after cultivation. Figure 12C It shows in Figure 12B Platelet deposition on the material surface of each tube section. Figure 12D This shows the effect of pro-inflammatory complement protein C3 after whole blood exposure. Figure 12B Deposits on the inner walls of each pipe section.

[0062] Figure 13A and 13B (Collectively referred to as FIG13) shows a cross-section of a planar extrusion apparatus, demonstrating that the operating principles of the invention described herein can be extended to different geometries.

[0063] Figure 14A and 14B (Collectively referred to as Figure 14) illustrates the usage Figure 1A The experiment conducted on the equipment investigated the effect of changes in volumetric flow rate on the corresponding outer diameter of the reaction products. Detailed Implementation

[0064] Throughout the following description, specific details are set forth in order to provide a more thorough understanding to those skilled in the art. However, well-known elements may not have been shown or described in detail to avoid unnecessarily obscuring this disclosure. Therefore, the descriptions and figures shown are intended to be illustrative rather than restrictive.

[0065] Slow viscous flow of miscible stratified fluids is a classic problem in fluid mechanics. When placed within narrow channels or pipes, these flows do not mix significantly, due to the reversibility of the steady-state flow field when the stress state is dominated by viscous shear, i.e., within the Re→0 limit. When the miscible stratified fluid is a Newtonian fluid, the fluids typically mix in the presence of inertia. That is, two miscible Newtonian fluids tend to mix, especially at higher flow rates.

[0066] By initiating or allowing a reaction (e.g., crosslinking of polymers) between two stratified fluids (Newtonian or non-Newtonian fluids), local conditions can be created at the interface region between the fluids, where these local conditions inhibit or prevent mixing of the fluids even at medium to high flow rates. The inventors have identified local conditions that can be created (e.g., through reactions) where the yield stress (i.e., the strength of the reaction products) associated with the reaction between the moving fluids exceeds the inertial forces (i.e., viscous and inertial forces) that tend to cause mixing of the moving fluids, thereby preventing or mitigating the mixing of other miscible fluids. The inventors have identified one possible (but not limiting) reaction for creating such conditions as an in-situ (i.e., within the flow) gelation reaction involving one or two fluids. Reactions other than gelation can also create local conditions where the yield stress associated with the reaction between the moving fluids exceeds the inertial forces that tend to cause mixing of the moving fluids.

[0067] Figure 1A This is a schematic diagram of an apparatus 10 for three-dimensional (3D) extrusion of a structure 20 (e.g., hydrogel tube 20) formed using multiple flowing fluid inputs 12, 16, according to a specific embodiment. Throughout this document, the term extrusion and its various derivatives are used to describe the various apparatuses, methods, and reaction products disclosed and / or claimed herein, because the term is used in multiple documents in the field (i.e., where multiple flows are introduced near each other to create reaction products). The term should be understood and interpreted in an illustrative sense, rather than in the sense of classical extrusion apparatus and methods, where material is forced through a die with a known cross-section to produce a product with a constant cross-section. The extruded structure 20 can be a reaction product of the flowing fluids 12, 16 in the apparatus 10. Figure 1AThe illustration is a cross-sectional view taken in a plane approximately parallel to the fluid flow (extrusion) direction indicated by arrow g. The cross-sectional geometry of the device 10 (and the corresponding stratified fluids 12, 16) taken in a transverse plane perpendicular to the flow / extrusion direction g can influence the shape of the resulting extrusion structure 20. There are [missing information - likely related to the presence of ... Figure 1A The device 10 conveys stratified fluids 12 and 16 in multiple possible geometries. In the embodiments and experiments described herein, fluids 12 and 16 are as follows: Figure 1A-1C As shown, an inner flow 12 (having a generally circular cross-section) and one or more outer flows 16A, 16B (collectively referred to as outer flows 16, having a generally annular cross-section) are arranged around the inner cylindrical flow 12. These flows 12, 16 can be created, for example, by pipes or conduits of appropriate shape that provide these flow geometries.

[0068] This geometry is not restrictive. Other cross-sectional geometries are also possible. In some applications, the cross-sections of various flows 12, 16 can be non-circular and non-annular. For example, one or more flows 12, 16 can have an elliptical cross-sectional geometry (e.g., Figure 1D In some applications, the stratified miscible fluids 12, 16 can be arranged such that the fluids come into contact without internal or external flow. For example, the two fluids can be introduced into a cylindrical pipe such that each fluid 12, 16 occupies an equal portion of the pipe's cross-sectional area (e.g., Figure 1E The transverse geometry of the flows 12 and 16 can be used to control the shape of the resulting extruded structure 20. For example, the flowing fluids 12 and 16 may have an elliptical cross-sectional geometry (e.g., Figure 1D In the case of extrusion structure 20, the extrusion structure 20 may include a hydrogel tube 20 having an elliptical cross-sectional geometry.

[0069] Given a specific cross-sectional geometry, the miscible fluids 12 and 16 used in device 10 can flow in feed pipes (feed channels) 14 and 18 (which may extend in the flow direction g) respectively before the fluids 12 and 16 enter into each other in the integral conduit 19. For example, in Figure 1A In some embodiments shown, the integral conduit 19 may be an extension of the outer conduit 18. For concentric cylindrical flows 12, 16, this can be achieved by having an inner conduit 14 that is shorter than the outer conduit 18, so that the inner fluid 12 exiting the inner conduit 14 interacts with the outer fluid 16 within the outer (integral) conduit 18, 19.

[0070] The lengths of the inner pipe 14 and the outer pipe 18 can be chosen such that they are long enough (along the flow direction g, also referred to herein as longitudinal g) that the velocity distribution of the fluids 12 and 16 becomes fully spread out, i.e., the pipes 14 and 18 can have sufficient length along the longitudinal g to allow the fluids 12 and 16 to spread out an invariant velocity distribution along the longitudinal g before the fluids 12 and 16 interact.

[0071] Pipes 14, 18, and 19 may be oriented such that the longitudinal flow direction g is in or closely aligned with the direction of gravity (e.g., less than 30° in some embodiments, less than 15° in others), although such orientation is not required. In some applications, pipes 14, 18, and 19 may be oriented in other ways.

[0072] like Figure 1A As shown in Figures 2 and 3, a first fluid 12 in the inner conduit 14 and a second fluid 16 in the outer conduit 18 are arranged such that the first fluid 12 and the second fluid 16 flow longitudinally g in the inner conduit 14 and the outer conduit 18. When the inner conduit 14 ends (i.e., at a longitudinal position beyond the outlet 14A of the inner conduit 14), the flowing fluids 12 and 16 come into contact with each other and begin to interact within the overall conduit 19. The interaction of the first fluid 12 and the second fluid 16 produces a reaction product 20. In some embodiments, the reaction product 20 may be an extruded structure 20 such as a hydrogel tubing.

[0073] Fluids 12 and 16 accumulate (i.e., contact) at the contact area 23 (which may include the contact surface 23). Figure 1A In the embodiment shown, contact region 23 coincides with outlet 14A of inner conduit 14. In contact region 23, fluids 12 and 16 begin to react with each other to create a reaction interface region 21 downstream of contact region 23. Contact region 23 may be located at the upstream end of reaction interface region 21. Fluids 12 and 16 may contact each other in contact region 23 and may be separated from each other by reaction product 20 downstream of contact region 23. In contact region 23, where fluids 12 and 16 are in contact, and downstream of contact region 23 in reaction interface region 21, chemical reactions or other interactions, such as state changes, may occur between the first fluid 12 and the second fluid 16. In some embodiments, the first fluid 12 comprises a solvent and a reactive substance A at a concentration of Ca, while the second fluid 16 comprises a solvent and a reactive substance B at a concentration of Cb. In contact region 23, where fluids 12 and 16 are in contact, and downstream of contact region 23 in reaction interface region 21, a chemical reaction between reactive substance A and reactive substance B produces reaction product 20. Figure 1AIn some embodiments, the reaction may be confined to a generally annular reaction interface region 21 downstream of the contact region 23 (e.g., in the pipe 19). The reaction interface region 21 (and the reaction product 20) may grow in lateral thickness as the fluids 12, 16 flow longitudinally g (e.g., the ring may become thicker).

[0074] Device 10 can be used to create conditions that prevent or mitigate mixing of other miscible flowing fluids 12, 16 (e.g., in the reaction interface region 21 between flowing fluids 12, 16). Such conditions are characterized, for example, by the local Reynolds number (local Re, defined using the viscosity of the reaction product 20) of the reaction product 20 in the interface region 21. Such conditions may also be characterized by the Damcoller value (Da) of the reaction and the respective Reynolds numbers (Re1, Re2), fluid velocities (u1, u2), and flow rates (Q1, Q2) of fluids 12, 16. The velocities u1, u2 of fluids 12, 16 can be defined by dividing the flow rates Q1, Q2 of fluids 12, 16 by the area of ​​their respective conduits upstream of the contact region 23—that is... and Where A1 is the cross-sectional area of ​​pipe 14, and A2 is the cross-sectional area of ​​the annular pipe, wherein fluid 16 flows upstream of contact area 23 (i.e., in the illustrated embodiment, A2 is the cross-sectional area of ​​the outer pipes 18, 19 that is smaller than the cross-sectional area of ​​pipe 14).

[0075] Typically, the Reynolds number of a fluid flowing in a pipe can be expressed as: Where ρ is the fluid density, d is the characteristic dimension scale, u is the average velocity of the fluid, and μ is the fluid viscosity. Because the characteristic dimension scale d may differ for different materials in device 10 (and another device described herein) at an upstream location where the different fluids come into contact with each other (e.g., upstream of contact area 23), the Reynolds number described and / or claimed herein should be considered at or downstream of the location where the different fluids first come into contact with each other (e.g., at or downstream of contact area 23). At this location (and downstream of this location), the characteristic dimension scale d can be considered as the inner diameter (or other cross-sectional dimension) of the outer conduit. For example, in the case of device 10, the Reynolds number should be considered at or downstream of contact area 23 where the characteristic dimension scale d is the inner diameter of the outer conduits 18, 19. As used herein, one characteristic is the Reynolds number of either fluid 12, 16 at or downstream of contact area 23. As used herein, the “local” Reynolds number (local Re) of the reaction products can refer to the reaction products at or downstream of the contact area where the two fluids first come into contact (e.g., at...). Figure 1A In the case of an embodiment, the Reynolds number is measured at or downstream of the contact region 23 between fluids 12 and 16. The local Reynolds number of the reaction product can be expressed as... Where ρ is the characteristic density of fluids 12 and 16 (which can be reduced to the characteristic density of water at its dilution limit), d is the characteristic dimension scale (e.g., the inner diameter of outer pipes 18 and 19), and u c It is a velocity parameter, defined as the total flow rate Q. t =∑ i Q i (Where Q1 is the flow rate of internal fluid 12, and Q2 is the flow rate of external fluid 16) In addition to the cross-sectional areas of external pipes 18 and 19, μ p It is the apparent viscosity of the reaction product (e.g., reaction product 20).

[0076] The Reynolds numbers (Re1, Re2) of fluids 12 and 16 at or downstream of their initial contact point (e.g., at or downstream of contact region 23) can be determined according to the equation and Defined, where μ1 and μ2 are the viscosities of fluids 12 and 16 respectively, and other parameters have the meanings described above. The Damköhler value (Da) of the reaction in device 10 (and other devices described herein) can be obtained from the equation Define, where r a It is the reaction rate r a =kC X Where k is the rate constant, and C X This represents the concentration of substance X in the reaction; the other parameters have the same meaning as described above.

[0077] The flow rates (Q1, Q2) of fluids 12 and 16 (which affect the parameter u discussed above) c The reynolds number Re1 of the first fluid 12 and / or the reynolds number Re2 of the second fluid 16 can be greater than 100, 500, 1000, or 2000, based on the rheological properties of the first fluid 12 and the second fluid 16. At least one of the first fluid 12 and the second fluid 16 can have a reynolds number greater than 100, 500, 1000, or 2000. If the rheological properties of fluids 12 and 16 are non-Newtonian fluids, the fluid viscosity used in the definition of the reynolds number can be estimated at the nominal shear rate, i.e., u. c / d.

[0078] The reaction rates between the flowing fluids 12 and 16 in the reaction interface region 21 can typically be larger than advection or diffusion timescales, resulting in a larger Darmquerel number (Da) for the reaction. In some embodiments, the composition of fluids 12 and 16 (e.g., reactants dissolved in fluids 12 and 16) and / or other properties of fluids 12 and 16 can be determined to provide a 10-10 6 The range of Damkoller numbers. In some embodiments, this range is 100-10.5 The Damköhler value Da can be less than 10. 9 .

[0079] In reaction interface region 21, reaction product 20 is created through the reaction between fluids 12 and 16. The contact region 23 at the upstream end of reaction interface region 21 (e.g., where fluids 12 and 16 first contact and first create reaction product 20) can be referred to as the initial interface 23. Since fluids 12 and 16 flow longitudinally, they transport reaction product 20 forward, thus the reaction continues in reaction interface region 21 downstream of the initial interface 23. It should be understood that the first and second fluids 12 and 16 have circular and annular cross-sections, respectively. Figure 1A and 1B In the illustrated embodiment, the initial interface 23 and the reaction interface region 21 may have an annular cross-section, which will tend to produce a reaction product 20 with an annular cross-section and a continuous length, i.e., a tube. If the fluids 12 and 16 can interact continuously through the reaction product 20, further chemical reactions may occur, thereby thickening the lateral dimension of the reaction product 20 at the location of the reaction interface region 21 downstream of the initial interface 23.

[0080] Reaction product 20 can exist as a complete, continuous, and discrete material from fluids 12 and 16, and can exhibit well-defined interfaces such that reaction product 20 does not mix with fluids 12 and 16. If reaction product 20 behaves as a fluid, then at the local Reynolds number Re of reaction product 20 as defined above... p At sufficiently low levels, the tubular shape of reaction product 20 can remain continuous (and fluids 12 and 16 will not mix). In some embodiments, the local Reynolds number Re of reaction product 20 is... p Less than 100, 50, 20, 10 or 1. If the reaction product 20 is a solid, the tubular shape of the reaction product 20 can remain continuous when the stress applied to the reaction product 20 (due to its movement or other reasons) is less than the ultimate strength of the material of the reaction product 20.

[0081] The rheological properties of reaction product 20 can depend on the concentration of reactants. If reaction product 20 is solid and the velocities u1, u2 of fluids 12, 16 vary over time, the tubular shape of reaction product 20 can remain continuous (its inner and / or outer diameters may vary), while the stress exerted on it due to its movement is less than the strength of the material of reaction product 20. Beyond these criteria, reaction product 20 may not form a continuous tube, and the reactive substances (fluids 12, 16) may mix across the reaction interface region 21.

[0082] If the conditions allow reaction product 20 to form a continuous tube (and fluids 12 and 16 to remain unmixed), then for [Ca C b , u1, u2, u1, μ2, ρ1, ρ2, D a For [D], the trajectory of reaction product 20 remains generally parallel to the longitudinal / flow direction g, where μ1 and μ2 are the apparent viscosities of fluids 12 and 16, ρ1 and ρ2 are the densities of fluids 12 and 16, and D is the diffusivity of the reactants dissolved in fluid 16 to reaction product 20. If conditions allow reaction product 20 to form a continuous tube, the thickness of the tube wall can be increased at a location in the reaction interface region 21 downstream of the initial interface 23. The mechanism for this thickness increase at the downstream location is likely a diffusion process, i.e., the diffusion of reactive substances A and B into the reaction interface region 21 and / or reaction product 20. The growth of the tube wall of reaction product 20 can be continuous, while reactive substances A and B remain in the system. Therefore, the lateral dimension of the tube wall of reaction product 20 can be controlled by removing one or more reactive substances (e.g., by reaching the end of pipe 19 and allowing fluids 12 and 16 to be laterally spaced apart from each other or dispersed away from reaction product 20).

[0083] The lateral dimensions (e.g., inner and / or outer diameters) of the reaction product 20 can be further controlled by changing the inlet velocities u1 and u2 upstream of the initial interface 23 (e.g., the ratio of inlet velocities u1 and u2). If operated under suitable inlet velocity conditions, the lateral dimensions of the reaction product 20 can be shaped accordingly. With changes in the inlet velocity conditions, the lateral dimensions of the reaction product 20 can be altered along its axial length.

[0084] The extrusion structure (reaction product 20) production technology described herein can be modified. As a non-limiting example, Figure 1A The coaxial 3D extrusion equipment can be extended to multi-layer (three or more layers) 3D coaxial extrusion.

[0085] Simulation using two-layer equipment

[0086] For the gelation reaction between two Newtonian fluids, an illustrative simulation can be performed. Figure 1A The extrusion equipment 10. The gelation reaction can be idealized to have the following form:

[0087]

[0088] Where C i Defined Figure 1AThe concentrations of each substance are given, where C1 and C2 are the input fluids 12 and 16, respectively, C3 represents the hydrogel reaction product 20, and C4 represents the second reaction product. In the specific case where the inner fluid 12 is an ionically crosslinkable hydrogel (e.g., alginate, alginate, nanofibrillated cellulose (NFC), combinations of these materials, etc.) and the outer fluid 16 is a calcium solution, equation (1A) may have the following form:

[0089]

[0090] Where n is the degree of crosslinking (egg carton coefficient in the case of alginate), X represents alginate or NFC, P is reaction product 20 and chlorine is not specifically shown.

[0091] Numerical simulations were conducted at the dilution limit of the reactions of fluids 12 and 16 according to equation (1B). Within this limit, the total density ρ is a constant solvent density (e.g., water), and the shift equation is as follows:

[0092]

[0093]

[0094]

[0095] Here, is the two-dimensional velocity field, p is the pressure field, and τ is the deviatoric part of the Cauchy stress tensor. The reaction rate r i Defined by the following basic dynamic characteristics:

[0096]

[0097] and

[0098]

[0099] Where k i It is the molar mass fraction The rate of reaction is dispersed. Due to the large difference in the molar mass of the solute. Therefore, only the diffusion rate of calcium ions is modeled as non-negligible: and The system is closed using the Bingham constitutive model.

[0100] if

[0101] ||τ||≤τ y ,if

[0102] in

[0103]

[0104] Viscosity μ and yield stress τ y Because of all four fluids involved (pure solvent H2O and Ca) 2+ Solutions of X or P may vary spatially and temporally, and therefore may exhibit different rheological properties. The viscosity of the mixture was calculated using the Grunberg-Nissan model (as described in “L. Grunberg and AH Nissan, Mixture law for viscosity, Nature, 164(4175): 799-800, 1949”, which is incorporated herein by reference) and local yield stresses derived from a weighted average:

[0105] ln(μ)=∑ i x i ln(μ i )τ y =∑ i x i τ y,i (10)

[0106] Where μ i and τ y,i The viscosity and yield stress of the four fluids were determined experimentally, while x i These are their mole fractions in the mixture. Equations (2)-(4), (7), and (8) are supplemented with no-slip and no-penetration boundary conditions along the wall, fully expanded flow conditions at the outlet, and specified fluxes and concentrations of each substance at the inlet. The flow is initialized with a steady Stokes flow field and concentration C. i Layering throughout the domain (such as at the entry point).

[0107] The equations employ Glowinski's fractional step size θ scheme (as in "R. Glowinski. Viscous flowsimulation by finite element methods and related numerical techniques. In E.M. Murman and S.S. Barbanel, editors, Progress and Supercomputing in Computational Fluid Dynamics, pages 173–210, Boston, 1985). The literature described in “(included in this paper by reference)” is used as a second-order time-step scheme with very small numerical dissipation for numerical solution. At each time step, the entire simultaneous equations are decomposed into an advection-diffusion-reaction problem from equation (2) and a viscoplastic flow problem from equations (3)-(8), and then solved by block Jacobi loop iteration. An algebraic flux correction scheme (as described in “D. Kuzmin. Linearity-preserving flux correction and convergence acceleration for constrained Galerkin schemes. J. Comput. Appl. Math., 236(9): 2317–2337, 2012”, which is incorporated in this paper by reference) is applied to the mass transport module to solve the sharp gradient in the solution of equation (2) while forcing monotonicity, positivity and mass conservation. In order to solve its viscoplastic rheological properties in their original non-smooth form without artificial regularization, fixed-point iteration is adopted and De los Reyes and Gonzlez are used. Andrade's semismooth approximation was used for preprocessing (as described in "JCDe los Reyes and S. González Andrade. Numerical simulation of two-dimensional Bingham fluid flow by semismooth Newton methods. Journal of Computational and Applied Mathematics, 235(1):11–32, 2010", which is incorporated herein by reference). For spatial discretization, the hybridizable discontinuous Galerkin method of Rhebergen and Wells was adopted (as described in "S. Rhebergen and GN Wells. A hybridizable discontinuous Galerkin method for the Navier-Stokes equations with pointwise divergence-free velocity field. Journal of Scientific As described in Computing, 76(3):1484–1501, 2018 (which is incorporated herein by reference), it is based on the first-order triangular Brezzi-Douglas-Marini element of velocity, and piecewise constant approximations of pressure and stress tensors. This yields a stable scheme and leads to numerical solutions for conservation of momentum in the element direction and conservation of mass in the point direction.

[0108] After calibrating constitutive relations (e.g., diffusivity D) through independent experiments ca 2+ and yield stress τ y After that, the inventor controlled Figure 1A The relatively large parameter space of device 10 was explored. Figure 1A The hydrodynamic behavior of device 10. Specifically, the inventors considered the hydrodynamic behavior of the device 10.

[0109]

[0110] The Reynolds number (Re), Peyke number (Pe), Damcoulé number (Da), and Bingham number (Bi) are defined by the ratio of the velocity to viscosity between fluids 12 and 16 at the point of contact (e.g., contact area 23). For this study, the velocities u1 and u2 of fluids 12 and 16 are defined by dividing the flow rates Q1 and Q2 of fluids 12 and 16 by the area of ​​their respective pipes upstream of contact area 23—that is... and Where A1 is the cross-sectional area of ​​pipe 14, and A2 is the cross-sectional area of ​​the annular pipe, fluid 16 flows upstream of contact region 23 (i.e., in the illustrated embodiment, A2 is the cross-sectional area of ​​outer pipes 18 and 19, which is smaller than the cross-sectional area of ​​pipe 14). The inner diameter parameter d of outer pipes 18 and 19 is defined as a characteristic length scale, while the reaction rate... Where k is the rate constant, C n This refers to the concentration of substance n. Within the dilution limit, it is assumed that the density ρ of fluids 12 and 16 is equal to the density of water. Furthermore, the intrinsic viscosity μ... c The lowest viscosity in the system was chosen to characterize the maximum level of inertia. Therefore, in the simulation, the characteristic viscosity μ... c Selected as μ c =min(μ1,μ2). Average velocity u c From the total flow Q t =∑ i Q i (Where Q1 is the flow rate of the internal fluid 12, and Q2 is the flow rate of the external fluid 16) In addition to defining the cross-sectional areas of the external pipes 18 and 19, the mass flux of each flow can be defined as Ω. i =C j Q i , where j∈[water,Ca 2 +,X]. The Reynolds numbers (Re1, Re2) of fluids 12 and 16 are as described above according to... and Defined as μ1 and μ2, where μ1 and μ2 are the viscosities of fluids 12 and 16 respectively, and the other parameters have the meanings described above with respect to equation (11). In the specific case of the simulation results described herein, the diameter of the inner pipe 14 is set to 4 mm, and the diameters of the outer pipes 18 and 19 are set to 10 mm.

[0111] The equations (2)-(4), (7) and (8) described in the simulation section above have been supplemented with the following boundary conditions.

[0112] u = u in In Γ in Up (inflow)

[0113] u=0 in Γ wall Up (no slippage)

[0114] (τn)·np=-p atm In Γ out (Fully expanded)

[0115] u×n=0 in Γ out (Fully expanded)

[0116] C i =C i,i n in Γ in Up (inflow)

[0117]

[0118]

[0119] Among them, the inflow velocity u in atmospheric pressure p atm and inflow concentration C i,in It is the prescribed data.

[0120] Figures 2A-2D The simulation results for a pair of non-reactive fluids 12 and 16 in device 10 are shown. Figures 2A-2D The simulation shown was conducted with a large Pe constraint to minimize the diffusion effect and Da = 0 to eliminate the effect of the reaction between fluids 12 and 16. Figures 2A-2D Each of these parameters examined the behavior of the fluid in device 10 when a variable (shown at the top of the graph) changed. Figure 2A This illustrates the effect of Re on the flow of two fluids 12 and 16 at the same inlet velocity and viscosity in device 10. For Figure 2A The simulation series, fluids 12 and 16 are Newtonian fluids, where μ1 = μ2 = μ c =1×10- 3 Pa·second. Figure 2AThis indicates that as Re increases, interfacial instability dominates the flow state—that is, when Re reaches an excessively high level, fluids 12 and 16 mix. Figure 2B It shows the Figure 2A The simulation results for the condition Re = 1.8 (i.e., Re = 1.8, u1 / u2 = μ1 / μ2 = 1, Bi = 0 and Da = 0) are shown in the dashed outline and the effect of the velocity ratio (u1 / u2) in the range u1 / u2 ∈ [0.1, 10] is discussed. Figure 2B This indicates that under unmixed conditions, the diameter of the internal fluid 12 can be altered (e.g., increased) by changing (e.g., increasing) the velocity ratio (u1 / u2). Therefore, the velocity ratio (u1 / u2) can be used to control the cross-sectional area of ​​the reaction product 20. Figure 1A ). Figure 2C It shows the Figure 2A The dashed outline shows the simulation results for the Re=1850 condition (i.e., Re=1850, u1 / u2=1, μ1 / μ2=1, Bi=0 and Da=0), and then examines the effect of the viscosity ratio (μ1 / μ2) in the range μ1 / μ2∈[0.1,10]. Figure 2C This demonstrates that when the viscosity of one of fluids 12 and 16 is significantly greater than the viscosity of the other fluid 12 and 16, this leads to unmixing conditions. That is, when the inner fluid 12 has a viscosity (μ1) that is significantly greater than the viscosity (μ2) of the outer fluid 16 for Newtonian fluids (or vice versa), interfacial instability is reduced. Figure 2D It shows the Figure 2A The simulation results for the condition Re = 1850 (i.e., Re = 1850, u1 / u2 = 1, μ1 / μ2 = 1, Bi = 0 and Da = 0) are shown in dashed outline, and the effect of Bi in the range Bi ∈ [0, 11400] is examined. Figure 2D This demonstrates that the interfacial instability of non-Newtonian fluids decreases with increasing Bi (e.g., for Bi exceeding a threshold).

[0121] Then, the inventors expanded upon the... Figure 1A The simulation results related to device 10 are used to consider the reaction fluids 12 and 16. This is achieved by first identifying... Figures 2A-2D The subset of conditions that lead to instability is given, and then the reaction rate (Da) and diffusion rate (Pe) are slowly increased. -1 This process continues until the interface stabilizes. Figure 3A It shows the presence of reactive fluids 12 and 16. Figure 1A The representative simulation series of device 10 outlines the combinations (Pe, Da) that create unmixed conditions. Stable flows are characterized as stable (circular) or unmixed (rhomboid), the latter limited to cases where interfacial instability is reduced after contact region 23 or when symmetry is broken and the interface remains intact. Figure 3B Showing with Figure 3A The above data represents a series of representative snapshots of the concentration fields corresponding to multiple simulations 202, 204, 206, 208, 210, and 212. Reactant X (as shown in the equations above) is the inner fluid 12 (shown in white), and the outer fluid 16 (Ca...). 2+ The reaction product 20 (shown as black) is formed in the reaction interface region 21 between fluids 12 and 16, which is light gray. Figure 3A and 3B All simulations shown, Re = 1840, μ X =μ Ca 2 + = 1 × 10 -3 Pa·second, while u1 / u2 = 1. Reaction product 20 exhibits μ... P A Newtonian fluid with a strength of 0.1 Pa·s (Bi = 0) is significantly stronger than the reactants and contributes to interfacial stability. Figure 3C Expanded Figure 3A The simulation range was expanded, and the stability of the interface between reactants 12 and 16 was examined as a function of Da and the velocity ratio u1 / u2 at a fixed Pecley number Pe = 164 to understand... Figure 3A The simulation is sensitive to inlet conditions.

[0122] Figures 3A-3C (Collectively referred to as Figure 3) illustrates that the creation of a stable interface between fluids 12 and 16 is sensitive to the rate ratio u1 / u2, and that localized viscosity changes associated with reaction product 20 stabilize the interface when the reaction rate (Da) and mass transfer are sufficiently large. It is noteworthy that... Figures 3A-3C This indicates that reaction product 20 does not necessarily require viscoplastic rheological properties to achieve stability. Therefore, gelation at the interface is not a necessary condition for obtaining a stable interface, and interfacial disturbances can be reduced at high viscosity ratios.

[0123] Figure 4A and 4B (Collectively referred to as Figure 4) illustrates the use of reactive fluids 12 and 16. Figure 1A The non-mixed dynamics that may occur in device 10 are common for medium to large Pe, small Da and small speed ratio u1 / u2 and the inventors have demonstrated their existence in experiments. Figure 4A The concentration field is at Pe = 165, Da = 22, Re = 1850, The spatiotemporal diagram of device 10 at a selected location over a time span of 1.6 seconds. Reaction product 20 exhibits μ... P =1 Pa·second Newtonian fluid. Figure 4B It shows from Figure 4AFigure 4 is a snapshot taken from a portion of the spatiotemporal diagram at multiple time intervals. It shows that although the symmetry is broken, the interface between fluids 12 and 16 remains intact (i.e., there is no mixing between fluids 12 and 16). Figure 4B The flow snapshots highlight that local Newtonian rheological properties are sufficient to prevent mixing between fluids 12 and 16 when symmetry is broken, suggesting the feasibility of forming a gel (reaction product 20) under inertial conditions.

[0124] These numerical experiments show that using Figure 1A The flow of fluids 12 and 16 in the apparatus can be kept stable under inertial conditions (unmixed) by controlling the rheological properties, wherein the reaction product 20 has a higher viscosity than the reactants (fluids 12 and 16). Viscoplastic rheological properties are helpful, but not necessary to achieve stability. These results also show that the stability boundary is affected by (Pe, Da), where the range of stable Pe increases with increasing Da. The reaction rate between fluids 12 and 16 is faster than advection and diffusion, i.e., a relatively large Damköhler number (Da), and (ii) the local Reynolds number (Re) of the reaction product 20 in this interface region 21. p The stability of some simulations was observed when the value was on the order of ten (i.e., Re ~ o (10)).

[0125] Experimental results using a two-layer device

[0126] Inventor's use Figure 1A Experiments were conducted using device 10, which examined the reactions between ionically crosslinkable reactants (e.g., alginate, alginate, nanofibrillated cellulose (NFC), combinations of these materials, etc.) injected into inner conduit 14 to provide fluid 12 and surrounded by calcium solution (fluid 16) in outer conduit 18. Although the experiments described herein used divalent calcium ions (Ca... 2+ A salt solution may be used as one of the reactants, but other salts containing other metal ions are also known to react with ionically crosslinkable hydrogels and can be used according to specific embodiments of the methods and devices described herein. As a non-limiting example, such metal ions may include polyvalent metal ions, such as Pb. 2+ Cu 2+ Cd 2+ Ba 2+ 、Sr 2+ Co 2+ Ni 2+ Zn 2+ Mn 2+ Al 3+Combinations of these metal ions, etc. Suitable salt solutions containing these metal ions can be used as one reactant (along with ionically crosslinkable hydrogels as another reactant) and can be used as reactants in specific embodiments of the methods and apparatus described herein. In fact, a variety of suitable fluid reactants (e.g., fluids 12, 16, 112, 116, 132) can be used according to specific embodiments of the methods and apparatus described herein to obtain suitable and stable reaction products.

[0127] The device 10 is vertically oriented, where the longitudinal / flow direction g is the direction of gravity. Figure 5A It illustrates the point. Figure 5B , 5C The measurement conditions for the experimental data shown in Figure 5D are as follows, where the horizontal line 30 represents the measurement position, and Δz represents the longitudinal position (measured at this position). Figure 5B , 5C (and 5D measurements), where R represents the radius of the outer pipes 18 and 19. The design was successfully implemented, and a systematic study was conducted to characterize the stable operating window of the device 10. Experiments were repeated to characterize operational stability (e.g., generation of reaction product 20 without mixing fluids 12 and 16) as a function of the volumetric flow rate and concentration of the input fluids 12 and 16. Figure 5B The diagram shows a set of example results from these experiments, where the inner fluid 12 was 0.75% (w / w) alginate and the outer fluid 16 was 4.0% (w / w) CaCl₂. These results are consistent with theoretical predictions (e.g., ...). Figure 3A As shown in the figure, the experimental results indicate that these two have The local Reynolds number (Re) of the reactant will increase with the viscosity of the reaction product 20. p The ) decreases to Re ~o(10) and exhibits unconditional stability, and gelation is rapid (e.g., compared to advection and diffusion timescales). This stable (unmixed) state in Figure 5B The area shown is dark shaded region II. In this stable state (region II), the outer diameter (Do) of the tube is controlled by changing the flow rate ratio (Q2 / Q1) of fluids 16 and 12. The scalability of this method is demonstrated by producing hydrogel tubes with stable external dimensions of ~200 cm (as reaction product 20).

[0128] Figure 5C and 5D The time evolution (space-time plot) of the outer diameter (Do) of the tube (reaction product 20) measured as a function of time at position 30 is shown, where t max =2min. Figure 5C It shows the corresponding Figure 5B Under the conditions of region II, the outer diameter (D) of reaction product 20 o The stability of ).

[0129] exist Figure 5B Under the conditions shown in region I, instability exists (i.e., the mixing of fluids 12 and 16). Instability was found at the boundary between unstable region I and stable region II. Figure 5D The quasi-steady-state characteristics shown indicate that the outer diameter Do of the reaction product 20 varies periodically, and the trajectory of the resulting tube follows a spiral pattern. Figure 5D The Reynolds number of the example (as defined in equation (11)) is approximately on the order of 250. These complex behaviors are attributed to nonlinear rheological properties (see [reference]). Figure 6 The elastic mechanical response of the structure 20 of the gelation reaction product to the spatial gradient of osmotic pressure.

[0130] Figure 6 The use of 0.75% (w / w) alginate (C1=C1) is shown. X ) as internal fluid 12 and various concentrations Multiple flow curves from various experiments conducted using the external fluid 16. Unreacted (solid lines) and reacted (dashed lines) are fitted Herschel-Bulkley models. Figure 6 The results demonstrate the use of during the printing process Figure 1A The rheological properties of reaction product 20 printed by the device.

[0131] The inventors further examined the robustness and stability criteria of the process for conversion to multiphase flow by adding several additives to starting materials ranging in size from a few nanometers to a few millimeters. Such additives can include synthetic or naturally occurring fibers, nanotube materials, etc. Figures 7A-7D It shows the composition of alginate ( Figure 7A Alginate containing nanoscale fiber additives (especially nanofibrillated cellulose (NFC)). Figure 7B Alginate containing micron-sized fiber additives (especially rhythmically oxidized Northern Bleached Cork Kraft Paper (NBSK) cellulose fibers). Figure 7C ) and with millimeter-scale fiber additives (especially using Figure 1A The equipment used to construct NBSK cellulose fibers) alginate ( Figure 7D Examples of air-dried hydrogel tubes 20 made from [material name missing]. These experiments demonstrate that particles larger than those found in typical small 3D extruders can be added to large-scale [structures / materials]. Figure 1A In the device, and the size of the hydrogel tube 20 can be adjusted when operating in a stable configuration (e.g., in...). Figure 5BIn a stable region II, the additive is in-situ shaped (e.g., by switching between stable operating states) into the desired shape. In some embodiments, such natural and / or synthetic fiber additives may have an average aspect ratio (e.g., the ratio of length to cross-sectional dimension) greater than 25:1. In some embodiments, such additives have an average aspect ratio greater than 50:1. In some embodiments, such additives have an average aspect ratio greater than 90:1. In some embodiments, such natural and / or synthetic additives have an average length dimension greater than 1 mm. In some embodiments, such additives have an average length dimension greater than 2 mm. In some embodiments, such additives have an average length dimension greater than 5 mm.

[0132] Additives suitable for device 10 (and / or other devices described herein) are generally not limited to fibrous additives. Non-limiting examples of additives that can be added to the fluids of the devices described herein and thus embedded in the reaction products described herein include pharmaceuticals, fertilizers, biomaterials (e.g., stem cells), photoluminescent materials, reactive substances, antimicrobial agents (TiO2, Ag colloids, etc.), additives that modify the hydrophobicity of the outer surface (e.g., chitosan, etc.), viscosity modifiers, and other materials that provide additional functionality.

[0133] Figure 8A The use of a 0.25% (w / w) alginate (internal fluid 12) solution in contact with a 1.2% (w / w) CaCl2 solution (external fluid 16) is shown. Figure 1A The velocity field (along the flow direction) and outer diameter D of the hydrogel tube 20 of device 10. o Experimental measurements (using a particle imaging velocimeter). The outer diameter D of the hydrogel tube 20. o Represented by dashed white lines. Flow distribution along the axial direction, u. c (r,z) is shown using a solid black line. Figure 8A In the mean, when averaged, it equals u. c =18 mm / s. The flow distribution along the flow direction is called u. z The grayscale image shows the normalized velocity along the flow direction, with lighter shades corresponding to larger velocities. Figure 8A The axial (longitudinal) velocity field exhibits non-monotonic behavior, indicating the presence of a body force in addition to gravity. This force is osmotic pressure, generated in the system by the abrupt gradient of molar concentration between CaCl2 and alginate solutions, and it significantly affects the magnitude of the velocity field near the interface between fluids 12 and 16.

[0134] Figure 8B It shows that in relation to Figure 8A Numerical simulations under inertial conditions similar to those in the experiments. Figure 8B The conditions are Da = 527 and Pe = 1200. and μP = 0.1 Pa·s. By comparison Figure 8A and 8B It can be seen that the velocity field of the simulation results is similar to that of the experimental results.

[0135] Figure 8C and 8D It shows the use of Figure 1A The cross-sections of alginate tubes (reaction product 20) generated by device 110 at different reaction times, wherein... Figure 8D The reaction time shown is greater than Figure 8C The reaction time is long. These images involve using 0.75% (w / w) alginate solution as the external fluid 16 and using 1% (w / w) Ca 2+ The solution is considered as an internal fluid 12. As theoretically estimated, Figure 8C and 8D Explain the wall thickness l w According to An approximate estimate is given, where D is the diffusivity of the salt solution (internal fluid 12) and tr is the residence time in device 10.

[0136] like Figure 8E As shown, the inventors considered the hydraulic properties of the extruded hydrogel tube (reaction product) 20 by measuring the pressure change (ΔP / L) per unit distance (pressure drop) within a certain range of flow rate (Q) to check whether the material properties of the extruded hydrogel tube 20 can withstand typical extracorporeal circulation (ECC) conditions. Figure 8E The data shown are for a hydrogel tube 20 manufactured using 1.5% alginate as the inner fluid 12 and 2% CACl2 as the outer fluid 16. Figure 8E As shown, the hydraulic behavior of the extruded hydrogel tube 20 satisfies the standard pipe law for the case of 50% glycerol (circular data points) and water (square data points).

[0137] Three-layer equipment

[0138] Figure 9A This is a schematic diagram of an apparatus 110 for 3D extrusion of a structure 120 (e.g., hydrogel structure 120) formed using a plurality of flowing fluid inputs 112, 116, 132, according to a specific embodiment. The extruded structure 120 may be a reaction product of the flowing fluids 112, 116 in the apparatus 110. Figure 9A The illustration is a cross-sectional view taken in a plane generally parallel to the fluid flow (extrusion) direction indicated by arrow g. The cross-sectional geometry of the device 110 (and the corresponding stratified fluids 112, 116, 132) taken in a transverse plane perpendicular to the flow / extrusion direction g can affect the shape of the resulting extrusion structure 120. [The remaining text appears to be incomplete and possibly contains errors. A more accurate translation would require the full context.] Figure 9AThe device 110 can convey multiple possible geometries of stratified fluids 112, 116, and 132. In the embodiments and experiments described herein, fluids 112, 116, and 132 are arranged with an inner flow 112 (having a generally circular cross-section), an intermediate flow 116 (having a generally annular cross-section) surrounding the inner cylindrical flow 112, and an outer flow 132 (also having a generally annular cross-section) surrounding the intermediate flow 116. These flows 112, 116, and 132 can be created, for example, by conduits or pipes of appropriate shape that provide these flow geometries.

[0139] This geometry is not limiting. Other cross-sectional geometries are also possible, such as those discussed herein with respect to device 10. By giving a specific cross-sectional geometry, the miscible fluids 112, 116, 132 used in device 110 can flow in feed conduits (feed pipes) 114, 118, 134 (which may extend along the flow direction g) respectively before contacting each other in the integral conduit 119. In some embodiments, such as... Figure 9A As shown, the integral conduit 119 can be an extension of the outer conduit 134. This can be achieved by means of concentric cylindrical flows 112, 116, 132, through an inner conduit 114 and an intermediate conduit 118 that are shorter than the outer conduit 134, so that the inner fluid 112, the intermediate fluid 118 and the outer fluid 132 are in contact with each other within the outer (integral) conduit 134, 119.

[0140] The lengths of the inner, middle, and outer pipes 114, 118, and 134 can be chosen so that they are long enough (along the flow direction g, also referred to as longitudinal g in this document) that the velocity distribution of the fluids 112, 116, and 132 becomes fully expanded, i.e., a velocity distribution that remains constant along the longitudinal g, before the fluids 112, 116, and 132 come into contact with each other and interact with each other.

[0141] Pipes 114, 118, 134, and 119 can be oriented such that the longitudinal flow direction g is in or closely aligned with the direction of gravity, although such orientation is not required. In some applications, pipes 114, 118, 134, and 119 can be oriented in other ways.

[0142] Figure 9B The diagram shows the results from the stable conditions. Figure 9A A schematic diagram of the reaction interface regions 121 and 125 of the device 110 and the extruded reaction product 120.

[0143] like Figure 9AAs shown, a first (internal) fluid 112 in inner conduit 114, a second (intermediate) fluid 116 in intermediate conduit 118, and a third (external) fluid 132 in outer conduit 134 are arranged such that fluids 112, 116, and 132 flow longitudinally g within inner conduit 114, intermediate conduit 118, and outer conduit 134. When inner conduit 114 ends (i.e., at a longitudinal position beyond the outlet of inner conduit 114), the flowing fluids 112 and 116 come into contact with each other and begin to interact within the overall conduit 119. Similarly, when intermediate conduit 118 ends (i.e., at a longitudinal position beyond the outlet of intermediate conduit 118), the flowing fluids 116 and 132 come into contact with each other and begin to interact within the overall conduit 119. The longitudinal positions of the ends of inner conduit 114 and intermediate conduit 118 may be the same, but this is not required. In some embodiments, the end of one of inner conduit 114 and outer conduit 118 is located at a different position than the end of the other of inner conduit 114 and outer conduit 118. The interaction of fluids 112, 116, and 132 produces reaction product 120. In some embodiments, reaction product 120 may be an extruded structure 120, such as a hydrogel tube.

[0144] Fluids 112 and 116 accumulate (i.e., contact) at the contact area 123 (which may include the contact surface 123). Figure 9A , 9B In the embodiment shown, contact region 123 coincides with the outlet (downstream end) of inner conduit 114. In contact region 123, fluids 112 and 116 begin to react with each other to create a reaction interface region 121 downstream of contact region 123. Contact region 123 may be located upstream of reaction interface region 121. Fluids 112 and 116 may contact each other in contact region 123 and may separate from each other downstream of contact region 123 via internal reaction product 120A. Downstream of contact region 123, where fluids 112 and 116 contact, and in reaction interface region 121, chemical reactions or other reactions such as state changes may occur between inner fluid 112 and intermediate fluid 116. In some embodiments, inner fluid 112 may include a solvent and a concentration of C a The reactive substance A, while the intermediate fluid 116 includes a solvent and a concentration of C. b Reactive substance B. Downstream of contact region 123 in the contact area 123 of fluids 112 and 116, and in the reaction interface region 121, a chemical reaction between reactive substance A and reactive substance B produces internal reaction product 120A. Figure 9A and 9BIn some embodiments, the reaction may be confined to a generally annular reaction interface region 121 downstream of the contact region 123 (e.g., in the conduit 119). The reaction interface region 121 (and the internal reaction product 120A) may grow in lateral thickness as the fluids 112, 116 flow longitudinally g (e.g., the ring may become thicker).

[0145] Fluids 116 and 132 accumulate (i.e., contact) at the contact area 127 (which may include the contact surface 127). Figure 9A and 9B In the embodiment shown, contact region 127 coincides with the outlet of intermediate conduit 118. In contact region 127, fluids 116 and 132 begin to react with each other to create a reaction interface region 125 downstream of contact region 127. Contact region 127 may be located upstream of reaction interface region 125. Fluids 116 and 132 may contact each other in contact region 127 and may be separated from each other downstream of contact region 127 by external reaction product 120B. Internal reaction product 120A and external reaction product 120B may be collectively referred to herein as reaction product 120. Chemical reactions or other reactions such as state changes may occur between intermediate fluid 116 and external fluid 132 in contact region 127, and upstream of contact region 127 in reaction interface region 125. In some embodiments, intermediate fluid 116 may include a solvent and a concentration of C b The reactive substance B, while the external fluid 132 includes a solvent and a concentration of C. c The reactive substance C. In some embodiments, the reactive substance C of the external fluid 132 is the same as the reactive substance A of the internal fluid 112, although this is not necessary. Downstream of the contact region 127 in the contact region 127 of fluids 116 and 132 and in the reaction interface region 125, a chemical reaction between reactive substance B and reactive substance C produces an external reaction product 120B. Figure 9A and 9B In some embodiments, the reaction may be confined to a generally annular reaction interface region 125 downstream of the contact region 127 (e.g., in the conduit 119). The reaction interface region 125 (and the external reaction product 120B) may grow in lateral thickness as the fluids 116, 132 flow longitudinally g (e.g., the ring may become thicker).

[0146] Device 110 can be used to create conditions that prevent or mitigate the mixing of miscible flowing fluids 112, 116 and 116, 132 (e.g., in reaction interface regions 121, 125 between flowing fluids 112, 116, 132). Such conditions can be characterized, for example, by the local Reynolds number (local Re) of the reaction products 120A, 120B in the interface regions 121, 125 between fluids 112, 116 and 116, 132 (defined using the viscosity of reaction products 120A, 120B). Such conditions can also be characterized by the Damköhler value (Da) of the reaction and the respective Reynolds numbers (Re1, Re2, Re2), fluid velocities (u1, u2, u3), and flow rates (Q1, Q2, Q3) of fluids 112, 116, 132. The velocities u1, u2, u3 of fluids 112, 116, and 132 can be defined by dividing the flow rates Q1, Q2, and Q3 of fluids 112, 116, and 132 by the area of ​​their respective pipes upstream of the contact regions 123 and 127.

[0147] As described above, the Reynolds number described herein and / or claimed should be considered at or downstream of the location where the different fluids first come into contact with each other (e.g., at or downstream of contact areas 123, 127). At this location (and downstream of this location), the characteristic dimension d can be considered as the inner diameter (or other cross-sectional dimension) of the outer pipe. For example, in the case of device 110, the Reynolds number should be considered at or downstream of contact areas 123, 127 where the characteristic dimension is the inner diameter of the outer pipes 119, 134. Thus, the Reynolds numbers of fluids 112, 116, 132 at or downstream of contact areas 123, 127 can be characterized. The Reynolds numbers at or downstream of the contact areas where fluids 112, 116 first come into contact can also be described (e.g., at...). Figure 9A , 9B In the case of the embodiment, the "local" Reynolds number (local Re) of the reaction product 120A at or downstream of the contact region 123 between fluids 112 and 116 and at or downstream of the contact region where fluids 116 and 132 first come into contact (e.g., in Figure 9A , 9B In the case of the embodiment, the "local" Reynolds number (local Re) of the reaction product 120B (at or downstream of the contact region 127 between fluids 116 and 132). The local Re of the reaction product 120A can be expressed as Where ρ is the characteristic density of fluids 112, 116, and 132 (this characteristic density can be reduced to the characteristic density of water at its dilution limit), d is the characteristic dimension scale (e.g., the inner diameter of outer pipes 119 and 134), and u c It is a speed parameter, defined as the total flow rate Q. t =∑ i Q i(Where Q1 is the flow rate of the inner fluid 112, Q2 is the flow rate of the intermediate fluid 116, and Q3 is the flow rate of the outer fluid 132) excluding the cross-sectional areas of the outer pipes 119 and 134, and μ p This is the apparent viscosity of the reaction product (e.g., reaction product 120A). Similarly, the local Re of reaction product 120B can be expressed as... Where ρ is the characteristic density of fluids 112, 116, and 132 (this characteristic density can be reduced to the characteristic density of water at its dilution limit), d is the characteristic dimension scale (e.g., the inner diameter of outer pipes 119 and 134), and u c It is a speed parameter, defined as the total flow rate Q. t =∑ i Q i (Where Q1 is the flow rate of the inner fluid 112, Q2 is the flow rate of the intermediate fluid 116, and Q3 is the flow rate of the outer fluid 132 divided by the cross-sectional area of ​​the outer pipes 119 and 134, and μ) p It is the apparent viscosity of the reaction product (e.g., reaction product 120B).

[0148] The Reynolds numbers (Re1, Re2, Re3) of fluids 112, 116, and 132 at or downstream of their initial contact points (e.g., at or downstream of contact areas 123 and 127) can be determined according to... and Where μ1, μ2, and μ3 are the viscosities of fluids 112, 116, and 132, respectively, and the other parameters have the same meanings. The Damcole value (Da) of the reaction in device 110 (and other devices described herein) can be determined according to... Define, where r a It is the reaction rate r a =kC X Where k is a rate constant specific to a particular reaction, and C X This represents the concentration of substance X in the reaction; the other parameters have the same meaning as described above.

[0149] The flow rates (Q1, Q2, Q3) of the inner fluid 112, intermediate fluid 116, and outer fluid 132 can be set based on the local rheological properties of the inner fluid 112, intermediate fluid 116, and outer fluid 132 (which affect the above parameter u). cThis allows the Reynolds number Re1 of the inner fluid 112, the Reynolds number Re2 of the intermediate fluid 116, and / or the Reynolds number Re3 of the outer fluid 132 to be greater than 100, 500, 1000, or 2000. In some embodiments, at least one of the inner fluid 112, the intermediate fluid 116, and the outer fluid 132 may have a Reynolds number greater than 100, 500, 1000, or 2000. In some embodiments, at least two (or all) of the inner fluid 112, the intermediate fluid 116, and the outer fluid 132 may have a Reynolds number greater than 100, 500, 1000, or 2000. If the fluid rheological properties of any of the fluids 112, 116, and 132 are non-Newtonian, the fluid viscosity used in the definition of the Reynolds number can be estimated at the nominal shear rate, i.e., u. c / d.

[0150] The reaction rates between the flowing fluids 112 and 116 in reaction interface region 121 and between the flowing fluids 116 and 132 in reaction interface region 125 can typically be very large (e.g., compared to advection or diffusion timescales), resulting in large Damcole numbers (Da) for these reactions. In some embodiments, the components of fluids 112, 116, and 132 (e.g., reactants dissolved in fluids 112, 116, and 132) and / or other properties of fluids 112, 116, and 132 can be selected to provide a Damcole number of 10-10 in reaction interface regions 121 and / or 125. 6 The range of Damkoller numbers. In some embodiments, this range is 100-10. 5 In these reactive interface regions, the Damköhler value Da can be less than 10. 9 .

[0151] In reaction interface region 121, internal reaction product 120A is created by the reaction between fluids 112 and 116, while in reaction interface region 125, external reaction product 120B is created by the reaction between fluids 116 and 132. The contact region 123 at the upstream end of reaction interface region 121 (e.g., where fluids 112 and 116 first contact and create internal reaction product 120A) and the contact region 127 at the upstream end of reaction interface region 125 (e.g., where fluids 116 and 132 first contact and create external reaction product 120B) may be referred to as initial interfaces 123 and 127. Since fluids 112, 116, and 132 flow longitudinally (g), they transport reaction product 120 along the longitudinal flow direction (g) so that the reaction continues in reaction interface regions 121 and 125 downstream of the initial interfaces 123 and 127. It should be understood that in Figure 9A and 9BIn the illustrated embodiment, with the inner fluid 112 having a circular cross-section and the intermediate fluid 116 and outer fluid 132 having annular cross-sections, the initial interfaces 123, 127 and the reaction interface regions 121, 125 can also have annular cross-sections. This tends to produce inner reaction product 120A and outer reaction product 120B with annular transverse cross-sections and continuous lengths, i.e., tubes. If fluids 112, 116, 132 can continue to interact through the inner reaction product 120A and outer reaction product 120B, further chemical reactions may occur, thereby thickening the transverse dimensions of the inner reaction product 120A and outer reaction product 120B at the locations of the reaction interface regions 121, 125 downstream of the initial interfaces 123, 127.

[0152] Reaction products 120A and 120B can exist as complete, continuous, and discrete materials from fluids 112, 116, and 132, and can exhibit well-defined interfaces, ensuring that reaction products 120A and 120B do not mix with fluids 112, 116, and 132. If reaction products 120A and 120B behave as fluids, then the local Reynolds number Re of reaction products 120A and 120B will be... pA Re pB At sufficiently low values, the tubular shapes of reaction products 120A and 120B can remain continuous (and fluids 112, 116 and 116, 132 will not mix). In some embodiments, these local Reynolds numbers Re of reaction products 120A and 120B are... pA Re pB Less than 100, 50, 20, 10 or 1. If reaction products 120A and 120B are solids, the tubular shape of reaction products 120A and 120B can remain continuous when the stress applied to reaction products 120A and 120B (due to their movement or other reasons) is less than the ultimate strength of the material of reaction products 120A and 120B.

[0153] The rheological properties of reaction products 120A and 120B can depend on the concentration of reactants. If reaction products 120A and 120B are solids and the velocities u1, u2, and u3 of fluids 112, 116, and 132 change over time, the tubular shape of reaction products 120A and 120B can remain continuous (their inner and / or outer diameters may change), and the stresses applied to cause them to move are less than the strength of the materials of reaction products 120A and 120B. Apart from these criteria, reaction products 120A and 120B may not form continuous tubes, and the reactive substances (fluids 112, 116, and 132) may mix across reaction interface regions 121 and 125.

[0154] If the conditions allow reaction products 120A and 120B to form a continuous tube (and fluids 112, 116, and 132 to remain unmixed), then for [C a C b C c For various combinations of u1, u2, u3, μ1, μ2, μ3, ρ1, ρ2, ρ3, Da, D1, D3, the trajectories of reaction products 120A and 120B can remain generally parallel to the longitudinal / flow direction g, where μ1, μ2, μ3 are the apparent viscosities of fluids 112, 116, and 132, respectively, and ρ1, ρ2, ρ3 are the apparent viscosities of fluids 112, 116, and 132, respectively. 3是 The densities of fluids 112, 116, and 132 are given, while D1 and D3 are the diffusivity of reactants 112 and 132 dissolved in fluid 116 to reaction products 120A and 120B. If conditions allow reaction product 120 to form a continuous tube, the tube wall thickness can increase at locations in reaction interface regions 121 and 125 downstream of the initial interfaces 123 and 127. This downstream thickness increase can be achieved through diffusion, where reactive substances A and B diffuse into reaction interface region 121 and / or reaction product 120A, while reactive substances B and C diffuse into reaction interface region 125 and / or reaction product 120B. The growth of the tube walls of reaction products 120A and 120B can continue while reactive substances A, B, and C are still present in the system. Therefore, the lateral dimensions of the pipe walls of reaction products 120A and 120B can be controlled by removing one or more reactive substances (e.g., by reaching the end of pipe 119 and allowing fluids 112, 116, and 132 to be laterally spaced apart from or away from reaction products 120A and 120B).

[0155] The lateral dimensions (e.g., inner and / or outer diameters) of reaction products 120A and 120B can be further controlled by changing the inlet velocities u1, u2, u3 upstream of the initial interfaces 123 and 127 (e.g., the ratio of inlet velocities u1, u2, u3). If operated under suitable inlet velocity conditions, the lateral dimensions of reaction products 120A and 120B can be shaped accordingly. With changes in the inlet velocity conditions, the lateral dimensions of reaction products 120A and 120B can be altered along their axial length.

[0156] Under certain conditions, reaction products 120A and 120B may merge together to form a monolithic reaction product 120, although this is not necessary. In some embodiments, reaction products 120A and 120B may remain spaced apart from each other. In some embodiments, reaction products 120A and 120B may aggregate together in space, but may not form a monolithic reaction product. In some embodiments, reaction products 120A and 120B may exhibit mixing.

[0157] Although this document shows and describes a three-layer device 110 (i.e., using three layers of fluid, inner fluid 112, intermediate fluid 116, and outer fluid 132), it should be understood that the device can be constructed to have more than three layers of fluid.

[0158] Fiber reinforcement and other additives

[0159] Apparatus 10 and 110 can be used to rapidly produce tough, reinforced synthetic hydrogel tubes. Natural polymers (such as alginate or nanofibrillated cellulose (NFC)) are particularly suitable as hydrogel matrices because they gel upon contact with salt solutions (such as CaCl2). Apparatus 10 and 110 can be used to produce robust synthetic tubing 120 containing reinforcing fibers. Suitable additives for apparatus 10 and 110 include, but are not limited to, a variety of materials such as natural fibers, synthetic fibers, nanotube materials (e.g., carbon nanotubes), etc. In some embodiments, such natural and / or synthetic fiber additives may have an average aspect ratio (e.g., length to cross-sectional dimension ratio) greater than 25:1. In some embodiments, such additives have an average aspect ratio greater than 50:1. In some embodiments, such additives have an average aspect ratio greater than 90:1. In some embodiments, such natural and / or synthetic additives have an average length dimension greater than 1 mm. In some embodiments, such additives have an average length dimension greater than 2 mm. In some embodiments, such additives have an average length dimension greater than 5 mm.

[0160] Figure 10A and 10B (Collectively referred to as Figure 10) illustrates the process for producing fiber-reinforced hydrogel tubes 120. Figure 9A Device 110. Device 110 of the embodiment of FIG10 and Figure 9A The apparatus shown is the same as described above. In the embodiment of Figure 10, the inner fluid 112 and the outer fluid 132 are both the same salt (e.g., CaCl2) solution, while the intermediate fluid 116 is a fiber-reinforced crosslinkable biopolymer (e.g., alginate) solution. As described above, the reaction occurs in the layered contact regions 123, 127 (see Figure 10) between the inner fluid 112 and the intermediate fluid 116. Figure 10BThis process generates an internal-intermediate reaction product 120A, while an intermediate-external reaction product 120B is formed between the intermediate fluid 116 and the external fluid 132. Reaction products 120A and 120B may merge downstream of contact regions 123 and 127 to form a bulk reaction product 120, but this is not necessary. In some embodiments, reaction products 120A and 120B may remain spaced apart from each other. In some embodiments, reaction products 120A and 120B may aggregate in space but may not form a bulk reaction product. In some embodiments, reaction products 120A and 120B may exhibit mixing. Using the fiber reinforcement shown in FIG. 10, the stiffness of the fiber-reinforced tube (reaction product) 120 generated by device 110 can be greater than the stiffness of the reaction product 20 (without fiber reinforcement) generated by device 10.

[0161] Figure 11A This describes the characterization of the device used in Figure 10, specifically the 1.5% (w / w) alginate concentration used as the intermediate fluid 116 and the 1% (w / w) Ca concentration used as the inner fluid 112 and outer fluid 132 for various velocity ratios u3 / u2. 2+ Experimental results were obtained by analyzing the stress-strain curves of various alginate hydrogel tubes (reaction products) 120 produced without fiber reinforcement (using a dynamic mechanical analyzer (DMA) and an optical coherence tomography scanner). For Figure 11A In the experiment shown, the velocities of the inner fluid 112 and the outer fluid 132 were set to be equal (u1 = u3) and Q t =180 mL / min. Specifically, Figure 11A Stress-strain curve 32 is shown for u3 / u2=10 along the longitudinal (g) direction (machine direction (MD)), stress-strain curve 34 is shown for u3 / u2=10 along the transverse (CD) direction, and stress-strain curve 36 is shown for u3 / u2=0 along the longitudinal (g) direction (machine direction (MD)). Figure 11A The burst stress σ for an alginate tube 120 made of u3 / u2 = 10 is also shown. θ (P)38. Figure 11B It shows that in such Figure 11A The effect of alginate concentration (0.75% (w / w) and 1.5% (w / w)) on the Young modulus of alginate tube (reaction product) 120 under the same experimental conditions and rate ratio (u3 / u2) shown.

[0162] The inventors explored the reinforcing properties of the fiber additives through fluid dynamics. Elongation stress was generated in the apparatus 110 of Figure 10 by accelerating the fiber suspension in the intermediate fluid 116 at contact regions 123 and 127. The resulting directional distribution within the reaction product 120 was measured using X-ray tomography. The fiber arrangement order in the synthetic pipe reaction product 120 can be characterized using the following order parameters.

[0163]

[0164] The angle ζ represents the orientation of the fiber spindle relative to the flow direction g.

[0165] The inventors discovered that by increasing the velocity difference between fluid layers 112, 116, and 132, the fibers in the synthesis tube 120 align along the flow (longitudinal) direction g. This effect is shown in... Figure 11C The diagram depicts the effect of the velocity ratio u3 / u2 (between the outer fluid 132 and the intermediate fluid 116) on the distribution (Ψ) of the fiber orientation ζ (where ζ = 0° corresponds to the flow (longitudinal) direction g). For Figure 11C In the experiment shown, the velocities of the inner fluid 112 and the outer fluid 132 were set to be equal (u1 = u3) and Q t =180mL / min. Figure 11C The probability distribution of the orientation angle ζ, which clusters around the center value ζ = 0° representing the axial flow direction, is shown. Figure 11C This indicates that, as characterized by the order parameter S, the dispersion of the azimuth angle ζ distribution decreases as the velocity ratio u3 / u2 increases.

[0166] The mechanical properties of the synthetic hydrogel tubes 120 generated using the apparatus shown in Figure 10 were measured using a dynamic mechanical analyzer (DMA) to produce... Figure 11D The curves shown illustrate the use of natural fiber additives with 1.5% (w / w) and 1% (w / w) alginate (as intermediate fluid 116) and 1% (w / w) Ca 2+ Stress-strain curves (along the longitudinal direction g) of alginate (A) tubing 120 produced using the apparatus 110 of Figure 10 for various velocity ratios u3 / u2, inner fluid 112 and outer fluid 132. Figure 11D In the experiment shown, the velocities of the inner fluid 112 and the outer fluid 132 were set to be equal to each other (u1 = u3) and Q. t =180mL / min. Figure 11D This indicates that for the fiber-reinforced hydrogel matrix (reaction product 120), the stiffness of reaction product 120 increases in the region where the strain is less than the fiber length, with increasing velocity ratio u3 / u2. The fracture energy (reaction product) of the synthesized reinforced pipe is 4100 J / m. 2, defined as the integral of the stress-strain curve at u3 / u2 = 15. Not wishing to be bound by theory, the inventors attribute this strength enhancement to a stress in the device 110, as determined by X-ray tomography, that results in a reduced directional distribution of the stress at the contact region 127 (see [reference]). Figure 11C ).

[0167] The inventors repeated their experiment for reaction product 120 using the apparatus 110 of Figure 10 without fiber reinforcement and with fiber reinforcement having alginate and fiber concentrations of 1.5% and 1% (w / w) for various rate ratios u3 / u2. Figure 11E The elastic modulus of the fiber-reinforced (shaded) and non-fiber-reinforced (shaded) reaction product 120 is shown at various speed ratios u3 / u2. For Figure 11E In the experiment shown, the velocities of the inner fluid 112 and the outer fluid 132 were set to be equal (u1 = u3) and Q t =180mL / min.

[0168] It should be understood that while several specific reinforcing fibers are described herein, various embodiments may include or use a variety of different reinforcing fibers in the manner described herein. In some embodiments, additives other than or alternative to fiber additives may be added to various fluids to achieve desired functionality. Non-limiting examples of additives that may be added to the fluids of the devices described herein and thus embedded in the reaction products described herein include pharmaceuticals, fertilizers, biomaterials (e.g., stem cells), photoluminescent materials, reactive substances, antimicrobial agents (titanium dioxide, Ag colloids, etc.), additives that modify the hydrophobicity of the outer surface (e.g., chitosan, etc.), viscosity modifiers, and other materials that provide additional functionality.

[0169] Planar Implementation

[0170] Figure 13A and 13B (Collectively referred to as FIG. 13) shows a cross-section of a planar extrusion apparatus 310 for extruding hydrogel reaction products 310, demonstrating that the operating principles of the invention described herein can be extended to different geometries. Unless specifically described herein, apparatus 310 may be similar to or the same as apparatus 10, 110 described herein.

[0171] In the device 310 shown in the embodiment of Figure 13, the flow direction ( Figure 13A Outside the page and Figure 13BThe flow direction (from left to right, as shown by arrow 311) is generally orthogonal to the direction of gravity (e.g., generally horizontal), although this is not required. In some embodiments, device 310 may be used with flow directions within 30° or 15° of the horizontal. In some embodiments, device 310 may be used with flow directions coinciding with the direction of gravity (e.g., generally vertical flow directions). In some embodiments, device 310 may be used with flow directions within 30° or 15° of the vertical.

[0172] Device 310 includes an outer conduit 334 and a pair of parallel plates 314, 118, which provide conduits for flowing fluids 312, 316, 332, which flow in direction 311 and have a generally rectangular cross-section. For the orientation shown in FIG. 13, fluid 312 flows at the bottom, fluid 316 is the central fluid, and fluid 332 flows at the top. In some embodiments, flows 312, 332 comprise a salt solution (e.g., containing polyvalent metal ions such as Ca). 2+ The central fluid flow 316 contains alginate. Due to the rectangular geometry of the device 310, an edge effect exists, where the flow field is not locally one-dimensional. This edge effect creates the potential for alternative, and sometimes even undesirable, reaction interfaces. The inventors have determined that such alternative reaction interfaces typically manifest as additional reaction fronts propagating inward from the edge level. Disadvantageously, this can lead to channel blockage, as reaction products from these alternative reactions may adhere to the sidewalls 331A, 331B (collectively, sidewall 331). To overcome this drawback, the device 310 can be designed such that the central fluid flow 316 (in terms of its cross-sectional dimension w2) is narrower than the cross-sectional dimensions w1, w3 of the lower flow 312 and the upper flow 332, while the width (w4) of the sidewall 331 can be greater than the total thickness (h) of the stratified fluids 312, 316, 332, such that any (horizontal) disturbances created by the sidewall 331 are attenuated before contacting the central fluid 316. This structural feature helps ensure that the flow of the lower fluid 312 and the upper fluid 332 is locally one-dimensional when in contact with the central fluid 316.

[0173] In the embodiment illustrated in FIG13, fluids 312, 316, and 332 contact each other at contact regions 323 and 327 to provide reaction products 320A and 320B in reaction interface regions 321 and 325 within the orifice of the outer conduit 334. The lengths of the outer conduit 334 and plates 314 and 318 can be chosen such that they are long enough (in the flow direction 311) that the velocity distribution of fluids 312, 316, and 332 becomes sufficiently spread out before they contact and interact with each other, i.e., a velocity distribution that remains constant along the longitudinal direction 311.

[0174] like Figure 13B As shown, when plate 314 ends (i.e., at a longitudinal position downstream of plate 314), the flowing fluids 312 and 316 come into contact with each other and begin to interact within the integral outer conduit 334. Similarly, when plate 318 ends (i.e., at a longitudinal position downstream of plate 318), the flowing fluids 316 and 332 come into contact with each other and begin to interact within the integral outer conduit 334. The longitudinal positions of the ends of plates 314 and 318 may be the same, although this is not required. In some embodiments, the end of one of plates 314 and 318 is located at a different position than the end of the other of plates 314 and 318. The interaction of fluids 312, 316, and 332 produces reaction product 320. In embodiments, reaction product 320 may be an extruded structure 320, such as a hydrogel sheet or film.

[0175] Fluids 312 and 316 converge (i.e., contact) at a contact area 323 (which may include a contact surface 323). In the embodiment illustrated in FIG. 13, the contact area 323 coincides with the downstream end of plate 314. At the contact area 323, fluids 312 and 316 begin to react with each other to create a reaction interface region 321 downstream of the contact area 323. The contact area 323 may be at the upstream end of the reaction interface region 321. Fluids 312 and 316 may contact each other in the contact area 323 and may be separated from each other downstream of the contact area 323 by a first reaction product 320A. At the contact area 323 where fluids 312 and 316 contact, and downstream of the contact area 323 in the reaction interface region 321, a chemical reaction or other reaction such as a change of state may occur between fluids 312 and 316. In some embodiments, fluid 312 may include a solvent and a concentration of C a The reactive substance A, while fluid 316 includes a solvent and a concentration of C. b Reactive substance B. Downstream of the contact region 323 in the contact region 323 of fluids 312 and 316 and in the reaction interface region 321, a chemical reaction between reactive substance A and reactive substance B produces a first reaction product 320A. In the embodiment of Figure 13, the reaction can be confined to a generally flat reaction interface region 321 downstream of the contact region 323. The reaction interface region 321 (and reaction product 320A) can grow in transverse thickness as fluids 312 and 316 flow longitudinally 311 (e.g., reaction product 320A can grow in its cross-sectional dimension (in...). Figure 13B (The thickness is shown in the vertical direction).

[0176] Fluids 316 and 332 converge (i.e., contact) at a contact area 327 (which may include a contact surface 327). In the embodiment illustrated in FIG. 13, the contact area 327 coincides with the downstream end of plate 316. At the contact area 327, fluids 316 and 332 begin to react with each other to create a reaction interface region 325 downstream of the contact area 327. The contact area 327 may be located at the upstream end of the reaction interface region 325. Fluids 316 and 332 may contact each other in the contact area 327 and may be separated from each other downstream of the contact area 327 by a second reaction product 320B. Reaction products 320A and 320B may be collectively referred to herein as reaction product 320. A chemical reaction or other reaction, such as a change of state, may occur between fluids 316 and 332 at the contact area 327 where fluids 316 and 332 contact, and downstream of the contact area 327 in the reaction interface region 325. In some embodiments, fluid 316 may include a solvent and a concentration of C b The reactive substance B, while fluid 332 contains a solvent and a concentration of C. c The reactive substance C. In some embodiments, the reactive substance C of fluid 332 is the same as the reactive substance A of fluid 312, although this is not necessary. Downstream of the contact region 327 where fluids 316 and 332 contact and in the reaction interface region 325, a chemical reaction between reactive substance B and reactive substance C produces a second reaction product 320B. In the embodiment of FIG. 13, the reaction may be confined to a generally flat reaction interface region 325 downstream of the contact region 327. The reaction interface region 325 (and the reaction product 320B) may grow in transverse thickness as fluids 316 and 332 flow longitudinally 311 (e.g., the reaction product 320B may grow along its cross-sectional dimension (in Figure 13B The thickness is shown as vertical.

[0177] Device 310 can be used to create conditions that prevent or mitigate the mixing of miscible flowing fluids 312, 316 and 316, 332 (e.g., in reaction interface regions 321, 325 between flowing fluids 312, 316, 332). Such conditions can be characterized, for example, by the local Reynolds numbers (local Re, defined using the viscosity of reaction products 320A, 320B) of the reaction products 320A, 320B in the interface regions 321, 325 between fluids 312, 316 and 316, 332. Such conditions can also be characterized by the Damköhler value (Da) of the reaction and the respective Reynolds numbers (Re1, Re2, Re2), fluid velocities (u1, u2, u3), and flow rates (Q1, Q2, Q3) of fluids 312, 316, 332. The velocities u1, u2, and u3 of fluids 312, 316, and 332 can be defined by dividing the flow rates Q1, Q2, and Q3 of fluids 312, 316, and 332 by the area of ​​their respective pipes upstream of the contact areas 323 and 327.

[0178] As described above, the Reynolds number described and / or claimed herein should be considered at or downstream of the location where the different fluids first come into contact with each other (e.g., at or downstream of contact areas 323, 327). At this location (and downstream of this location), the characteristic dimension d can be considered as the cross-sectional dimension of the outer conduit 334. For example, in the case of device 310, the Reynolds number should be considered at or downstream of contact areas 323, 327 where the characteristic dimension d is the cross-sectional dimension of the outer conduit 334. Thus, the Reynolds numbers of fluids 312, 316, 332 at or downstream of contact areas 323, 327 can be characterized. The “local” Reynolds number (local Re) of reaction product 320A at or downstream of the contact area where fluids 312 and 316 first contact (e.g., at or downstream of contact area 323 between fluids 312 and 316 in the embodiment of FIG. 13) and the “local” Reynolds number (local Re) of reaction product 320B at or downstream of the contact area where fluids 316 and 332 first contact (e.g., at or downstream of contact area 327 between fluids 316 and 332 in the embodiment of FIG. 13) can also be described. The local Re of reaction product 320A can be expressed as Where ρ is the characteristic density of fluids 312, 316, and 332 (where this characteristic density can be reduced to the characteristic density of water at its dilution limit), d is the characteristic dimension scale (e.g., the cross-sectional dimension of the outer pipe 334), and u c It is a speed parameter, defined as the total flow rate Q. t =∑ i Q i (Where Q1 is the flow rate of the first fluid 312, Q2 is the flow rate of the second fluid 316, and Q3 is the flow rate of the third fluid 332) In addition to the cross-sectional area of ​​the pipe 334, μp This is the apparent viscosity of the reaction product (e.g., reaction product 320A). Similarly, the local Re of reaction product 320B can be expressed as... Where ρ is the characteristic density of fluids 312, 316, and 332 (where this characteristic density can be reduced to the characteristic density of water at its dilution limit), d is the characteristic dimension scale (e.g., the cross-sectional dimension of the outer pipe 334), and u c It is a speed parameter, defined as the total flow rate Q. t =∑ i Q i (Where Q1 is the flow rate of the first fluid 312, Q2 is the flow rate of the second fluid 316, and Q3 is the flow rate of the third fluid 332) In addition to the cross-sectional area of ​​the pipe 334, μ p It is the apparent viscosity of the reaction product (e.g., reaction product 320B).

[0179] The Reynolds numbers (Re1, Re2, Re2) of fluids 312, 316, and 332 at or downstream of their initial contact points (e.g., at or downstream of contact areas 323 and 327) can be determined according to... and Defined, where μ1, μ2, and μ3 are the viscosities of fluids 312, 316, and 332 respectively, and other parameters have the same meaning. The Damköhler value (Da) of the reaction in device 310 (and other devices described herein) can be determined according to... Define, where r a It is the reaction rate r a =kC X Where k is a rate constant specific to a particular reaction, and C X This represents the concentration of substance X in the reaction; the other parameters have the same meaning as described above.

[0180] Based on the local rheological properties of fluids 312, 316, and 332, the flow rates (Q1, Q2, Q3) of the first fluid 312, the second fluid 316, and the third fluid 332 can be set (the influence of which is as described above on parameter u). cThis allows the Reynolds number Re1 of fluid 312, Re2 of fluid 316, and / or Re3 of fluid 332 to be greater than 100, 500, 1000, or 2000. In some embodiments, at least one of fluids 312, 316, and 332 may have a Reynolds number greater than 100, 500, 1000, or 2000. In some embodiments, at least two (or all) of fluids 312, 316, and 332 may have a Reynolds number greater than 100, 500, 1000, or 2000. If the rheological properties of any of fluids 312, 316, and 332 are non-Newtonian, the viscosity of the fluid used in the definition of the Reynolds number can be estimated at the nominal shear rate, i.e., u. c / d.

[0181] The reaction rates between the flowing fluids 312 and 316 in reaction interface region 321 and between the flowing fluids 316 and 332 in reaction interface region 325 can typically be very large (e.g., compared to advection or diffusion timescales), resulting in large Darmquerel numbers (Da) for these reactions. In some embodiments, the components of fluids 312, 316, and 332 (e.g., reactants dissolved in fluids 312, 316, and 332) and / or other properties of fluids 312, 316, and 332 can be selected to provide a Darmquerel number (Da) of 10-10 in reaction interface regions 321 and / or 325. 6 The range of Damkoller numbers. In some embodiments, this range is 100-10. 5 In these reactive interface regions, the Damköhler value Da can be less than 10. 9 .

[0182] In reaction interface region 321, reaction product 320A is created by the reaction between fluids 312 and 316, while in reaction interface region 325, reaction product 320B is created by the reaction between fluids 316 and 332. The contact region 323 at the upstream end of reaction interface region 321 (e.g., where fluids 312 and 316 first contact and create reaction product 320A) and the contact region 327 at the upstream end of reaction interface region 325 (e.g., where fluids 316 and 332 first contact and create reaction product 320B) can be referred to as initial interfaces 323 and 327. Since fluids 312, 316, and 332 flow longitudinally along 311, they transport reaction product 320 forward, thus continuing the reaction in reaction interface regions 321 and 325 downstream of the initial interfaces 323 and 327. If fluids 312, 316, and 332 can continue to interact through reaction products 320A and 320B, further chemical reactions may occur, thereby thickening the lateral dimensions of the internal reaction product 320A and the external reaction product 320B at the reaction interface regions 321 and 325 downstream of the initial interfaces 323 and 327.

[0183] Reaction products 320A and 320B can exist as complete, continuous, and discrete materials from fluids 312, 316, and 332, and can exhibit well-defined interfaces, preventing reaction products 320A and 320B from mixing with fluids 312, 316, and 332. If reaction products 320A and 320B behave as fluids, then at the local Reynolds number Re of reaction product 320A... pA The local Reynolds number Re of reaction product 320B pB At sufficiently low levels, the shapes of reaction products 320A and 320B can remain continuous (and fluids 312 and 316, as well as 316 and 332, will not mix). In some embodiments, the local Reynolds number Re of reaction product 320A is... pA The local Reynolds number Re of reaction product 320B pB Less than 100, 50, 20, 10 or 1. If reaction products 320A and 320B are solids, their shapes can remain continuous when the stress applied to them (due to their movement or other reasons) is less than the ultimate strength of the materials of reaction products 320A and 320B.

[0184] The rheological properties of reaction products 320A and 320B can depend on the concentration of reactants. If reaction products 320A and 320B are solids and if the velocities u1, u2, and u3 of fluids 312, 316, and 332 vary over time, the shapes of reaction products 320A and 320B can remain continuous (their dimensions may change), and the applied shear stress (generated by the estimated movement at the interface) causes their movement to be less than the material strength of reaction products 320A and 320B. In addition to these criteria, reaction products 320A and 320B may not form continuous products, and the reactive substances (fluids 312, 316, and 332) may mix across reaction interface regions 321 and 325.

[0185] If the conditions allow reaction products 320A and 320B to form a continuous sheet or film, then for [C a C b C c Various combinations of μ1, μ2, μ3, μ1, μ2, μ3, ρ1, ρ2, ρ3, Da, D1, D3] allow the trajectories of reaction products 320A and 320B to remain approximately parallel to the longitudinal / flow direction 311, where μ1, μ2, μ3 are the apparent viscosities of fluids 312, 316, and 332; ρ1, ρ2, ρ3 are the densities of fluids 312, 316, and 332; and D1 and D3 are the diffusivity of reactants 312 and 316 dissolved in fluid 316 into reaction products 320A and 320B. If conditions allow reaction products 320 to form continuous reaction products 320A and 320B, the thickness of the reaction product wall may increase at locations 321 and 325 downstream of the initial interfaces 323 and 327. The mechanism by which the thickness increases downstream can be a diffusion process, i.e., reactive substances A and B diffuse into reaction interface region 321 and / or reaction product 320A, and reactive substances B and C diffuse into reaction interface region 325 and / or reaction product 320B. The growth of the walls of reaction products 320A and 320B can continue while reactive substances A, B, and C are still present in the system. Therefore, the lateral dimensions of the walls of reaction products 320A and 320B can be controlled by removing one or more reactive substances (e.g., by reaching the end of pipe 334 and allowing fluids 312, 316, 332 to be laterally spaced apart from or dispersed away from reaction products 120A and 120B).

[0186] The transverse dimensions of reaction products 320A and 320B can be further controlled by changing the inlet velocities u1, u2, and u3 upstream of the initial interfaces 323 and 327 (e.g., the ratio of inlet velocities u1, u2, and u3). If operated under suitable inlet velocity conditions, the transverse dimensions of reaction products 320A and 320B can be shaped accordingly. By changing the inlet velocity conditions, the transverse dimensions of reaction products 320A and 320B can be altered along their axial length.

[0187] Under certain conditions, reaction products 320A and 320B may merge to form a monolithic reaction product 320, although this is not necessary. In some embodiments, reaction products 320A and 320B may remain spaced apart from each other. In some embodiments, reaction products 320A and 320B may aggregate in space but may not form a monolithic reaction product. In some embodiments, reaction products 320A and 320B may exhibit mixing.

[0188] Cross-section shaping

[0189] The inventors also tested the volumetric flow rates (Q1, Q2) of the internal fluid 12 and external fluid 16 of the device 10 in Figure 1 over time between two previously established stable operating condition sets to determine the effect of time variation on the shape of the reaction product (hydrogel tubing) 20. Figure 14A A representative cycle illustrating how the volumetric flow rates (Q1, Q2) of the internal fluid 12 and external fluid 16 change within device 10 according to a specific experiment is shown. Figure 14A In the specific experiment shown, this waveform of volumetric flow rate change was repeated every 3.0 seconds. Figure 14B It shows Figure 14A The change in volumetric flow rate affects the outer radius of the reaction product (tube 20) (in Figure 14B The result is shown as r). Specifically, Figure 14B The outer radius r of reaction product 20 and the inner radii of outer pipes 18 and 19 are shown (in... Figure 14B The ratio of R to tf is shown in the figure. c The relationship is given by f, where t is time and f is time. c = (3.0s) -1 yes Figure 14A The frequency of the volumetric flow rate cycle. Figure 14BThe diagram illustrates how changing the relative flow rates (Q1, Q2) of the inner fluid 12 and the outer fluid 16 results in a corresponding change in the inner radius r (i.e., inner diameter) of the reaction product 20. Specifically, as the volumetric flow rate Q1 of the inner fluid 12 increases relative to the volumetric flow rate Q2 of the outer fluid 16, the outer diameter of the reaction product 20 increases (i.e., the reaction product 20 becomes thicker), while as the volumetric flow rate Q1 of the inner fluid 12 decreases relative to the volumetric flow rate Q2 of the outer fluid 16, the outer diameter of the reaction product 20 decreases (i.e., the reaction product 20 becomes thinner).

[0190] Applications – Blood Compatibility

[0191] The inventors tested tubes 20 and 120 extruded from devices 10 and 110 under fluid pressures up to 35 kPa (far above the potential range of human blood pressure (~9-25 kPa)) and even close to the arterial lumen pressure (~46 kPa) and venous lumen pressure (~35 kPa) of a hemodialysis machine. Because previous reports have indicated that material spalling (or the release of tube fragments from the lumen surface of the ECC tube into the bloodstream) promotes blood clot formation and is a major impairment of blood compatibility, several long-term flow studies were conducted using tube 20 (t>200 hours, Q=68 mL / min, using 50% glycerol). The inventors have observed experimental limitations for wall thickness variations greater than ~200 μm, demonstrating promise in limiting spalling for blood transport.

[0192] Figure 12A This schematically illustrates that the adsorption of pro-inflammatory complement proteins, platelet adhesion, and erythrocyte hemolysis are important markers of biocompatibility between the material and whole blood. Specifically, Figure 12A A schematic diagram of platelet-mediated thrombosis on ECC tubing is shown. Figure 12B An experimental setup was shown to demonstrate how the inventors tested the blood compatibility of extruded hydrogel tubing 20 under ECC-like conditions using alginate as the internal fluid 12 and CaCl2 and MgCl2 as the external fluids 16. Figure 12B The tube 40 comprises a PVC tube segment 42 and a hydrogel tube 20 (tube segment 44) formed using the device 10, connected in series (made with 3% alginate as the inner fluid 12 and 2% CaCl2 and MgCl2 as the outer fluid 16). The tube 40 is filled with whole blood. Figure 12B (i)-(iv) show scanning electron microscopy (SEM) images of the inner walls of the PVC tube portion 42 and the hydrogel tube portion 44 before and after whole blood culture. Specifically, Figure 12B (i)-(ii) show the PVC pipe 42 before and after cultivation, while Figure 12B(iii)-(iv) show the hydrogel tubing 44 formed using device 10 before and after culture. These SEM images show a significant reduction in platelet adhesion and activation on the hydrogel tubing 44 formed using device 10 (compared to PVC tubing 42).

[0193] Figure 12C This demonstrates the quantification of lactate dehydrogenase (LDH) release at [a certain level]. Figure 12B Platelet deposition on the material surface of the tube portion (PVC tube portion 42 and hydrogel tube portion 44). Figure 12C This indicates that after 4 hours of whole blood circulation, the extruded hydrogel tube portion 44 rapidly reduced platelet adhesion by approximately 6 times compared to the PVC tube portion 42. Figure 12D This shows the effects of pro-inflammatory complement protein C3 after whole blood exposure. Figure 12B Deposits were found on the inner walls of the PVC pipe section 42 and the hydrogel pipe section 44. Paired comparisons using a nonparametric t-test showed significance with p < 0.001. That is, Figure 12C and 12D The data present strong evidence to reject the null hypothesis. Deposition of pro-inflammatory C3 complement protein and erythrocyte hemolysis are similar in both materials, suggesting that the extruded hydrogel tubing portion 44 performs similarly to the clinical-standard PVC tubing portion 42.

[0194] As described above, regarding device 10, hydrogel tubing (reaction product) 20 is formed in situ (e.g., within device 10) by a reaction (e.g., a crosslinking reaction), wherein the local Reynolds number of reaction product 20 in the reaction interface region 21 is [missing information]. Compared to diffusion and advection timescales, reaction rates (e.g., gelation or polymerization) are extremely rapid. These methods and apparatuses can be extended to apparatus 110 of Figure 10, which features an inertial three-layer extrusion apparatus (where the chemical composition between the layers is combined with local rheological properties).

[0195] Blood compatibility test

[0196] Whole blood from healthy donors was collected into citrate vacuum blood collection tubes. Heparin was added to the collected blood to a final concentration of 0.7 U / mL, and the blood was recalcified before each experiment by adding calcium chloride solution to achieve a final concentration of 2.2 mM.

[0197] A closed loop was fabricated using 25cm medical-grade PVC tubing, which was then connected to an extruded tubing 20 with an approximately 7cm inner diameter (approximately 3.18mm). The mechanical properties of the extruded tubing 20 were pre-analyzed using dynamic mechanical analysis (TA Instruments). TMThe DMA Q800 was used to check the flow pressure drop along a 1-m length of a sample with an open, blocked sample. The volumetric flow rate was set using a syringe pump, with the deflection of the inner wall measured using an optical coherence tomography (OCT) scanner (ThorLabs). TM Record. The estimated value of the circumferential stress is determined by the following relationship.

[0198]

[0199] Where R i (P) and R o (P) represents the inner and outer radii of the pipe under fluid pressure P (standard measurement).

[0200] The hybrid tubing rings used for blood compatibility testing were placed in a peristaltic roller pump (WF300-TH16, PreFluid) and sterilized for 5 minutes with 70% ethanol at a flow rate of 68 mL / min. The rings were then thoroughly rinsed with sterile phosphate-buffered saline (PBS). Blood was introduced into the rings before inserting it into the roller pump. All air bubbles were removed by allowing the blood to flow against gravity. The blood was circulated in the rings at 37°C for 4 hours at 68 mL / min, similar to the shear stress acting at the boundary of extracorporeal circulation (ECC). After circulation, the blood was removed from the tubing, the substrate was gently washed with PBS buffer, and incubated in PBS for 2 hours prior to further analysis.

[0201] Hemolysis measurements were recorded before and after circulation to observe the effect of circulation on erythrocyte damage. 1 mL of recalcified and heparinized whole blood samples were collected before and after circulation and centrifuged at 12 kg for 2 minutes. 100 μL of the supernatant was taken from the centrifuged samples and added to 550 μL of Drabkins solution. The erythrocytes were analyzed by UV / Vis spectroscopy (λ). abs =540nm) The hemoglobin content of the supernatant was measured in triplicate.

[0202] Four hours after exposure to blood, the washed 1 cm tube segment was fixed overnight with 2.5% glutaraldehyde. The tube was longitudinally cut to obtain a flat material sheet and washed three times with PBS. The sample was then coated with FITC-labeled anti-human component C3 monoclonal antibody (product number CL7631F, Cedarlane). TM The sample (from Canada) was incubated for 1 hour at room temperature in PBS buffer (0.5 mL, 1:20 dilution). A second sample was incubated in PBS buffer with a FITC-labeled mouse IgG1 isotype control at the same concentration and conditions as the C3 antibody. Both samples were washed three times with PBS and imaged using confocal microscopy. Specific protein adsorption was determined by measuring the intensity difference between the C3 antibody and the isotype sample.

[0203] Lactate dehydrogenase (LDH) assays were also used to quantify platelet adhesion on the printed tubes. A 2cm section of PBS-washed tube was incubated for 1 hour at room temperature with 1.5 mL of 0.1% Triton X-100 buffer. The platelet adhesion was determined according to a commercial kit (Biovision). TM The LDH-cytotoxicity assay kit provides a protocol for measuring LDH activity in the supernatant in triplicate. A calibration curve is created using a series of dilutions of known concentrations of platelet suspension lysed under identical conditions.

[0204] For scanning electron microscopy (SEM) (Hitachi) TM Samples from three independent blood circulation experiments (i.e., three donors) were prepared using an S3000N VP-SEM. The inner surface of the tubing was gently washed three times with 1 mL of PBS buffer (0.15 M) for 10 seconds each time, followed by fixation in 2.5% glutaraldehyde with PBS (1 mL) for 1 hour. The tubing was then cut into quadrants to expose the inner surface, rinsed three times with PBS, then three times with milli-Q water, and dehydrated by standard critical point drying. The samples were sputter-coated with gold (Edwards S150 Sputter Coater) to enhance contrast. SEM images were taken at five random locations on the inner wall of the tubing using a 10 kV operating voltage and 1000x magnification.

[0205] While several exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain modifications, arrangements, additions, and partial combinations thereof. Therefore, the appended claims are intended to be interpreted as including all such modifications, substitutions, additions, and partial combinations consistent with the broadest interpretation of the entire specification.

Claims

1. A method for moving materials to create reaction products, the method comprising: The first fluid is made to flow axially, and the first fluid is characterized in that inertial force dominates the viscous force of the first fluid. The second fluid flows axially, and the first fluid and the second fluid are miscible. The first fluid and the second fluid are brought into contact with each other to create an axially extending interface region between the first fluid and the second fluid and to allow the reaction to create reaction products in the interface region; The reaction products reduce turbulent mixing between the first and second fluids and allow the first and second fluids to flow axially as stratified fluids.

2. The method of claim 1, wherein the first fluid and the second fluid have a contact region in the upstream range of the interface region, and the first fluid and the second fluid are in contact with each other in the contact region.

3. The method according to claim 1, wherein the inertial force of the first fluid is greater than the viscous force of the first fluid, such that the Reynolds number of the first fluid at the axial position corresponding to the upstream range of the interface region is greater than 100.

4. The method according to claim 1, wherein the inertial force of the first fluid is greater than the viscous force of the first fluid, such that the Reynolds number of the first fluid at an axial position corresponding to the upstream range of the interface region is greater than 500.

5. The method of claim 1, wherein the second fluid is characterized in that inertial force dominates the viscous force of the second fluid.

6. The method of claim 5, wherein the inertial force of the second fluid is greater than the viscous force of the second fluid, such that the Reynolds number of the second fluid at an axial position corresponding to the upstream range of the interface region is greater than 100.

7. The method of claim 5, wherein the inertial force of the second fluid is greater than the viscous force of the second fluid, such that the Reynolds number of the second fluid at an axial position corresponding to the upstream range of the interface region is greater than 500.

8. The method of claim 1, wherein the flow of one or more of the first fluid and the second fluid is turbulent flow.

9. The method of claim 1, wherein the reaction in the interface region is characterized by a Damkohler number less than 10 9 .

10. The method of claim 1, wherein the reaction in the interface region is characterized by a Damcoller value of 10-10. 6 Within the range.

11. The method of claim 1, wherein the reaction in the interface region is characterized by a Damcoller value of 100-10. 5 Within the range.

12. The method of claim 1, wherein the reaction product flows axially and the local Reynolds number in the interface region is less than 100.

13. The method of claim 1, wherein the reaction product flows axially and the local Reynolds number in the interface region is less than 20.

14. The method of claim 1, further comprising modifying one or more of a first fluid inlet velocity and a second fluid inlet velocity to control the cross-sectional dimensions of the reaction product.

15. The method of claim 1, wherein in the interface region, the rate of change of rheological properties associated with the reaction is greater than the advection rate of the first fluid and the second fluid.

16. The method of claim 1, wherein the reaction in the interface region causes a change in local rheological properties, wherein the ratio of local viscous force to local inertial force in the interface region is less than 1.

25.

17. The method of claim 1, wherein the reaction causes a change in local rheological properties in the interface region, wherein the viscous force in the interface region is less than the inertial force in the interface region.

18. The method of claim 1, wherein the first fluid is a solution of the first reactant, and the second fluid is a solution of the second reactant.

19. The method of claim 18, wherein the first reactant is a polyvalent cation, the second reactant is an alginate, and the reaction product is a hydrogel.

20. The method of claim 19, wherein the concentration ratio of the first reactant to the second reactant is less than or equal to 4.

21. The method of claim 19, wherein the concentration ratio of the first reactant to the second reactant is greater than or equal to 0.

5.

22. A method for moving materials to create reaction products, the method comprising: To make the first fluid flow axially; To make the second fluid flow axially; The first fluid and the second fluid are brought into contact with each other to create an axially extending interface region between the first fluid and the second fluid and to allow the reaction to create reaction products in the interface region; The Reynolds number of the first fluid at the axial position corresponding to the upstream range of the interface region is greater than 500; and The reaction products have a local Reynolds number of less than 100 in the interface region, and the first fluid and the second fluid flow axially as stratified fluids.

23. The method of claim 22, wherein the first fluid and the second fluid have a contact region at the upstream extent of the interface region, and the first fluid and the second fluid are in contact with each other at the contact region.

24. The method of claim 22, wherein the first fluid and the second fluid are miscible with each other.

25. The method of claim 22, wherein the Reynolds number of the first fluid at an axial position corresponding to the upstream extent of the interface region is greater than 1000.

26. The method of claim 22, wherein the Reynolds number of the second fluid at an axial position corresponding to the upstream range of the interface region is greater than 500.

27. The method of claim 22, wherein the Reynolds number of the second fluid at the axial position corresponding to the upstream range of the interface region is greater than 1000.

28. The method of claim 22, wherein the local Reynolds number of the reaction product in the interface region is less than 10.

29. The method of claim 22, wherein the reaction in the interface region is characterized by a Damköhler value of 10-10. 6 Within the range.

30. The method of claim 22, wherein the reaction in the interface region is characterized by a Damcoller value of 100-10. 5 Within the range.

31. The method of claim 22, wherein the flow of one or more of the first fluid and the second fluid is turbulent flow.

32. The method of claim 22, further comprising modifying one or more of a first fluid inlet velocity and a second fluid inlet velocity to control the cross-sectional dimensions of the reaction product.

33. The method of claim 22, wherein in the interface region, the rate of change of rheological properties associated with the reaction is greater than the advection rate between the first fluid and the second fluid.

34. The method of claim 22, wherein the reaction in the interface region causes a change in local rheological properties, wherein the ratio of local viscous force to positional inertial force in the interface region is less than 1.

25.

35. The method of claim 22, wherein the reaction causes a change in local rheological properties in the interface region, wherein the viscous force in the interface region is less than the inertial force in the interface region.

36. The method of claim 22, wherein the first fluid is a solution of the first reactant, and the second fluid is a solution of the second reactant.

37. The method of claim 36, wherein the first reactant is a polyvalent cation, the second reactant is an alginate, and the reaction product is a hydrogel.

38. The method of claim 37, wherein the concentration ratio of the first reactant to the second reactant is less than or equal to 4.

39. The method of claim 37, wherein the concentration ratio of the first reactant to the second reactant is greater than or equal to 0.

5.

40. A method for moving a material, the method comprising: Provide a first fluid that flows axially; A second fluid is provided that flows axially, and the first fluid and the second fluid are miscible with each other; The first fluid and the second fluid are brought into contact with each other to create an axially extending interface region between the first fluid and the second fluid and to allow a reaction to occur in the interface region; The reaction creates locally unmixed conditions, thereby reducing the mixing between the first fluid and the second fluid and allowing the first fluid and the second fluid to flow axially as stratified fluids.

41. The method of claim 40, wherein contacting the first fluid and the second fluid with each other comprises generating a reaction product in the interface region, the reaction product alleviating mixing between the first fluid and the second fluid.

42. The method of claim 40, wherein contacting the first fluid and the second fluid with each other comprises providing a state change of at least one of the first fluid and the second fluid in the interface region, the state change mitigating mixing between the first fluid and the second fluid.

43. A method for moving a material along an axial direction, the method comprising: Provide a first fluid that flows axially; A second fluid is provided that flows axially, and the first fluid and the second fluid are miscible with each other; The first fluid and the second fluid are brought into contact with each other to create an axially extending interface region between the first fluid and the second fluid; The properties or composition of the first fluid are provided to react with the second fluid in the interface region, thereby reducing the local Reynolds number in the interface region to below 100; The first fluid and the second fluid have a Reynolds number greater than 500 at an axial position corresponding to the upstream range of the interface region, and the first fluid and the second fluid flow axially as stratified fluids.

44. A method for moving a material, the method comprising: To make the first fluid flow axially; To make the second fluid flow axially; The first fluid and the second fluid are brought into contact with each other to create an axially extending interface region between the first fluid and the second fluid, the first fluid and the second fluid flowing under miscible conditions; and The first fluid and the second fluid react to create local immiscibility between the first fluid and the second fluid in the interface region, and the first fluid and the second fluid flow axially as stratified fluids.

45. A method for moving a material, the method comprising: To make the first fluid flow axially; To make the second fluid flow axially; The first fluid and the second fluid are brought into contact with each other to create an axially extending interface region between the first fluid and the second fluid; The first fluid and the second fluid react in the interface region, thereby generating a local Reynolds number of less than 100 in the interface region; The first fluid and the second fluid have a Reynolds number greater than 500 at the axial position corresponding to the upstream range of the interface region, and the first fluid and the second fluid flow axially as stratified fluids.

46. ​​A method for moving a material, the method comprising: To make the first fluid flow axially; To make the second fluid flow axially; The first fluid and the second fluid are brought into contact with each other to create an axially extending interface region between the first fluid and the second fluid; and Allowing a reaction to occur between the first fluid and the second fluid in the interface region; in: The Reynolds number of the first fluid and the second fluid at the axial position corresponding to the upstream range of the interface region is greater than 500; The reaction between the first fluid and the second fluid will produce a local Reynolds number of less than 100 in the interface region; The reaction between the first fluid and the second fluid has a time interval of 10-10. 6 The range of Damcohl values; and The first fluid and the second fluid flow axially as stratified fluids.

47. The method according to any one of claims 1-46, wherein the shape of the first fluid flow is rectangular in a cross-section transverse to the axial direction.

48. The method according to any one of claims 1-46, wherein the shape of the second fluid flow is rectangular in a cross-section transverse to the axial direction.

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