Powder Flow Research Articles

Integrated framework of multi−physics mechanism models for gas−powder flow, molten pool evolution and part deformation in high alloy steel additive manufacturing process

Multi−physics numerical models for metal additive manufacturing (MAM) could replace the expensive trial−and−error experiments, reveal the mechanisms of printing process, and provide an effective means of optimizing process parameters and mitigating part defects. However, the existing simulations of MAM process seldom consider the coupling effects between multiple recursive processes. There is an urgent need to overcome the dilemma of limiting MAM process simulation to a localized single sub−process. For directed energy deposition (DED) additive manufacturing process, the integrated simulation framework proposed in this study consists of a gas−powder flow model, a heat and fluid flow model, and a sequentially coupled thermal–mechanical model, which can be used to predict the feedstock feeding process, the evolution of molten pool, and the residual deformations of metal part, respectively. The accurate results of the three recursive sub−processes can be obtained by delivering the validated parameters between models. Corresponding experiments are conducted to verify the accuracy of the integrated framework based on 12CrNi2 alloy powders. The deviation of the predicted focal distance of powder streams is 5.14 %, and the deviations of the predicted molten pool height and width are all less than 8.5 %. The integrated framework could rapidly and accurately predict the residual deformation tendency and the position where the maximum deformation occurs. For single−track and eight−layer line deposition, the deviations of the predicted maximum deformation are all within 0.1 mm. The integrated framework could efficiently provide accurate and comprehensive solutions for optimizing DED process.

Unmasking hidden ignition sources: A new approach to finding extreme charge peaks in powder processing

Powders acquire a high electrostatic charge during transport and processing. Consequently, in the aftermath of dust explosions, electrostatic discharge is often suspected to be the ignition source. However, definite proof is usually lacking since the rise of electrostatic charge cannot be seen or smelled, and the explosion destroys valuable evidence. Moreover, conventional methods to measure the bulk charge of powder flows, such as the Faraday pail, provide only the aggregate charge for the entire particle ensemble. Our simulations show that, depending on the flow conditions, contacts between particles lead to bipolar charging. Bipolar charged powder remains overall neutral; thus, a Faraday pail detects no danger, even though individual particles are highly charged. To address this gap, we have developed a machine learning-enhanced measurement technology to resolve the powder charge spatially. The first measurements have revealed a critical discovery: a localized charge peak near the inner wall of the conveying duct that is 85 times higher than the average charge that would be measured by the Faraday pail. This finding underscores the possibility of extremely high local charges that can serve as ignition sources, even though they remain undetected by conventional measurement systems. Our new technology offers a solution by spatially resolving the charge distribution within powder flows, unmasking hidden ignition sources, and preventing catastrophic incidents in the industry.

Effect of carboxymethyl cellulose binder on physical, thermal, and rheological properties of milk protein isolate/guar gum mixture powder

This study examined the effect of fluidized-bed agglomeration with a carboxymethyl cellulose (CMC) binder on the physical, thermal, and rheological properties of agglomerated milk protein isolate (MPI)-guar gum (GG) mixtures (AMGs). The agglomeration process produced larger and more porous particles, improving solubility and powder flowability. An exothermic event followed by an endothermic event was observed in DSC thermograms. These thermal events tended to occur at a higher temperature with lower enthalpy values as the binder concentration increased. All samples exhibited shear-thinning behavior, with apparent viscosity at 100 s−1 values (0.27–0.29 Pa s) for AMGs being lower than for non-agglomerated MPI-GG mixture (NAMG; 0.34 Pa s). Viscoelastic moduli values showed similar trends. Additionally, compared to NAMG, larger and more guar gum lumps occurred in the AMGs. These findings suggest that the agglomeration process with CMC promoted depletion interactions between the protein and polysaccharide components in the mixture system.

Influence of the inner roughness of powder channels on the powder propagation behavior in laser metal deposition

The powder propagation behavior of powder nozzles for the laser metal deposition process has a significant influence on powder utilization rate and track geometry. A well-focused powder stream will lead to a higher process efficiency and lower material loss. Powder channels with different roughness and a constant diameter of 1.5 mm were placed by wire electrical discharge machining into a copper alloy printed by powder bed fusion. Nickel base powder with a size of −106 to +45 μm was delivered through the powder channels with varied carrier gas flow rates and varied powder mass flow rates. High-speed imaging was used to analyze the powder flow. From these recordings, the dispersion angle of the powder stream from single channels could be measured as well as the velocity of particles. Moreover, the relationship between individual particle velocity and individual particle flight angle was investigated. It was found that the inner roughness of powder channels has a major impact on powder propagation behavior. It could be shown that with a decrease in Ra from 2.16 to 0.27 μm the divergence angle decreased by around 61% while the particle velocity was increased by at least 28% for all varied parameters. Particles with a high velocity tend to have a lower particle flight angle.

Process parameter translation strategies for variable directed energy deposition spot size using 316L, copper, and Inconel 625

Directed energy deposition (DED) is a form of additive manufacturing available across a variety of laser spot diameter values, often referred to as spot sizes. However, there is no method to easily transfer process parameters across discrete spot sizes, leading to DED process parameters that are equipment specific and not widely applicable. In this study, a strategy is proposed and investigated for five spot sizes that keep the areal energy density constant while varying power, feed rate, and powder flow during the deposition of 316L stainless steel. An assessment of trends in hardness and microstructure is possible due to the novel production of components of a single material across several spot sizes using a single nozzle on a single DED system. The proposed strategy was used to nullify the hardness drop during functional grading of Inconel 625 and pure copper, enabling fabrication of multi-material sample that does not compromise desirable properties. This application shows the value in establishing more efficient process parameter development and understanding spot size influences on geometric and material property flexibility, to enable a more diverse powder-based DED design space and to increase the industry adoption of DED systems.

Exploring the potential of browntop millet (Urochloa ramosa) starch: Physicochemical, morphological, thermal and rheological properties across four cultivars

This comprehensive research explores the starch isolated from four browntop millet cultivars to determine physicochemical, thermal, morphological, powder flow, pasting, and rheological properties. Significant variations (p ≤ 0.05) were observed among the cultivars. Aerated bulk density (ABD) and Tapped bulk density (TBD) values ranged from 0.476 g/mL (BTM4) to 0.591 g/mL (BTM1), and 0.591 g/mL (BTM1) to 0.476 g/mL (BTM4). Amylose content varied from 22.55% (BTM4) to 25.86% (BTM3), influencing gelling strength and film-forming properties. Water absorption capacity ranged from 1.78 g/g to 1.92 g/g, while oil absorption capacity varied from 2.20 g/g to 2.47 g/g. DSC analysis showed gelatinization temperatures (Tp, and Tc) ranging from 85.44–91.61 °C, and 147.08–154.21 °C, respectively. X-ray diffraction (XRD) patterns revealed A-type crystalline patterns, with relative crystallinity ranging from 22.66% (BTM3) to 27.81% (BTM2). Pasting properties exhibited variations among cultivars, with peak viscosity ranging from 2480 c P to 3119 cP, and pasting temperature from 77.50 °C to 82.35 °C. Rheological analysis indicated shear-thinning behavior. The findings offer insights into the diverse properties of browntop millet starch, contributing to its potential applications in various industries and potentially guiding future studies on browntop millet starch modifications and novel utilization.

Rational Function-Based Approach for Integrating Tableting Reduced-Order Models with Upstream Unit Operations: Dry Granulation Case Study.

We present a systematic and automatic approach for integrating tableting reduced-order models with upstream unit operations. The approach not only identifies the upstream critical material attributes and process parameters that describe the coupling to the first order and, possibly, the second order, but it also selects the mathematical form of such coupling and estimates its parameters. Specifically, we propose that the coupling can be generally described by normalized bivariate rational functions. We demonstrate this approach for dry granulation, a unit operation commonly used to enhance the flowability of pharmaceutical powders by increasing granule size distribution, which, inevitably, negatively impacts tabletability by reducing the particle porosity and imparting plastic work. Granules of different densities and size distributions are made with a 10% w/w acetaminophen and 90% w/w microcrystalline cellulose formulation, and tablets with a wide range of relative densities are fabricated. This approach is based on product and process understanding, and, in turn, it is not only essential to enabling the end-to-end integration, control, and optimization of dry granulation and tableting processes, but it also offers insight into the granule properties that have a dominant effect on each of the four stages of powder compaction, namely die filling, compaction, unloading, and ejection.

Efficient Improvement of Eugenol Water Solubility by Spray Drying Encapsulation in Soluplus® and Lutrol F 127.

Herein, we present an elegant and simple method for significant improvement of eugenol water solubility using the polymers Soluplus® and Lutrol F 127 as carriers and spray drying as an encapsulation method. The formulations were optimized by adding myo-inositol-a sweetening agent-and Aerosil® 200 (colloidal, fumed silica)-an anticaking agent. The highest encapsulation efficiency of 97.9-98.2% was found for the samples containing 5% eugenol with respect to the mass of Soluplus®. The encapsulation efficiencies of the spray-dried samples with 15% eugenol are around 90%. Although lowering the yield, the addition of Lutrol F 127 results in a more regular particle shape and enhanced powder flowability. The presence of Aerosil® 200 and myo-inositol also improves the rheological powder properties. The obtained formulations can be used in various dosage forms like powders, granules, capsules, creams, and gels.

Correlation analysis of feedstock flowability and temperature for laser-based powder bed fusion of polymers

PurposeFor additive manufacturing (AM) through laser-based powder bed fusion of polymers (PBF-LB/P), accurate characterization of powder flowability is vital for achieving high-quality parts. However, accurately characterizing feedstock flowability presents challenges because of a lack of consensus on which tests to perform and the diverse forces and mechanisms involved. This study aims to undertake a thorough investigation into the flowability of eight feedstock materials for PBF-LB/P at different temperatures using various techniques.Design/methodology/approachFor ambient temperature assessments, established metrics such as avalanche angle and Hausner ratio, along with the approximated flow function coefficient (FFCapp), are used. The study then focuses on the influence of elevated temperatures representative of in-process conditions. FFCapp and differential scanning calorimetry (DSC) are performed and analyzed, followed by a correlation analysis as a holistic approach to identify key aspects for flowability. Furthermore, two feedstock materials are compared with a previous study to connect the present findings to PBF-LB/P processing.FindingsThe study revealed intrinsic material properties such as mechanical softening near the melting point to become significant. This partially explains why certain powders with poor ambient temperature flowability are consistently demonstrated to produce high-quality parts. FFCapp and thermal characterization through DSC are identified as critical metrics for optimizing feedstock material characteristics across temperature ranges.Originality/valuePrevious studies emphasized specific characterizations of feedstock material at ambient temperature, presented a limited materials selection or focused on metrics such as shape factors. In contrast, this study addresses a partially understood aspect by examining the critical role of temperature in governing feedstock material flowability. It advocates for the inclusion of temperature variables in flowability analyses to closely resemble the PBF-LB/P process, which can be applied to material design, selection and process optimization.

Impact of cocoa variety on physical and chemical properties, reconstitutability, and flowability of cocoa powders

Cocoa of the Criollo, Forastero, and Trinitario varieties grown in the same production area of the Republic of the Congo were simultaneously harvested and similar post-harvesting operations (fermentation in crates followed by sun-drying) were performed. Cocoa powders were then produced according the same process consisting in successive roasting, grinding, fat extraction by pressing, and ultrafine grinding of the defatted mass. In order to investigate the influence of cocoa variety, the main physical and chemical properties (proximate composition, pH, particle size and shape distributions) of powders were characterized and related to cocoa powders abilities to reconstitute and flow. The three varieties showed very close proximal compositions, with lipid contents varying between 21 and 23 % (w/w), which classifies them as defatted cocoa powders. Cocoa powders of all varieties were non-wettable, and not soluble (solubility index around 0.15 g/g), consistently with their high lipid content. The fatty, fibrous, and proteic nature of the product has an impact on the grinding process, resulting in non-wettable powders and particles of varying sizes and shapes. All powders had bimodal particle size distributions, with large particles around 500 μm and small ones around 25 μm. However, slight differences between varieties were observed for some shape and functional properties. Trinitario and Forastero cocoa particles were slightly less spherical. The Criollo cocoa powder was relatively more compressible than the Trinitario variety. No significant difference of flow properties was attributable to cocoa variety. Basic flowability energy of all cocoa powders were relatively high, ranging from 908 to 973 mJ, which could denote a low aptitude to flow that may be related to the probable softness and stickiness of particle surface due to the high lipid content of cocoa powders. Specific energy values required to make studied cocoa powders flow were in the range between 6.61 and 6.99 mJ/g, which corresponds to intermediate values indicating a moderate level of cohesion and thus a fair flowability. The flow parameters obtained from the shear cell test showed no significant difference of cohesion (comprised between 1.54 and 1.70 kPa), flow factor (ranging from 2.53 to 2.76), and internal angle of friction (between 33.4 and 33.9°) linked to cocoa variety. This may be explained by the impact of particle size, as higher particles are generally less cohesive due to their lower surface specific area implying less interparticular contact points. Apart from these slight differences, all varieties showed similar properties and thus could be blended instead of being sorted in the cocoa manufacturing process. This study permitted to highlight that the terroir, the method of harvesting and preparing the beans, and then producing the powder have probably more impact on the physical and chemical and functional properties of cocoa powders than their variety.

Granule efficiency evaluation process using two-way CFD-DEM coupling analysis

Amino acid granulation using a fluidized bed is an important process that can improve the fluidity of powders and provide better process control. In this study, a granulation process evaluation procedure using numerical analysis is presented. Before analyzing the flow and particle behavior during the process, experiments and analyses such as pour angle of repose, drained angle of repose, and static angle of repose were performed to measure material properties and ensure the reliability of the numerical model. Material properties determined through experiments and numerical analyses were applied to an evaluation model of the granulation process. The granulation process is characterized by the interdependent behavior of a strong flow and large amounts of powder inside the equipment. A Computational Fluid Dynamics (CFD)-Discrete Element Model (DEM) coupled numerical model was presented for simulating particle and multiphase flow phenomena. Additionally, because there is a strong correlation between particle behavior and flow, a two-way coupling model was applied.The particle behavior characteristics are directly related to the granulation efficiency. Particle behavior was analyzed by setting four process conditions depending on the flow intensity. In this study, the concept of a dead zone was introduced to evaluate the kinetic performance of the particles under different process conditions. A dead zone is an area where the particles do not move actively and are unable to mix. The creation and size of the dead zone were compared based on the process conditions. Additionally, this study presents a procedure to evaluate the mass, volume, and size increase due to the granulation process based on the time spent in the granulation region. The granulation region is defined as the area in which the granulation of the particles is expected to proceed using the material sprayed from the nozzle. The granule quantity and uniformity were evaluated according to the process conditions. The granule amount refers to the mass and volume of individual particles that increase during the granulation process, and uniformity refers to the variation in granule amount between particles. The process efficiency can be evaluated as good when the granule amount of the work particles reaches the target value and is evenly distributed. Although the behavioral characteristics of the analyzed process did not represent all similar processes, it was confirmed that separate process conditions should be set according to the initial size distribution of the particles, target granule amount, and uniformity. Consequently, a series of processes was organized to obtain the properties of the target particles, effectively simulate the behavior inside the equipment, and reasonably determine the granulation region. Additionally, it presents a method to evaluate the amount and uniformity of granules rather than simply evaluating the time spent in the granulation region.

A Review of Recent Techniques for Granulation

Granulation is the process of designing particles by combining primary power particles into massive multiparticle structures known as granules. Its primary purposes are to boost the flow of power, prevent segregation, improve the compaction characteristics of mix uniformity, and improve the flow and compressibility of powders. It also produces a combination that is uniform. Wet granulation and dry granulation are the two primary categories of granulation methods. The granulation process is contingent upon the description of the ingredient entity and its ability to surge appropriately, compact, and collapse. Choosing the appropriate granulation method necessitates a methodical examination of each ingredient in the combination and how they interact. Granule particle size is determined by the amount and feeding rate of the granulating liquid. New methods have been added to the granulation process to improve it: foam binder granulation, fluidized bed granulation, melt granulation, activated dry granulation, heat adhesion granulation, steam granulation, spray drying granulation, and freeze granulation. The major purpose of this page is to provide an overview of each advancement, including its limitations and relevance.

Experimental study of the wall particle motion in a screw reactor

Screw reactors are gas/solid systems widely employed in industrial applications. Understanding the local powder mixing within these reactors is crucial, particularly at the reactor wall where wall/solid heat transfer occurs. This study proposes a non-invasive measurement method utilizing optical devices to assess wall particle motion. Two techniques for evaluating the particle motion are compared: a simple visual tracking method and particle image velocimetry. Both methods yield similar results, demonstrating consistent wall particle motion across the tube periphery during experimentation. The influence of operational and geometric parameters has been investigated, revealing that filling degree, powder flowability, and screw geometry significantly impact wall particle motion. Symbolic regression has been employed to derive dimensionless models that effectively predict experimental data. These models can be utilized to forecast wall particle motion, serving as a valuable tool for screw conveyor design.

Internal friction and flowability of clay powder depend on particle moisture, size and normal stress

This work investigates the impact of changes in the moisture content of bulk materials. The regularity of moisture change in bulk materials was evaluated for three different particle size classes of clay powders. The research measures the angle of internal friction and flowability under four different normal loads, reflecting the varying pressures during bulk material storage. The influence of moisture change in bulk materials was most pronounced for the smallest particle size fraction, where even a very small moisture change in the order of tenths of a percent steeply affected flowability due to internal friction. After increasing the moisture content by a few percent, a steady state of flow occurred. Critical value was determined when water in the bulk material caused liquefaction. For larger particle size fractions, the impact of moisture change was evident only at higher values (12.5%), with no liquefaction occurring even at 30% moisture. The change in normal load, on the other hand, affected particles of larger size fractions, resulting in improved flow properties.

Achieving efficient hardfacing on stainless steel using single SiC powder in laser directed energy deposition

Generally, in a laser hardfacing process, a mixture of ceramic and metal powder is used to clad a hard surface, resulting in enhanced wear characteristics of metal parts. This study proposes an efficient hardfacing process that uses a single and minimal amount of ceramic powder (0.079 g/min in this work). This process, named as Laser Directed Energy Deposition of Minimal Ceramic Powder (LDED-MCP), features that the melt pool is generated inwardly because only the substrate participates in forming the melt pool. Furthermore, due to the minimal powder flow rate used and sparse particle-melt pool collision events, ripple formations leading to the convective melt pool flow and inhomogeneous microstructures would be suppressed. Consequently, the produced layer is nearly flat and free of incompletely melted metallic particles, thus minimizing post-machining. For a 316 L substrate and SiC powder material combination, a crack-free layer about 560 μm thick with an average hardness of about 417 HV was created through process parameter optimization. This layer showed a eutectic structure composed of γ-austenite and chromium carbides, partially melted SiC particles between dendrites, and in-situ synthesized SiC nanoparticles decorating the cell walls. Through this work, near-net-shape hardfacing of stainless steels is realized through LDED-MCP process minimizing powder pre-processing and post surface machining.

Improvement of powder properties of milk protein isolate by fluidised bed agglomeration with guar gum binder

A goal of this study was to investigate the influence of fluidised bed agglomeration process with guar gum (GG) binder (0–0.3%) on the physical and rheological properties of agglomerated milk protein isolate (MPI). Larger and more porous particles were formed by the agglomeration process, resulting in an improvement in powder flowability, wettability and solubility. The agglomerate with 0.1% GG binder exhibited higher viscoelastic properties than other agglomerates, with viscoelastic moduli values decreasing as the binder concentration increased (0.1–0.3%). The findings demonstrate that the agglomeration process with GG improved the powder characteristics of MPI and influenced its rheological properties.

Multi-fidelity surrogate with heterogeneous input spaces for modeling melt pools in laser-directed energy deposition

Multi-fidelity (MF) modeling is a powerful statistical approach that can intelligently blend data from varied fidelity sources. This approach finds a compelling application in predicting melt pool geometry for laser-directed energy deposition (L-DED). One major challenge in using MF surrogates to merge a hierarchy of melt pool models is the variability in input spaces. To address this challenge, this paper introduces a novel approach for constructing an MF surrogate for predicting melt pool geometry by integrating models of varying complexity, that operate on heterogeneous input spaces. The first thermal model incorporates five input parameters i.e., laser power, scan velocity, powder flow rate, carrier gas flow rate, and nozzle height. In contrast, the second thermal model can only handle laser power and scan velocity. A mapping is established between the heterogeneous input spaces so that the five-dimensional space can be morphed into a pseudo two-dimensional space. Predictions are then blended using a Gaussian process-based co-kriging method. The resulting heterogeneous multi-fidelity Gaussian process (Het-MFGP) surrogate not only improves predictive accuracy but also offers computational efficiency by reducing evaluations required from the high-dimensional, high-fidelity thermal model. The tested Het-MFGP yields an R2 of 0.975 for predicting melt pool depth. This surpasses the comparatively modest R2 of 0.592 achieved by a GP trained exclusively on high-dimensional, high-fidelity data. Similarly, in the prediction of melt pool width, the Het-MFGP excels with an R2 of 0.943, outshining the GP's performance, which registers a lower R2 of 0.588. The results underscore the benefits of employing Het-MFGP for modeling melt pool behavior in L-DED. The framework successfully demonstrates how to leverage multimodal data and handle scenarios where certain input parameters may be difficult to model or measure.

Isolation and physiochemical characterization of Red kidney bean (Phaseolus vulgaris L.) starch

The current study focuses on the isolation and physiochemical characterisation of starch from Phaseolus vulgaris L. The yield of the starch was about 25.8 %. The size of the starch granules ranged between 10 and 25μm. The starch had a higher water binding capacity, swelling power and solubility but had low paste clarity. P. vulgaris starch exhibited high freeze thaw stability. The bulk, tapped and particle densities of the starch were 1.64 g/cm3, 2.06 g/cm3 and 0.66 g/cm3 respectively. The porosity of the starch was about 64.1%. The estimated Carr index and Hausner’s ratio indicated good flowability of the starch powder. X-ray diffraction analysis indicated that the starch was C-type starch. Fourier-transform infrared spectroscopy revealed the functional group corresponding to that of starch. Thermo gravimetric analysis indicated good thermostability.

An Advanced Twin-Screw Granulation Technology: The use of Non-Volatile Solvents with High Solubilizing Capacity

PurposeTwin-screw wet granulation (TSWG) is a manufacturing process that offers several advantages for the processing of water-insoluble active pharmaceutical ingredients (APIs) and has been used for increasing the solubility and dissolution rates. Here we introduce a novel TSWG approach with reduced downstream processing steps by using non-volatile solvents as granulating binders.MethodsHerein, TSWG was carried out using Transcutol a non-volatile protic solvent as a granulating binder and dissolution enhancer of ibuprofen (IBU) blends with cellulose polymer grades (Pharmacoat® 603, Affinisol™, and AQOAT®).ResultsThe physicochemical characterisation of the produced granules showed excellent powder flow and the complete transformation of IBU into the amorphous state. Dissolution studies presented immediate release rates for all IBU formulations due to the high drug-polymer miscibility and the Transcutol solubilising capacity.ConclusionsOverall, the study demonstrated an innovative approach for the development of extruded granules by processing water-insoluble APIs with non-volatile solvents for enhanced dissolution rates at high drug loadings.Graphical

An experimental study on flow behaviour of pharmaceutical powders during suction filling

Die filling is a crucial step in the pharmaceutical tablet manufacturing process. For industrial-scale production using rotary presses, suction filling is typically employed due to its significant efficiency advantages over gravity filling. Despite its widespread use, our understanding of the suction filling process remains limited. Specifically, there is insufficient comprehension of how filling performance is influenced by factors such as suction velocity, filling velocity, and the properties of the powder materials. Building on our previous research, this study aims to further investigate the effects of powder properties and process parameters (e.g., filling velocity, suction velocity, fill depth) on suction filling behaviour. A systematic experimental investigation was conducted using a model suction filling system, considering both cohesive and free-flowing pharmaceutical powders. The effect of fill depth on suction filling of these powders was examined at different filling and suction velocities. The results demonstrate that two distinctive flow regimes for suction filling can be identified: slow filling and fast filling. These regimes are delineated by a critical filling-to-suction velocity ratio. In the slow filling regime, the filling-to-suction velocity ratio is lower than the critical ratio, meaning that the filling phase is slower than the suction phase. Conversely, the fast filling regime occurs when the filling-to-suction velocity ratio exceeds the critical ratio, implying that the filling phase is faster than the suction phase. This study reveals, for the first time, that when the powder flow pattern during suction filling is dominated by plug flow, full die fill (i.e., the fill ratio equals unity) is achieved in the slow filling regime. However, in the fast filling regime, incomplete die fill is obtained. It is also found that when plug flow prevails during fast filling, the fill ratio has an inverse correlation with the filling-to-suction velocity ratio. This study further reveals that when the plug flow assumption is valid, the filling ratio at various fill-to-suction velocity ratios can be well predicted mathematically. Furthermore, it is also found that once the powder flow pattern differs from the ideal plug flow, which could be induced by the filling conditions and powder cohesion, the fill ratio can be overpredicted.