KONA Powder and Particle Journal
Online ISSN : 2187-5537
Print ISSN : 0288-4534
ISSN-L : 0288-4534
Volume 35
Displaying 1-27 of 27 articles from this issue
Front Cover
Editorial
Review Papers
  • Anthony J. Hickey
    2018 Volume 35 Pages 3-13
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: April 08, 2017
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    Pharmaceutical aerosol powders intended for inhalation are required to have unique performance characteristics that are highly dependent on their physico-chemical properties. A wide range of analytical methods have been applied to study particle structure, size distribution, surface properties and subsequent behaviour of powders with the intention of predicting their performance. However, particle interactions are dictated by complex fundamental forces that impact on the efficiency and reproducibility of delivery and thereby the quality, efficacy and safety of the final product. This manuscript reviews the interplay of physico-chemical properties of powder and the complex process and analytical variables that must be monitored and controlled to effectively predict powder performance.

  • Yiannis Deligiannakis
    2018 Volume 35 Pages 14-31
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: March 18, 2017
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    Environmental remediation and energy production are currently listed among the priority tasks by administration bodies, stakeholders and market competition. In this context, nanomaterials present competitive advantages in terms of performance and production costs. In the present critical review, the current state of the art of nanomaterials used in environmentally benign technologies exploiting solar irradiation such as H2 production, water-splitting and photocatalysis are discussed. Factors determining the overall efficiency are articulated in a single “photophysical efficiency” equation. The physical meaning, limits and constraints of each factor are analyzed, updated and examples are discussed. The article highlights the main structure-function relationships in tandem with the limitations posed by the particle’s physicochemical properties, production method, and the prerequisites posed by regulatory bodies and market needs. Several misconceptions are highlighted with regard to performance and yields that ultimately impact the end use of the nanomaterials. Current targets/limitations posed by the US Department of Energy are discussed as case studies. For context-coherence reasons, the present review focuses on metal and metal-oxide nanoparticles, i.e. carbon nanomaterials are not covered herein.

  • Hojae Yi, Anuranjan Pandeya, Apoorva Karamchandani, Virendra M. Puri
    2018 Volume 35 Pages 32-48
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: April 08, 2017
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    For processes involving particulate materials, mechanical properties of green compacts are of great interest when they are final or intermediate products. Optimal quality of green compacts is achieved usually with empirical approaches, i.e., unexpected issues in processes or products’ quality are usually mitigated by time and resource consuming trial-and-error methods. Issues of the powder compaction are commonly observed when there are problems in feed materials or operational conditions even without any substantial change in a formula. Such divergent behavior of particulate materials is especially problematic for product developments and reliable operations. It has been widely accepted hypothesis that properties of particles are determinants of mechanical behavior of powder during compaction and the quality of resulting compacts. With recent developments in nanotechnology, characterization and engineering of individual particles at a microscopic or sub-microscopic scale are now feasible. Leveraging recent technological advancements, there has been a good progress in regard to quantitative understanding of mechanical relationships between properties of particles, particle system and final product. This review highlights the recent developments and gaps in engineering mechanical quality of powder compacts in conjunction with the characterization of particle systems and compaction at multiple scales.

  • Hideya Nakamura, Satoru Watano
    2018 Volume 35 Pages 49-65
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: July 30, 2017
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    Nanoparticles have attracted much attention as a key material for new biomedical and pharmaceutical applications. For success in these applications, the nanoparticles are required to translocate across the cell membrane and to reach to inside of the cell. Among several translocation pathways of nanoparticles, the direct permeation pathway has a great advantage due to its high delivery efficacy. However, despite many research efforts, key properties and factors for driving the direct permeation of nanoparticle and its underlying mechanisms are far from being understood. In this article, experimental and computational studies regarding the direct permeation of nanoparticles across a cell membrane will be reviewed. Firstly, experimental studies on the nanoparticle-cell interactions, where spontaneous direct permeation of nanoparticles was observed, are reviewed. From the experimental studies, potential key physico-chemical properties of nanoparticles for their direct permeation are discussed. Secondly, physical methods such as electroporation and sonoporation for delivering nanoparticles into cells are reviewed. Current status of technologies for facilitating the direct permeation of nanoparticle is presented. Finally, we review molecular dynamics simulation studies and present the latest findings on the underlying molecular mechanisms of the direct permeation of nanoparticle.

  • Tetsuya Yamamoto, Ko Higashitani
    2018 Volume 35 Pages 66-79
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: August 31, 2017
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    The process of synthesis of polymeric particle in soap-free system was observed in-situ on the molecular scale by using an atomic force microscope (AFM). Using cationic water-soluble initiators enabled all of the polymeric materials to be adsorbed on the mica surface electrostatically. This adsorption technique of polymeric materials in the bulk obtained the AFM images of them throughout the reaction and to discuss the real growth mechanism of polymeric particles. The followings are found; the polymeric materials are continuously generated in the bulk throughout the reaction; and they make a contribution to the particle growth. Furthermore, soap-free emulsion polymerization (SFEP) of aromatic vinyl monomer using oil-soluble initiators was studied to synthesize micron-sized particles. Oil-soluble initiator, such as AIBN, worked like a water-soluble initiator in SFEP to prepare monodispersed particles with negative charges, probably because of the pi electron cloud of phenyl ring in a monomer. The addition of an electrolyte enabled secondary particles in the bulk to enhance hetero-coagulation rate for particle growth. Changing the concentration and valence of electrolyte enabled us to control the size in SFEP using AIBN. These methods enabled reaction time to be reduced for the synthesis of micron-sized polymeric particles in soap-free system.

  • Toshihiko Myojo, Mariko Ono-Ogasawara
    2018 Volume 35 Pages 80-88
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: August 31, 2017
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    In this paper we review the risk assessment of carbonaceous nanomaterials, such as single-wall carbon nanotubes (SWCNTs), multi-walled carbon nanotubes (MWCNTs), fullerenes and carbon black, and summarize elemental carbon (EC) analyses for the determination of the those nanomaterials, focusing on the inhalation exposure of airborne nanomaterials. In the reports of hazard assessment, the proposed OELs (Occupational Exposure Limits) of MWCNTs and SWCNTs ranged from 1 to 50 μg/m3. The fullerenes and carbon black seem to be less toxic than the CNTs. In the reports of exposure assessment, the aerosol concentrations of MWCNTs and SWCNTs in work environments were from less than 0.1 to more than 100 μg/m3. The expected minimum concentration of airborne MWCNTs in the EC analyses was around 1 μg/m3, but the concentrations of EC in ambient particulate matters (APM) were more than 1 μg/m3 in urban environments. The EC analysis introduced in this paper is a convenient method to quantify the carbonaceous nanomaterials in the samples, but size-classification of aerosol samples by cascade impactor and observation using electron microscopes are needed to confirm the characteristics of the nanomaterials.

  • Suryani Saallah, I. Wuled Lenggoro
    2018 Volume 35 Pages 89-111
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: September 30, 2017
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    In the past few decades, enormous advances have been achieved in the field of particle technology and the trend has been shifted from macro to micro and recently to the nanoscale. Integration of nanotechnology and biotechnology has paved the way to the development of biological nanoparticles, derived from biomolecules, and biomolecule-nanoparticle conjugates for numerous applications. This review provides an overview of various types of biological nanoparticles and the methods of their fabrication with primary emphasis on the drying methods, particularly on the newly emerging technique, the electrospraying. Recent advances in the integration of biomolecules with nanoparticles in the past five years to present are also discussed. Finally, the application of the biomolecule-nanoparticle conjugates in various fields including medicals and pharmaceuticals, biosensors and bioelectronics, foods, and agricultures are also highlighted.

  • Kenji Kato, Keiji Matsueda
    2018 Volume 35 Pages 112-121
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: September 30, 2017
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    Coal is a very important resource for power generation and cokemaking. Moreover, coal is a very useful resource for producing city gas and chemical materials by gasification technology. Low grade coals are suitable for the coal gasification resources because they are easily decomposed and converted to generate gas in the gasifier. On the other hand, high quality coals such as good quality bituminous coals are required for producing metallurgical coke. Recently, the amount of high quality coals has been decreasing. The expansion of raw coal brands for producing metallurgical coke is very important. In this paper, the development of high energy efficiency gasification technology, ECORO®, and new cokemaking technologies such as the DAPS and the SCOPE21 enabling the expansion of coal resources are introduced. These technologies are contributed to the expansion of coal resources and energy savings.

  • Tomasz R. Sosnowski
    2018 Volume 35 Pages 122-138
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: September 30, 2017
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    The paper discusses essential engineering challenges related to the application of powder medicines for pulmonary delivery as inhaled aerosol. Starting from a physically based description of the complexity of aerosol dynamics inside the respiratory system, the paper discusses several technical factors responsible for efficient drug delivery to the lungs: (i) interparticle interactions—which can be tuned by selection and control of powder manufacturing methods, (ii) inhaler design—as a determinant of flow dynamics through the inhaling device and degree of powder dispersion, (iii) the dynamics of inhalation in a given inhaler—which is related to patient-device interaction. Basic information on the standard (compendial) methods of the quantitative evaluation of dry powder inhalers (DPIs) are presented with a special focus on the correct data interpretation and the consequences for in vivo-in vitro correlation (IVIVC) problems. Some issues regarding the development of inhalation products (including generics) are also briefly highlighted. Finally, possible strategies of powder particle functionalization to obtain the required bioavailability are outlined on the basis of knowledge on the physicochemical interactions of inhaled particles with the lung fluids.

  • Kenji Tanno, Hisao Makino
    2018 Volume 35 Pages 139-149
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: September 30, 2017
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    Coal is an important energy resource for meeting future demands for electricity, as coal reserves are much more abundant than those of other fossil fuels. However, coal utilization technologies exhaust carbon dioxide more than other fossil fuels, because of the higher carbon content of coal. To control of global warming, development of new technologies for the reduction of carbon dioxide emission from a coal-utilized power station are thus required. For reduction of carbon dioxide emission, it is very important to utilize low carbon content fuel such as subbituminous coal and lignite, as well as carbon neutral biomass, and develop new technologies needed for a high efficiency power generation system. For the further reduction of carbon dioxide, effective removal and storage technologies are also necessary. In this paper, the utilization technology of low carbonized sub-bituminous coal and carbon neutral biomass in pulverized coal combustion is at first introduced. The development situation of a high efficiency coal-fired power generation technique including an integrated coal gasification combined cycle system (IGCC) and an integrated coal gasification fuel cell combined cycle system (IGFC) are overviewed, and carbon dioxide removal technologies in a thermal power station are investigated. Finally, the high efficiency power generation oxy-fuel IGCC system with CO2 removal is presented, and the characteristics of this system are examined.

Special Contribution
  • George E. Klinzing
    2018 Volume 35 Pages 150-159
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: July 30, 2017
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    This document attempts to cover the development of pneumatic conveying over the past 100 years or so. The individual researchers who worked in the field are highlighted along with their photograph which is included at the end of the document. As time progressed in the scientific and engineering developments of these years one see a transition from a purely experimental approach with considerable empiricism to adapt to the development of numerical procedures in attempt to predict the flow characteristics. The basic physics of the phenomena of pneumatic still is not completely understood and new and novel experimental techniques are always welcome in the field.

Original Research Papers
  • Ming Li, Mikel Leturia, Khashayar Saleh
    2018 Volume 35 Pages 160-171
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: March 18, 2017
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    This study focuses on the periodic motion observed in the FT4 Powder Rheometer and aims to develop a new testing method to evaluate powder flowability. This new method is based on the autocorrelation analysis of the torque measurements. The test results of powders belonging to different Geldart’s groups show that the torque measurements are periodic and that the cycle time (period) depends on the flowability. When the powder cohesiveness increases, the oscillations’ amplitude and the cycle time increase. Conversely, a free-flowing powder exhibits a liquid-like behavior and shows almost no periodic motion.

  • Christian Spötter, Kurt Legenhausen, Alfred P. Weber
    2018 Volume 35 Pages 172-185
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: February 25, 2017
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    Although the deflector wheel classifier is the dominant separation device in the industrial separation of fine-grained particle fractions, the classifying mechanisms at high particle loadings are still not described and understood sufficiently. The existing models for the calculation of the separation efficiency, which are mostly based on a single particle’s fate, fail to capture the behavior at high particle loading where particle-particle and particle-wall collisions are encountered. To overcome this knowledge gap, a high-speed camera was used to analyze the particle movement in the separation process of a deflector wheel classifier representing real physical conditions. It is shown that particle-particle and particle-wall collisions must be included in a consistent theoretical model to represent the effective particle behavior in the separation process. In addition, the influence of process parameters such as revolution rate and mass loading on the separation efficiency of a deflector wheel classifier at high loadings is presented here.

  • Assefa Kebede Melorie, Deo Raj Kaushal
    2018 Volume 35 Pages 186-199
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: February 04, 2017
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    Chemical additives are widely used in iron ore industry in various processing steps such as classification, crushing, grinding, and pelletization. These additives are also used in transportation of iron ore through highly concentrated slurry pipelines which are currently operating and coming up in large number across the world. These additives are usually categorized by their functions rather than chemical composition. In this study, the effect of quick lime (QL), hydrated lime (HL), Sodium hexametaphosphate (SHMP) and Acti-Gel on the rheological behaviors of iron ore slurries at volumetric concentrations (Cv) of 18.8 %, 22.1 % and 25.8 % and dosages of additives ranging from 0.05–2 % were investigated. The rheological parameters were measured using computerized rotational rheometer. All the sample data were best represented by Herschel-Bulkley model. Minimum shear stress and viscosity were obtained at 2 % dosage of QL for 18.8 % and minimum flow behaviour index was obtained at 25.8 % with 2 % additive dosage. The addition of HL markedly increases all the rheological parameters. When SHMP is used, minimum shear stress and viscosity were obtained at dosage of 1.5 %, 2 % and 2 % for Cv of 18.8 %, 22.1 % and 25.8 % respectively. Acti-Gel resulted higher values of yield stress and flow behaviour indices at all solid concentrations.

  • Charley Sprenger, Lope G. Tabil, Majid Soleimani
    2018 Volume 35 Pages 200-208
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: March 31, 2017
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    The compression and relaxation characteristics of municipal solid waste (MSW) refuse-derived-fuel (RDF) fluff were investigated with respect to biodegradable fraction, grind size, moisture content, applied load, and pelleting temperature. Experimental trials were performed by using a single pelleting unit mounted on an Instron universal testing machine. Two grind sizes of each sample were prepared, 3.18 mm and 6.35 mm, and moisture contents were increased to 8 %, 12 %, and 16 % w.b. The applied loads were set at 2 kN, 3 kN, and 4 kN at two temperature settings, 50 °C and 90 °C. The experimental data for these trials was collected and multiple compression and relaxation models were fitted to the applied pressure, compact density or volume data. The results indicated that the compact density of RDF improved by increasing the grind size, while the compact density of biodegradable pellets increased with increasing pelleting load and temperature. The compact density of pellets produced from RDF ranged from 880–1020 kg/m3; the compact density of the biodegradable pellets ranged from 1120–1290 kg/m3. The Walker and Jones models both indicated that the biodegradable material fraction has a higher compressibility than the RDF material, where neither moisture content nor grind size at all levels had a significant effect on the compressibility of either material. The Kawakita-Lüdde model estimated the porosity of the pelleted samples, while the Cooper-Eaton model indicated that the primary mechanism of densification was particle rearrangement. Application of the Peleg and Moreyra model for analysis of relaxation properties of the compressed materials determined the asymptotic modulus of the residual stress to be between 89 and 117 MPa for all experimental parameters; however, the RDF material produced more rigid pellets than the biodegradable material.

  • Yuki Fujisawa, Yoshiteru Takahashi, Reiko Teraoka, Shuji Kitagawa
    2018 Volume 35 Pages 209-215
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: June 24, 2017
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    The purpose of this study is to evaluate the photostabilization mechanism of risperidone tablets. Risperidone is widely used for sensory integration disorder. It is formulated as tablets, orally disintegrating tablets, fine granules, oral solutions, and intramuscular injections. We found that risperidone was unstable in tablets and generated oxidized products. Formation of the oxidized product R5 was promoted in the presence of hydroxypropylcellulose by photoirradiation. On the other hand, photostability improved greatly when carmellose (CMC) or carmellose calcium (CMC-Ca) was used as a disintegrant. Since CMC and CMC-Ca are acidic substances, the photostability of tablets may have been affected by pH. Therefore, the effects of different pHs were examined. Risperidone was dissolved in methanol and the buffer (in the presence or absence of hydroxypropylcellulose) at different pHs (1.2, 3.0, 4.0, 5.0, and 6.8) was added. The photodegradation of risperidone was not observed at less than pH 3.0 in the presence of hydroxypropylcellulose, and low pHs improved the photostability of risperidone. On the other hand, risperidone solution without hydroxypropylcellulose was stable at all pH values. Therefore, risperidone was photochemically oxidized in the presence of hydroxypropylcellulose at high pHs.

  • Fernando O. Boechat, Rodrigo M. de Carvalho, Luís Marcelo Tavares
    2018 Volume 35 Pages 216-225
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: June 24, 2017
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    The increase in production of steel in electric arc furnaces in recent years influenced directly the world production of direct reduction iron (DRI). Amongst the most widely used technologies for DRI production is the MIDREX® process. The behavior of the metallic charge used in these furnaces, mainly made up of iron ore pellets, influences directly their productivity. Fines contained in the feed are typically removed by screening, in order to prevent them from impacting negatively the productivity of the furnace. However, fines still may be generated inside the furnace as a result of the collisions amongst pellets and between them and internals of the furnace as they move downwards from the feed to the discharge of the shaft furnace. Predicting and preventing such mechanical degradation is critical in the furnace operation. The present work deals with the prediction of degradation of iron ore pellets during reduction in a MIDREX furnace. Collision energies involved in the vertical flow of pellets along a MINIMOD® MIDREX direct reduction furnace were estimated using the discrete element method. Using this technique along with a model of degradation that considered assumptions based on information from the literature it was possible to estimate the proportion of fines generated inside the reactor, which was consistent with plant practice. Finally, it was predicted that the generation of fines in the reduction zone of the furnace would vary from 3.4 % to 4.6 % as the throughput of the furnace increased in 50 %.

  • Hao Shi, Rahul Mohanty, Somik Chakravarty, Ramon Cabiscol, Martin Morg ...
    2018 Volume 35 Pages 226-250
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: September 23, 2017
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    The bulk properties of powders depend on material characteristics and size of the primary particles. During storage and transportation processes in the powder processing industry, the material undergoes various modes of deformation and stress conditions, e.g., due to compression or shear. In many applications, it is important to know when powders are yielding, i.e. when they start to flow under shear; in other cases it is necessary to know how much stress is needed to keep them flowing. The measurement of powder yield and flow properties is still a challenge and will be addressed in this study.

    In the framework of the collaborative project T-MAPPP, a large set of shear experiments using different shear devices, namely the Jenike shear tester, the ELE direct shear tester, the Schulze ring shear tester and the FT4 powder rheometer, have been carried out on eight chemically-identical limestone powders of different particle sizes in a wide range of confining stresses. These experiments serve two goals: i) to test the reproducibility/consistency among different shear devices and testing protocols; ii) to relate the bulk behaviour to microscopic particle properties, focusing on the effect of particle size and thus inter-particle cohesion.

    The experiments show high repeatability for all shear devices, though some of them show more fluctuations than others. All devices provide consistent results, where the FT4 powder rheometer gives lower yield/steady state stress values, due to a different pre-shearing protocol. As expected, the bulk cohesion decreases with increasing particle size (up to 150 μm), due to the decrease of inter-particle cohesion. The bulk friction, characterized in different ways, is following a similar decreasing trend, whereas the bulk density increases with particle size in this range. Interestingly, for samples with particle sizes larger than 150 μm, the bulk cohesion increases slightly, while the bulk friction increases considerably—presumably due to particle interlocking effects—up to magnitudes comparable to those of the finest powders. Furthermore, removing the fines from the coarse powder samples reduces the bulk cohesion and bulk density, but has a negligible effect on the bulk friction.

    In addition to providing useful insights into the role of microscopically attractive, van der Waals, gravitational and/or compressive forces for the macroscopic bulk powder flow behaviour, the experimental data provide a robust database of cohesive and frictional fine powders for industrially relevant designs such as silos, as well as for calibration and validation of models and computer simulations.

  • Jaclyn D. Ray, James R. Nagel, Dave Cohrs, Raj K. Rajamani
    2018 Volume 35 Pages 251-257
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: September 30, 2017
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    Electrodynamic sorting is a process that sorts metals based on conductivity, density, and geometry. The process works by inducing electrical eddy currents within particles placed in a time-varying magnetic field. For the special case of a perfect, uniform sphere, an approximate equation can be used to predict the net force under a linear magnetic gradient. This paper explores the accuracy of that model by measuring the net force on spherical samples of copper, brass, and aluminum with varying sizes and excitation frequencies. Results consistently show strong agreement with the approximate models over all conditions. We also explore several non-spherical geometries, including cylinders, cubes, and disks. We found that they could be modeled as equivalent spheres, given an appropriate radius, and had reasonable accuracy over frequency.

  • Florent Bourgeois, Sébastien Teychené, Béatrice Biscans
    2018 Volume 35 Pages 258-272
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: September 30, 2017
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    Microfluidics tools have been developing rapidly over the past decade, as they offer unparalleled ability for controlling nucleation and tracking crystallisation events inside very large numbers of individual nanolitre-size droplets. They have demonstrated a significant potential for screening protein crystallization conditions and for the direct determination of inorganic products solubility curves. The accepted basis for analysing microfluidics data is the probabilistic nucleation model originally proposed by Pound and La Mer (1952). Given the significance of this model for the purpose of analysing microfluidics data, the paper conducts a review of its hypotheses, usage and applicability. A step-by-step derivation of the model equations confirms that the time variation of the proportion of empty droplets which microfluidics experiments can provide with high accuracy is indeed the recommended method for estimation of nucleation kinetic parameters from microfluidics experiments. The paper shows that, depending on its implementation, the model predicts different rates of appearance of crystals inside individual droplets. The paper focuses on two distinct implementation modes, referred to as constant supersaturation and single nucleation event modes. By confronting model prediction with microfluidics measurements for eflucimibe in octanol, the paper finds that both modes yield different model predictions, shedding light on the potential and limits of the probabilistic nucleation model for the analysis of microfluidics data.

  • Xuewen Wang, Zhaojian Yang, Bo Li
    2018 Volume 35 Pages 273-282
    Published: 2018
    Released on J-STAGE: February 28, 2018
    Advance online publication: September 30, 2017
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    Referring to the classification of vertical silos, the classification rules for deep silos and shallow silos on pyramidal silos and conical silos have been established. Based on the basic assumptions of Janssen Formula, the friction stress distribution of loose materials to silo walls was discussed in detail on deep pyramidal silos. An analytic equation was established used the slice method. Finite element model was developed to simulate the friction stress distribution. The analytic result was almost the same with the simulation result. However, the equation yielded a minor error mainly because there were some differences between the assumptions presented in the equation and the real state of materials. Based on the simulation results, the analytic equation was revised. The results showed that the friction stress distribution of loose materials to silo walls in deep pyramidal silos was related to the material characteristics and design parameters of silo walls, as well as the material powder attribute. The revised equation precisely indicated the contact friction stress behaviors of loose materials and provided a shortcut method of calculation for related research.

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