The effect of volume loading on the extrusion of bimodal glass bead mixtures | npj Advanced Manufacturing

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Additive manufacturing has provided new methods for generating complex geometries of composite energetic materials. Additive manufacturing of ammonium-perchlorate composite propellants through direct-ink-write experiences extrusion limitations due to the high viscosities of highly solids loaded propellants. Vibration-assisted printing (VAP) was developed as a method to extend the extrudability limits and extrusion speeds observed with direct-ink-write systems. This study compares the mass flowrates and extrudability limits for bimodal mixtures of glass beads and hydroxyl-terminated polybutadiene (HTPB) binder for both VAP and direct-ink-write printing as a function of volume percent solids loading. The VAP system was able to print higher volume loadings and significantly higher mass flowrate than the direct-ink-write system. The bimodal glass bead mixtures were also compared to a previous study that focused on the extrusion of monomodal glass beads/HTPB mixtures. Interestingly, bimodal mixtures were shown to extrude quicker than monomodal mixtures at all volume loadings and across both printing systems.

Advancements in additive manufacturing (AM) have been used in many industries to fabricate unique geometries that are either difficult or impossible to achieve utilizing traditional manufacturing techniques. The rapid production of intricate geometries has been observed with a variety of materials1,2,3. These materials include polymers1,4, metals5,6,7,8, energetic materials9,10,11,12,13,14,15,16,17,18, food production19,20,21,22, batteries23, and slurries of ceramics and concrete24,25,26,27,28,29,30,31,32,33. The advancements in additive manufacturing have been driven by improvements in printing techniques such as fused deposition modeling (FDM), direct-ink-write (DIW)34,35, vat photopolymerization36, and stereolithography37. These different printing methods each have their advantages and disadvantages. The printing methods that apply to composite mixtures are limited by the volume loading of solid particles that can be extruded. This may not be an issue in all industries, but when applying these techniques to energetic materials, the ability to print highly loaded mixtures is critical to the density, and therefore performance, of the printed materials. Many metrics of performance for energetic materials are closely related to a material’s density and solids loading. The increase in density due to the increased percentage of solid particles in the mixture leads to a higher energy density and performance (specific impulse, detonation velocity, detonation pressure) for the energetic material38. However, when extruding highly loaded mixtures, the increased percentage of solid particles can lead to inconsistent flowrates, jamming, de-wetting, and complete blockage of the flow.

The difficulties of extrusion apply to both suspended solid particles and non-suspended solid particles. Force chains and mechanical arching can occur, creating blockages near the nozzle outlet or within narrow channels39,40. In the agricultural industry, studies have shown that solid flow is affected by particle size, nozzle angle, and nozzle outlet diameter41,42,43,44,45. Although this study focuses on solid particles suspended in binder, the methods used to prevent clog formation and control mass flowrate of non-suspended solid particles provides the framework for solutions that can be applied to suspended solid particles. One of the common solutions for mass flowrate control and clog prevention of solid and suspended particles, used in the agricultural industry, is incorporating vibrational perturbations. The use of vibrations was shown to provide flowrate control, unjamming of particles, and prevention of the formation of clogs46,47,48. The prevention of clogs and unjamming of particles was attributed to breaking the force chains and mechanical arches that formed within the solid flow, typically near the nozzle outlet49.

The addition of vibrations was shown to influence solid flow behavior; however, the main interest of this study pertains to suspended solid particles. A study by Sehgal et al. examined the use of acoustic perturbations to tune the shear thickening of colloidal suspensions40. The study demonstrated that the acoustic perturbations resulted in a viscosity of the suspension that could be dynamically tuned, allowing the viscosity to be lowered. The authors theorized that the reduction in shear thickening and subsequent decreases in viscosity are results of the acoustic perturbations disrupting the force chains that form within the colloidal suspension. The study also mentions that the acoustic perturbations not only allow for viscosity control, but function to increase the mass flowrate and unclog the system40. This similar ability to break force chains and alter the behavior of granular flow with vibrational perturbations shows a connection between the methods used for flow control of both suspended and non-suspended solid particles. In addition to disrupting force chains and mechanical arches, the application of vibrations has been shown to reduce the coefficient of friction and the required extrusion force for different materials49,50,51,52. The use of ultrasonic vibrations in direct-ink-write printing, known as vibration-assisted printing (VAP), has been recently utilized to tune the suspension viscosity of both inert and energetic solid particle suspensions11,53.

Vibration-assisted printing has shown improvements compared to traditional direct-ink-write printing. DIW printing is typically accomplished through two methods. The first is ram extrusion, which uses applied back pressure to extrude the material. The second is auger screw extrusion, which uses an auger screw to extrude the material through the nozzle outlet. Traditional direct-ink-write printing has been used to successfully print composite mixtures; however, these mixtures are typically limited by the volume loading of solid particles that can be extruded (< 65 vol.%) due to the high viscosities of highly loaded solid particle suspensions11,54,55. Increasing the back pressure or force of the auger screw is required to overcome the viscosity of the highly loaded suspensions, potentially leading to increased flowrate and solids loading that can be extruded. The use of high pressures when printing has drawbacks as it can cause flowrate inconsistencies, sputtering of the print material, and liquid phase filtration (de-wetting)11,56. When considering DIW printing for extrusion of energetic materials, the increased back pressure required to extrude highly loaded suspensions could also lead to safety concerns. Extrudable inks are another method used to overcome the difficulty of extruding high solids loading composites with direct-ink-write57,58. These methods typically use a solvent to reduce the mixture viscosity and have been shown to extrude aluminum/AP/hydroxyl-terminated polybutadiene (HTPB) mixtures up to 91 wt.% solids loading57. A recent study using pressure-assisted binder jetting by Kirby et al. printed mock energetic composites consisting of granular sugar and HTPB with densities up to 83.4% theoretical maximum density and solids loadings up to 95.4 wt.%59. This method consists of first transferring a small amount of powder to the print bed, that powder is then compacted at a specified pressure. After the powder is compressed, binder is deposited onto the layer. This process continues until the specified object has been printed. Considerable applied pressure (3–9 MPa), which as previously mentioned has associated safety concerns with energetic materials, was required to achieve the specified density and solids loading results. A considerable amount of solvent (55 wt.% hexane dilute solvent) was also used for the binder formulation. A drawback to solvent extrusion is that during the curing process of the printed materials, the solvent evaporation can lead to high porosity and lower densities.

The development of vibration-assisted printing has been shown to overcome the issue of printing high solids loaded mixtures which limit traditional direct-ink-write printing. VAP has been shown to be able to print complex geometries with a volume loading of 75 vol.% (85 wt.% AP), a large increase compared to DIW printing11. Although VAP has shown improvements over DIW printing, the printing technique still has aspects that require characterization, and the parameter space has not been mapped out. The effect of different high-amplitude vibrations on the printing parameters was characterized in a recent study by Fleck et al., which showed a direct relationship between increasing the high-amplitude vibrations and the nozzle temperature60. This nozzle temperature is important to characterize as the increased temperature alters the viscosity of the extruded material. Vibration-assisted printing and traditional direct-ink-write printing were compared by Afriat et al., where the turning ability, feature resolution, print speed, overhang, and porosity for a polymer clay were compared16. The results of the study showed higher print speed, print resolution, turning ability, and consistency of porosity for the VAP system compared to the DIW system. VAP and DIW extrusion were also compared directly by Montaño et al. and the results showed that the VAP system could extrude at higher mass flowrates for all volume loadings tested61. The study by Montaño et al. only examined monomodal mixtures of glass beads and binder, not multiple particle distributions61. Bimodal mixing can be used to increase the packing density and decrease the viscosity of a mixture, compared to monomodal mixtures. The increased packing density results from the ability of the fine particles to fill the interstices between the coarse particles62,63,64. The decreased viscosity for a bimodal mixture has been observed experimentally and was attributed to the release of capillary forces within the suspension65,66,67. Bimodal mixing has been shown to drastically reduce the viscosity of the mixture compared to monomodal mixtures at the same volume loading of solid particles65. A study by McGeary examined the mechanical packing of different sized spherical particles, including single, binary, ternary, and quaternary packings63. The results for the bimodal spherical packing showed that the coarse to fine weight ratio for optimal packing density was 72.7:27.3 and the ideal particle size ratio between the coarse and fine particles was approximately 7 to 1.

The objectives of this work were to explore the parameter space of bimodal glass bead mixtures and demonstrate a methodology to determine the mass flowrate for a range of volume loadings and the maximum extrudable volume loading achievable for a specific nozzle diameter, extrusion technique, back pressure, and formulation. An instrumented test stand was used to compare the mass flowrate of a bimodal mixture of glass beads and binder for both vibration-assisted and direct-ink-write extrusion. In addition, the results of this study are compared to the extrusion study of various sized monomodal glass bead mixtures by Montaño et al.61.

An experimental study was conducted to compare the mass flowrate of a bimodal mixture of glass beads suspended in HTPB binder for vibration-assisted printing and traditional direct-ink-write printing. The mass flowrate comparison as volume loading increases for the VAP and DIW printing is shown in Fig. 1. The mass flowrate for each printing method is shown as well as the volume loading at which the extrudability limit was reached, denoted with a hollow symbol. The extrudability limit is defined as the volume loading at which the mixture can no longer be extruded from the nozzle. A linear trend was observed for both printing methods and the error bars denote the standard error, which was calculated as the standard deviation divided by the square root of the number of samples tested for each volume loading. The results of the mass flowrate comparison of VAP and DIW printing for the bimodal suspension of glass beads in HTPB showed not only higher mass flowrates for the VAP system, but a larger range of extrudable volume loadings. The DIW samples reached an extrudability limit at 72.26 vol.%, whereas the VAP samples did not reach an extrudability limit until tested at a volume loading of 79.49 vol.% (91.5 wt.% glass beads). Both printing techniques had decreased mass flowrates as volume loading was increased. This was likely a result of the increased percentage of solid particles leading to more geometric interactions between particles. These interactions are related to the viscosity of the mixture, as several studies have shown an increased viscosity as volume loading of solid particles increases67,68. The DIW samples only have the applied back pressure to disrupt the force chains that form as the solid loading increases, which caused geometric blockages and eventually a full extrusion stoppage. The liquid binder may still respond to the back pressure and result in liquid phase filtration (de-wetting) of the suspension, functionally increasing the solid loading of the remaining mixture in the syringe reservoir. This was observed in the bimodal samples tested with direct-ink-write printing as small amounts of material would be extruded at volume loadings higher than 72.26 vol.%, but this extrusion was likely due to the de-wetting of the binder from the solid particles. The mass flowrate recorded for these experiments was less than 0.025 g/min.

Trend lines are derived using a linear fit. VAP: m = −0.1297, b = 10.31 (R2 = 0.96); DIW: m = −0.2131, b = 14.86 (R2 = 0.99).

Unlike DIW printing, the additional force provided by the ultrasonic vibrations in VAP break the force chains that form within the solid particle suspensions. In addition to the shear thinning resulting from the vibrations, studies have shown the oscillatory motion and temperature increase due to the ultrasonic VAP tip have improved material flowrates. A study by Gunduz et al. showed that the oscillatory motion introduced causes wall slip between the material and the nozzle53, reducing the overall friction between the nozzle and particles as the wall moves away from the material. This breaks the force chains that form, reducing the clogging of the system and effectively reducing the viscosity since the wall friction is momentarily reduced due to vibration. The influence of temperature for the ultrasonic VAP tip was observed by Fleck et al.60. This study showed an increase in the flowrate of clay with increasing temperature, which was due to the decrease in viscosity of the material as temperature increases. This combination of viscosity reducing mechanisms due to the addition of vibrations to the system allowed the samples extruded with vibration-assisted printing to exceed both the mass flowrates and extrudability limits observed with traditional direct-ink-write printing.

The results of the bimodal mixture extrusion study were compared to the results of a HTPB suspended monomodal glass bead study by Montaño et al.61. Both studies compared the difference in extrusion rate for vibration-assisted printing and direct-ink-write printing. The closest particle diameter tested by Montaño et al.61 to the coarse sized glass bead used in the bimodal experiments was 167 μm. Figure 2 shows the comparison between the VAP and DIW monomodal extrusion results to the results of the bimodal extrusion study. The exponential fits shown for the monomodal results were reproduced from Montaño et al.61, who tested a volume loading of 53.36 vol.%. This volume loading was not tested in the bimodal extrusion study. The additional volume loading, which had a significantly higher mass flowrates than the other monomodal volume loadings, and the limited volume loadings tested before the extrusion limit was reached likely resulted in the difference in relationship between mass flowrates and volume loading for the bimodal and monomodal mixtures.

Monomodal (167 μm)61 and bimodal glass bead mixture extrusion comparisons for both VAP and DIW printing.

The results showed that the monomodal DIW printing has the lowest mass flowrates and lowest extrusion limit as it was unable to extrude past a volume loading of 65.4 vol.%. This result was expected as a monomodal mixture will have a higher viscosity than a bimodal mixture at the same volume loading65. The VAP bimodal glass bead results follow the same trend as the monomodal study, where the VAP test series extruded at faster mass flowrates and extruded at higher volume loadings than its DIW counterpart. These results are due to the reduced viscosity (heating) and friction resulting from the use of ultrasonic vibrations52,53,60. The DIW results for the bimodal glass bead mixture had both higher mass flowrates and extrudability limit (72.26 vol.%) than the monomial glass bead extrusion with vibration-assisted printing (69.81 vol.%). Both the monomodal vibration-assisted printing and the bimodal direct-ink-write test series have viscosity lowering attributes. The addition of vibrations has been shown to reduce the viscosity and bimodal mixtures, through the filling of interstitial voids between coarse particles, have also been shown to reduce viscosity40,62,63,64. The results of the bimodal direct-ink-write test series indicate that the viscosity reduction from the bimodal mixture was more substantial than the viscosity reduction due to the ultrasonic vibrations in the monomodal study. The bimodal test series using vibration-assisted printing had the highest mass flowrates and highest extrudability limit (79.49 vol.%) compared with all mixtures tested. The combination of bimodal particle packing, and the vibrational perturbations introduced by the ultrasonic VAP tip resulted in the most significant reduction in viscosity (or more precisely the resistance to flow), which led to the fastest mass flowrates and the highest extrudability limit.

The presented study continues to advance the field of additive manufacturing of energetic materials through the further characterization of vibration-assisted printing. This was accomplished by demonstrating the extrusion limits of the technique at a specified pressure and nozzle diameter as well the ability of vibration-assisted printing to print highly loaded mixtures of glass beads and binder (up to 78.45 vol.%), which is a limitation for direct-ink-write and other additive manufacturing techniques for energetic materials. In addition to the comparison to monomodal extrusion, glass beads were selected as the solid particle in the bimodal mixture to allow for characterization of bimodal extrusion performance for both vibration-assisted printing and direct-ink-write extrusion. This was done to allow for future comparison to bimodal ammonium perchlorate mixtures. Future research would examine the viability of these bimodal glass bead and binder formulations as simulants for similarly sized bimodal ammonium perchlorate and binder rocket propellant formulations. A similar performing simulant for AP mixtures would allow for further development of additively manufactured propellants without the use of energetic materials, improving safety. Future research efforts could also apply the extrusion characterization to 3D printing of this formulation to examine the translation of the extrusion results to additive manufacturing applications.

The formulation used in this study was a bimodal mixture of coarse (Millipore Sigma) and fine (Cospheric) glass bead particles, suspended in a binder consisting of hydroxyl-terminated polybutadiene (HTPB) and isodecyl pelargonate plasticizer (IDP). Glass beads were selected as the solid particles due to their nearly perfect spherical shape and wide range of available particle sizes. The larger/coarse size glass beads (150–212 μm) were sieved between ASTME11 number 70 and 100 mesh size sieves to ensure narrow size distribution. The smaller/fine size glass beads (20–30 μm) were sieved between ASTME11 number 325 and 625 mesh size sieves. One-gram (g) samples of both the fine and coarse glass beads were analyzed using a Malvern Mastersizer 3000 Aero S particle size analyzer. The circularity, average particle diameter (D50), D10, and D90 for both the coarse and fine glass beads as well as the associated standard deviation (σ) are shown in Table 1. Spherical particles were selected for this study to achieve consistent packing of particles. The shape of the particle has been shown to alter flow characteristics in solid flow, as irregular shaped particles can have different packing arrangements69,70. The spherical particles used in this study help mitigate these effects as well as to allow direct comparison to the monomodal extrusion study by Montaño et al.61. The binder used in the formulation matches the binder composition from Montaño et al., which was comprised of 97 wt.% HTPB-R45HTLO (Rocket Motor Components) and 3 wt.% IDP (Rocket Motor Components) as a plasticizer61.

The initial sample formulations used in this study were based on the volume loadings tested by Montaño et al. in the extrusion study of monomodal mixtures of suspended glass bead particles61. After initial testing, additional volume loadings were tested in order to characterize the extrusion limits of vibration-assisted printing and direct-ink-write printing for bimodal mixtures. All volume loadings and the corresponding solids loading tested for the bimodal glass bead mixtures are shown in Table 2. A minimum of six 10 g mixtures were prepared for each volume loading, allowing for at least three samples to be tested for VAP and DIW extrusion. The coarse to fine weight ratio used in the mixture was 72.7:27.3, which was specified by McGeary to result in the densest packing63. When each sample was mixed, the fine and coarse particles were added to the binder and wetted by hand mixing. The samples were then mixed on a Resodyn resonant acoustic mixer (LabRam). This mixing approach was consistent with previous studies investigating solid propellant and explosive characteristics10,11,71,72,73. Sample formulations with a volume loading less than 75 vol.% were mixed at 70 g’s for two (2), three-minute cycles, and formulations with volume loadings greater than 75 vol.% were mixed for three (3), three-minute cycles each at 70 g’s to ensure that the samples were well mixed. A vacuum pump was attached to the resonant acoustic mixer and was used for all mixing cycles to remove air bubbles that may be present in the binder. In between each mixing cycle, the formulations were hand mixed to prevent particle agglomeration near the seams of the mixing container71. After mixing, airtight containers were used to store the samples until testing.

The system overview of the instrumented extrusion test stand is shown in Fig. 3. The extrusion system used for the bimodal glass bead mixture is identical to the system used by Montaño et al.61. An 800 N (180 lbf) linear actuator (ServoCity I6-30) applies the back pressure required to extrude the different formulations. An Arduino microcontroller was used to control the linear actuator. A 1.1 kN (250 lbf) rated FUTEK load cell (LSB200) was attached to the linear actuator to record the force that was exerted by the linear actuator during testing. The material deposition during testing was recorded via a 50-gram S-beam FUTEK load cell (LSB200). The microcontroller and load cells were controlled by a computer connected with FUTEK USB digital amplifiers (FUTEK USB220). The USB connections and FUTEK SENSIT software were used for recording the mass deposition and force observed during testing. A PZT ultrasonic transducer was attached to the extrusion syringe nozzle and was used to generate the vibrations used for VAP53. A signal generator (Agilent 33120 A Waveform Generator) was used to control the vibrations. For these experiments, the frequency was set to 28.2 kHz. The signal generator was used in conjunction with a linear amplifier (Piezo Linear Amplifier EPA-104), which outputs a peak-to-peak voltage (VPP). A study by Fleck et al. showed that the selected peak-to-peak voltage has a quantifiable effect on the printing speed60. In order to mitigate the effect of variation due to the VPP, the peak-to-peak voltage used in this study was set to 250 VPP, and this voltage was checked prior to each test. This voltage was selected as it was the VPP used by Montaño et al., which allows direct comparison to the results from the study on extrusion of monomodal suspensions of glass beads in binder61. Testing was performed on the same day as mixing to ensure glass beads did not settle towards the bottom of the container.

A linear actuator, (B) force load cell, (C) syringe containing sample to be tested, and (D) mass deposition load cell.

The testing procedure for the suspended bimodal glass bead mixtures matched the procedure used by Montaño et al.61. Before testing, a taper tip syringe (McMaster 7510A662), with a taper angle of approximately 5°, was loaded with the 10-gram sample. The inner tip diameter of the syringe was 710 µm. The material was then compacted to remove any potential air bubbles within the reservoir. Then an aluminum plunger, with an attached rubber bushing, was inserted into the reservoir of the syringe. The loaded syringe was then placed into the instrumented test stand. Following the placement of the sample, the syringe was primed to allow material to fill the entire nozzle. All tests were conducted at a back pressure of 0.827 MPa (120 psi). The length of each test was 135 s, or until the mass accumulation on the 50 g load cell contacted the syringe tip. The mass deposited was collected by the 50 g load cell at a sampling frequency of 300 samples per second and data was collected for the entirety of the 135 s test. A minimum of three samples of each volume loading were tested for VAP and DIW samples. When testing the samples with vibration-assisted printing, the ultrasonic tip was placed on the syringe nozzle prior to testing.

After the raw data from the load cells was collected, it was imported into a MATLAB code developed by Montaño et al. to determine the mass flowrate of the different formulations61. The mass flowrate was determined using the data from the 50-gram load cell and a three-point forward difference method, which was used to numerically differentiate the raw mass data. A single value for mass flowrate for each mixture was determined by averaging the mass flowrate across the entire test series for each volume loading. Zero-mass deposition portions during the start of the test and end of the test were excluded from the mass flowrate calculations. This includes the zero-mass deposition region at the start of each experiment, as time is required for the sample to be compressed and for the extruded material to contact the 50 g load cell. It also includes the region of zero-mass deposition at the end of the experiment when the linear actuator is retracted, removing the applied pressure from the sample. For mixtures that did not display steady flow behavior throughout the entirety of the test, a region of consistent mass deposition was used to determine the mass flowrate of the mixture. The maximum theoretical mass deposited could then be calculated from mass flowrate for the region of consistent mass deposition. The actual mass deposited was then compared to the maximum theoretical mass deposited to distinguish steady from unsteady flow for the different mixtures tested. If the actual mass deposited was greater than or equal to 95% of the maximum theoretical mass deposited, then the flow was considered steady. If the actual mass was less than the 95% requirement, the flow was considered unsteady. Typically, the tests that exhibited this unsteady behavior would have noticeable signs of clogging and jamming, such as sputtering of material or complete blockage of material through the nozzle outlet.

Due to the high sensitivity of the 50 g S-beam load cell, noise existed in the collected data. A fourth order Butterworth lag low-pass filter with a normalized cutoff frequency of Wn was used to filter this noise. Wn was calculated using,

where Fc is the cutoff frequency and Fs is the sampling frequency. Residual analysis was used to determine the cutoff frequency (Fc) for the filter. The purpose of this residual analysis was to select a cutoff frequency that would balance noise reduction with signal distortion. With too low of a cutoff frequency, noise would dominate the signal while with too high a cutoff frequency, distortion of the signal would occur. A Butterworth filter was applied using a forward-backward filtering method. This method applies the filter forward through the data in sequence, then applies the filter to the data sequence in reverse order. The benefits of forward-backward filtering include zero phase distortion of the signal as well as sharpening the cutoff frequency by applying the fourth order filter twice, resulting in an overall eight order filter.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The underlying code for this study is not publicly available but may be made available to qualified researchers on reasonable request from the corresponding author.

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This research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-20-2-0189. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. The authors would like to thank Brandon Montaño for the assistance and expertise he provided throughout this work. Additional thanks are due to Austin Koeblitz for his assistance with sieving and sample preparation.

School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47906, USA

Joseph R. Lawrence, Hugh R. Lipic, Timothy D. Manship & Steven F. Son

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Joseph R. Lawrence, Timothy D. Manship, and Steven F. Son made substantial contributions to the conception and design of the work. Joseph R. Lawrence and Hugh R. Lipic acquired, analyzed, and interpreted the data. Joseph R. Lawrence wrote the main manuscript text. All Authors reviewed and revised the manuscript. All authors read and approved the final manuscript.

Correspondence to Joseph R. Lawrence.

Steven F. Son reports on a relationship with Next Offset Solutions, Inc. that includes board membership. The other authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Lawrence, J.R., Lipic, H.R., Manship, T.D. et al. The effect of volume loading on the extrusion of bimodal glass bead mixtures. npj Adv. Manuf. 1, 5 (2024). https://doi.org/10.1038/s44334-024-00008-7

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Received: 02 August 2024

Accepted: 10 September 2024

Published: 25 September 2024

DOI: https://doi.org/10.1038/s44334-024-00008-7

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