Particle shape and orientation in laser diffraction and static image analysis size distribution analysis of micrometer sized rectangular particles

Laser diffraction (LD) and static image analysis (SIA) of rectangular particles [United States Pharmacopeia, USP30-NF25, General Chapter <776>, Optical Miroscopy.] have been systematically studied. To rule out sample dispersion and particle orientation as the root cause of differences in size distribution profiles, we immobilize powder samples on a glass plate by means of a dry disperser. For a defined region of the glass plate, we measure the diffraction pattern as induced by the dispersed particles, and the 2D dimensions of the individual particles using LD and optical microscopy, respectively. We demonstrate a correlation between LD and SIA, with the scattering intensity of the individual particles as the dominant factor. In theory, the scattering intensity is related to the square of the projected area of both spherical and rectangular particles. In traditional LD the size distribution profile is dominated by the maximum projected area of the particles (A). The diffraction diameters of a rectangular particle with length L and breadth B as measured by the LD instrument approximately correspond to spheres of diameter Ø_L and Ø_B respectively. Differences in the scattering intensity between spherical and rectangular particles suggest that the contribution made to the overall LD volume probability distribution by each rectangular particle is proportional to A²/L and A²/B. Accordingly, for rectangular particles the scattering intensity weighted diffraction diameter (SIWDD) explains an overestimation of their shortest dimension and an underestimation of their longest dimension. This study analyzes various samples of particles whose length ranges from approximately 10 to 1000 μm. The correlation we demonstrate between LD and SIA can be used to improve validation of LD methods based on SIA data for a variety of pharmaceutical powders all with a different rectangular particle size and shape.     

A new method for calculating the diameters of partially-sintered nanoparticles and its effect on simulated particle properties

In this paper a new method for the calculation of the diameter of a partially-sintered particle is introduced and shown to be more accurate than the standard d_p=6v/a formula. The method was used to determine the particle sintering rates in a flame producing SiO₂ nanoparticles. The results of the simulations return a value for the average particle fractal dimension closer to the experimental values than is obtained using the standard formula. The particle ensemble was simulated using an efficient bivariate stochastic particle method, which for the first time, was applied to the non-isothermal environment of a premixed laminar flame. The transition from a bimodal particle size distribution to a unimodal particle size distribution for the silica particles was observed. This paper also contains the results of a test simulation which examines the stochastic algorithm under various simple starting conditions and determines its convergence properties.     

Determination of the collision frequency between bubbles and particles in flotation

Collision efficiency for a spherical bubble rising in a uniform concentration of small non-inertial particles is studied by direct numerical simulations (DNS). The Stokes number of the particles is negligibly small so that the particle trajectories follow the streamlines. The effect of the bubble interface contamination is studied for the flow surrounding the bubble using the spherical cap model. Numerical results are obtained for a wide range of bubble Reynolds number (based on bubble diameter d_b) ranging from 0.01 to 1000 and for different angles of contamination ranging from 0^° to 180^°. The collision efficiency is found to be increased with the Reynolds number and significantly decreased with the level of contamination. Correlations of the numerical results are proposed for efficiencies versus d_p/d_b (d_p being the particle diameter), bubble Reynolds number and interface contamination degree. For clean (respectively, fully contaminated) spherical bubbles, the efficiency evolves as d_p/d_b (respectively (d_p/d_b)²) whatever the bubble Reynolds number and the particle size. For partially contaminated bubbles, efficiency can be scaled with d_p/d_b or (d_p/d_b)² depending on both the level of contamination and the particle size.     

A study of particle shape and size effects on hydrodynamic parameters of trickle beds

Uniform-spherical and cylindrical-extrudate particles are employed to study air-water downflow in a packed bed of 14 cm i.d. The effect of particle shape, neglected in the literature so far, is shown to be very significant. A packed bed of extrudates displays significantly greater global dynamic liquid holdup h_d and pressure drop, as well as a trickling-to-pulsing transition boundary at higher gas flow rates, compared to beds of spheres of comparable size. Moreover, packed extrudates exhibit a significant increase of holdup, h_d, in the axial flow direction, a trend reported for the first time as there are no similar data available in the literature; on the contrary beds of spherical particles are characterized by practically constant h_d in the axial direction. Although an explanation for this h_d axial variation is not obvious, one might attribute it to the anisotropy and non-uniformity of interstitial voids of packed cylindrical particles. For beds of uniform spheres, in the diameter range examined (3-6 mm), the effect of size on both dynamic holdup and pressure drop, although quite pronounced, is not as significant as the effect of particle shape. An extensive survey of literature data, obtained with similar spherical particles, suggests that small bed diameters have an appreciable influence on trickling-to-pulsing transition boundary. Comparisons are reported with literature methods for predicting the measured parameters; discrepancies between data and predictions may be partly due to the inadequacy of a single “equivalent” diameter to represent both shape and size of non-spherical particles; predictive methods performing best are also identified.     

Experimental investigation of pressure drop in packed beds of irregular shaped wood particles

The knowledge of the pressure drop across a packed bed of irregular shaped wood particles is of great importance for achieving optimal control and maximum efficiency in many applications, such as wood drying, pyrolysis, gasification and combustion. In this work the effect of porosity, average particle size and main particle orientation on the pressure drop in a packed bed is investigated. To this end, particle size distributions and porosities are determined experimentally.Based on the experimental results obtained in this study, the form coefficient C and the permeability K of the Forcheimer equation are calculated for different packed beds. The Ergun equation requires an average equivalent particle diameter that is derived from the measured particle size distribution. This equivalent diameter and the corresponding bed porosity are used in the well known Ergun equation in order to derive adapted shape factors A and B.Since a change in bed porosity and particle size, caused by the degradation of the wood particles and gravity, can be expected in a reacting packed bed, a set of shape factors for use with the Ergun equation is determined that are independent of porosity and particle diameter and fit the experimental data very well.     

Determination of the adhesion force between particles and a flat surface, using the centrifuge technique

By using a centrifuge technique, the influence of powdery material particle size on the adhesion force particle-surface was determined. In order to achieve this, the adhesion of phosphatic rock (ρ_p = 3.090 kg m^− 3) and of manioc starch particles (ρ_p = 1.480 kg m^− 3) on a steel surface were studied. A microcentrifuge that reached a maximum speed rotation of 14000 rpm and which contained specially designed centrifuge tubes was used. There tubes contained the flat surface where the test particles were deposited. The powder particles were dispersed on these disks and the particles detachment were performed using diverse centrifugal speeds. The graphics of particle percentages still adhering on the surface of the disks as a function of the applied detachment force showed that the profile of adhesion force followed a log-normal distribution. The adhesion force increased with particle size. The manioc starch particles presented adhesion forces greater than those for the phosphatic rock particles for all particle sizes studied. The results obtained were compared with the theory proposed by Derjaguin, Muller and Toporov whose theoretical adhesion presented values close to the experimental data for the phosphatic rock particles adhesion on the stainless steel surface. On the contrary, the theoretical values were lower than the experimental ones for the manioc starch particles maybe due to the small roughness of these particles, their physical properties (softer and deformable material) and/or specific chemical interactions since the organic composition of the manioc starch particles that can dominate the adhesion force. Finally, the separation distance among the surfaces in contact (Z₀) was estimated in approximately 1.0 × 10^− 9 m for the phosphatic rock and 5.0 × 10^− 10 m for the manioc starch. These results were weakly dependent on the particle size range.     

Localization of spherical nanoparticles within lamellar AB diblock copolymer melts through self-consistent field theory

Here we report the results of a three dimensional hybrid self-consistent field theoretic (HSCFT) model describing the equilibrium particle distribution of spherical nanoparticles within symmetric AB diblock copolymer melts. Holding the polymer composition and morphology fixed, we consider a comprehensive parameter space comprised of the Flory interaction parameter describing interactions between B segments and the particle surface compared to the segment-segment interaction parameter (χBP/χAB), the particle volume fraction (?_P), and the ratio of the particle diameter to block copolymer domain spacing (dP/dAB). Analysis of the free energy over this parameter space yields phase diagrams showing the conditions under which particles segregate to the intermaterial diving surface (IMDS) or the center of the domain. Interestingly, w e predict a particle concentration-dependent “reentrant” phase transition in which particles move from the domain interior, to the IMDS, and back as ?_P increases. These results are interpreted as a subtle consequence of the competition between enthalpic polymer-particle interactions and the chain packing frustration imposed by the particulate inclusion. These results are consistent with recent experiments on block copolymer nanocomposites.     

Measurement of size-dependent dynamic shape factors of quartz particles in two flow regimes

Understanding and modeling the behavior of quartz dust particles, commonly found in the atmosphere, requires knowledge of many relevant particle properties, including particle shape. This study uses a single particle mass spectrometer, a differential mobility analyzer, and an aerosol particle mass analyzer to measure quartz aerosol particles mobility (d_m), vacuum aerodynamic, and volume equivalent diameters, mass, composition, effective density, and dynamic shape factor as a function of particle size, in both the free molecular and transition flow regimes. The results clearly demonstrate that dynamic shape factors can vary significantly as a function of particle size. For the quartz samples studied here, the dynamic shape factors increase with size, indicating that larger particles are significantly more aspherical than smaller particles. In addition, dynamic shape factors measured in the free-molecular (χ_v) and transition (χ_t) flow regimes can be significantly different, and these differences vary with the size of the quartz particles. For quartz, χ_v of small (d_m < 200 nm) particles is 1.25, while χ_v of larger particles (d_m ～ 440 nm) is 1.6, with a continuously increasing trend with particle size. In contrast, χ_t of small particles starts at 1.1 increasing slowly to 1.34 for 550 nm diameter particles. The multidimensional particle characterization approach used here goes beyond determination of average properties for each size, to provide additional information about how the particle dynamic shape factor may vary even for particles with the same mass and volume equivalent diameter.

© 2016 American Association for Aerosol Research     

Machine vision based particle size and size distribution determination of airborne dust particles of wood and bark pellets

Dust management strategies in industrial environment, especially of airborne dust, require quantification and measurement of size and size distribution of the particles. Advanced specialized instruments that measure airborne particle size and size distribution apply indirect methods that involve light scattering, acoustic spectroscopy, and laser diffraction. In this research, we propose a simple and direct method of airborne dust particle dimensional measurement and size distribution analysis using machine vision. The method involves development of a user-coded ImageJ plugin that measures particle length and width and analyzes size distribution of particles based on particle length from high resolution scan images. Test materials were airborne dust from soft pine wood sawdust pellets and ground pine tree bark pellets. Subsamples prepared by dividing the original dust using 230 mesh (63 μm) sieve were analyzed as well. A flatbed document scanner acquired the digital images of the dust particles. Proper sampling, layout of dust particles in singulated arrangement, good contrast smooth background, high resolution images, and accurate algorithm are essential for reliable analysis. A “halo effect” around grey-scale images ensured correct threshold limits. The measurement algorithm used Feret's diameter for particle length and “pixel-march” technique for particle width. Particle size distribution was analyzed in a sieveless manner after grouping particles according to their distinct lengths, and several significant dimensions and parameters of particle size distribution were evaluated. Results of the measurement and analysis were presented in textual and graphical formats. The developed plugin was evaluated to have a dimension measurement accuracy in excess of 98.9% and a computer speed of analysis of < 8 s/image. Arithmetic mean length of original wood and bark pellets airborne dust particles were 0.1138 ± 0.0123 and 0.1181 ± 0.0149 mm, respectively. The airborne dust particles of wood and bark pellets can be described as non-uniform, finer particles dominated, very finely skewed with positive skewness, leptokurtic, and very well sorted category. Experimental mechanical sieving and machine vision methods produced comparable particle size distribution. The limitations and merits of using the machine vision technique for the measurement of size and size distribution of fine particles such as airborne dust were discussed.     

Minimizing the effect of density in determination of particle aerodynamic diameter using a time of flight instrument

Particle aerodynamic diameter measurement using an aerosizer (a time-of-flight (TOF) particle size measurement instrument) requires assuming the density of particle being measured. In this paper, a relationship between TOF of spherical particles with different densities through three laser beams, and the lumped parameter, Log[d_aeC_D^−1/2], is found. This allows the effect of density in particle aerodynamic diameter measurement to be minimized.     

Blending of irregularly shaped particles

Existing blending theories have mostly been verified in the past by mixing of monosized, smooth, spherical particles. In this study, binary mixing of non-spherical particles with rough surfaces is shown to adhere to diffusional mixing equations as long as the mean diameters of the two fractions (A and B) are identical, i.e.d_A = d_B. When this is not the case, blending rates (diffusional coefficients of blending, D) reduce drastically when the small particles are not of such a size that they will fit into the interstices between the larger particles. It is shown also that the final standard deviation in these cases is many orders of magnitude higher than the predicted random standard deviation. When d_A = d_B, the diffusion coefficient will depend on the magnitude of d_A. The diffusion coefficient is not a function of the ratio of A to B. In blending in a horizontal mixer, D decreases with addition of lubricant. This is not the case in a V-blender, where bulk mass transfer appears to be the controlling step. In all other respects, V-blending is identical, functionally, to the profiles obtained in cylindrical blending.     

Nanosize Effect on the Deliquescence and the Efflorescence of Sodium Chloride Particles

The deliquescence and efflorescence relative humidity values of 6- to 60-nm NaCl particles were measured using a tandem nano-Differential Mobility Analyzer. The deliquescence relative humidity (DRH) increased when the dry particle mobility diameter decreased below approximately 40 nm. The efflorescence relative humidity (ERH) similarly increased. For example, the DRH and ERH of 6-nm particles were 87% and 53%, respectively, compared to 75% and 45% for particles larger than 40 nm. Power law fits describing the nanosize effect are: DRH(d _m) = 213 d _m ^?1.6+ 76 and ERH(d _m) = 213 d _m ^?1.65+ 44, which are calibrated for 6 < d _m < 60 nm with less than 1% RH uncertainty and where d _m is the dry particle mobility diameter (nm). Two independent methods were used to generate the aerosol particles, namely by vaporizing and condensing granular sodium chloride and by electrospraying a high-purity sodium chloride aqueous solution, to investigate possible effects of impurities on the results. The DRH and ERH values were the same within experimental uncertainty for the particles generated by the two methods. The physical explanation for the nanosize effect of increasing DRH and ERH for decreasing dry particle mobility diameter is that the free energy balance of NaCl increasingly favors smaller particles (i.e., those without water) because the surface areas and hence surface free energies per particle are less for small, anhydrous particles than for bloated, aqueous particles. [Supplementary materials are available for this article. Go to the publisher's online edition of Aerosol Science and Technology for the following free supplemental resources: Graphs and data of the size distribution measurements of the deliquescence- and the efflorescence-mode experiments of the 6-, 8-, 15-, 20-, 30-, and 60-nm dry mobility diameter particles.]     

Effect of initial particle size on grain microstructure of textured ferroelectric ceramics: A phase-field method and brush technique

A phase-field model was employed to simulate the grain microstructure evolution of the textured ceramics. Textured KSr₂Nb₅O₁₅ (KSN) ceramics were chosen as the research object and prepared by using acicular KSN particles as raw materials. A method combining the brush technique with the rolling process was proposed for the directional arrangement of the acicular particles. The effects of the initial particle length distribution and diameter on the grain growth behavior and electrical properties were investigated. It was found the influence of the initial particle length distribution on the grain growth rate mainly depended on its diameter. The use of coarse particles was beneficial to obtain a microstructure with a strongly anisotropic morphology and homogeneous grain size. The obtained KSN ceramics exhibited a high piezoelectric constant d₃₃ of 68 pC/N and Curie temperature of 120 ℃, which was closely related to the grain microstructure.     

Spray drying formulation of hollow spherical aggregates of silica nanoparticles by experimental design

The present work employs an experimental design methodology to optimize the spray-drying production of micron-size hollow aggregates of biocompatible silica nanoparticles that are aimed to serve as drug delivery vehicles in inhaled photodynamic therapy. To effectively deliver the nanoparticles to the lung, the aerodynamic size (d_A) of the nano-aggregates, which is a function of the geometric size (d_G) and the degree of hollowness, must fall within a narrow range between 2 and 4 μm. The results indicate that (1) the feed concentration, (2) the feed pH, and (3) the ratio of the gas atomizing flow rate to the feed rate are the three most significant parameters governing the nano-aggregate morphology. Spray drying at a low pH (<7) and at a low feed concentration (<1%, w/w) generally results in nano-aggregates having small geometric and aerodynamic sizes (d_A = d_G ≈ 3 μm) with a relatively monodisperse size distribution. Spray drying at a higher feed concentration produces nano-aggregates having a larger d_G but with a multimodal particle size distribution. A trade-off therefore exists between having large d_G to improve the aerosolization efficiency and obtaining a uniform particle size distribution to improve the dose uniformity.     

Spin Polarization and Quantum Spins in Au Nanoparticles

The present study focuses on investigating the magnetic properties and the critical particle size for developing sizable spontaneous magnetic moment of bare Au nanoparticles. Seven sets of bare Au nanoparticle assemblies, with diameters from 3.5 to 17.5 nm, were fabricated with the gas condensation method. Line profiles of the X-ray diffraction peaks were used to determine the mean particle diameters and size distributions of the nanoparticle assemblies. The magnetization curves M(H_a) reveal Langevin field profiles. Magnetic hysteresis was clearly revealed in the low field regime even at 300 K. Contributions to the magnetization from different size particles in the nanoparticle assemblies were considered when analyzing the M(H_a) curves. The results show that the maximum particle moment will appear in 2.4 nm Au particles. A similar result of the maximum saturation magnetization appearing in 2.3 nm Au particles is also concluded through analysis of the dependency of the saturation magnetization M_P on particle size. The M_P(d) curve departs significantly from the 1/d dependence, but can be described by a log-normal function. Magnetization can be barely detected for Au particles larger than 27 nm. Magnetic field induced Zeeman magnetization from the quantum confined Kubo gap opening appears in Au nanoparticles smaller than 9.5 nm in diameter.     

The Dynamics of Particles with Translation–Rotational Coupling in the Stokes Flow Regime

Most naturally and industrially generated solid particles are irregular in shape. One type of particle commonly encountered can be identified as flakes and their aggregates. This class of particles exhibits translation-rotational coupling. Based on the principle of similarity, we have conducted an experimental investigation of the dynamics of flake-type particles, employing model particles settling in an oil tank. These model particles are about 1–2 cm in size. The particle Reynolds number is kept under 0.02 to simulate the motion of the flaky aerosols. By introducing factors representing the effects of configuration (e.g., finite thickness and rod diameter) and interaction, shape factors for the composite particles can be determined from the constituent disks. The translational configuration factor λ_t is found to depend mainly on the thickness-to-diameter ratio l _s/d _s and to satisfy λ_t = A + B(1 _s/d _s)^0.14. Furthermore, the ratio of the rotational and coupling configuration factors generally increases with the length of the rod connecting the disks. The wall effect depends linearly on the ratio d _s/D _T (where D _T is the tank diameter) for translational motion but is insignificant for rotational motion.     

Attrition of Victorian brown coal during drying in a fluidized bed

Analyzing the attrition of Victorian brown coal during air and steam fluidized bed drying, the change in particle size distribution over a range of initial moisture contents (60% to 0%) and residence times (0 to 60 minutes) was determined. Dried at a temperature of 130°C with a fluidization velocity 0.55 m/s and an initial particle size of 0.5–1.2 mm, both fluidization mediums show a shift in the particle size distribution between three and four minutes of fluidization, with a decrease in mean particle size from 665 µm to around 560 µm. Using differential scanning calorimetry (DSC), the change in particle size has been attributed to the transition between bulk and non-freezable water (approximately 55% moisture loss) and can be linked to the removal of adhesion water, but not to fluidization effects. This is proved through the comparison of air fluidized bed drying, steam fluidized bed drying, and fixed bed drying—the fixed bed drying is being used to determine the particle size distribution as a function of drying. The results show the three drying methods produce similar particle size distributions, indicating that both fluidization and fluidization medium have no impact upon the particle size distribution at short residence times around ten minutes. The cumulative particle size distribution for air and steam fluidized bed dried coal has been modeled using the equation P_d = A₂ + (A₁ ? A₂)/(1 + (d/x₀)^p), with the resultant equations predicting the effects of moisture content on the particle size distribution. Analyzing the effect of longer residence times of 30 and 60 minutes, the particle size distribution for steam fluidized bed dried coal remains the same, while air fluidized bed dried coal has a greater proportion of smaller particles.     

Online monitoring of drop/particle size and size distribution in liquid–liquid dispersions and suspension polymerizations by optical reflectance measurements

Evolutions of drop/particle size and size distribution in liquid–liquid dispersions and suspension polymerizations of methyl methacrylate (MMA) were monitored by using an online optical reflectance measurement (ORM), and effects of operating parameters such as the agitation rate, concentration of poly(vinyl alcohol) (PVA) dispersant, and initial concentration of poly(methyl methacrylate) (PMMA) in MMA monomer on the Sauter mean diameter (d₃₂) and size distribution of drop/particle were investigated. According to the variations of d₃₂ of drops/particles with time, four characteristic particle formation stages can be identified for suspension polymerization process. The factors that lead to increase the rate of drop break up, such as increasing of concentration of PVA and decreasing of viscosity of dispersed phase, would postpone the particle growth stage. The d₃₂ and size distribution breadth of drops/particles were significant increased when the liquid–liquid dispersions or suspension polymerizations were conducted at low PVA concentrations or MMA/PMMA solutions with high PMMA contents were used as the dispersed phase, in consistent with the scanning electron micrograph observation on final PMMA particles. It is clear that ORM can be effectively applied in online monitoring of size and size distribution of drops/particles in the liquid–liquid dispersions and suspension polymerizations. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43632.     

Drag coefficients of irregularly shaped particles

The steady-state free-fall conditions of isolated groups of ordered packed spheres moving through Newtonian fluids have been studied experimentally. Measurements of the drag coefficients are reported in this paper for six different geometrical shapes, including isometric, axisymmetric, orthotropic, plane and elongated conglomerates of spheres. From these measurements, a new and accurate empirical correlation for the drag coefficient, C_D, of variously shaped particles has been developed. This correlation has been formulated in terms of the Reynolds number based on the particle nominal diameter, Re, the ratio of the surface-equivalent-sphere to the nominal diameters, d_A/d_n, and the particle circularity, c. The predictions have been tested against both the experimental data for C_D collected in this study and the ones reported in previous works for cubes, rectangular parallelepipeds, tetrahedrons, cylinders and other shapes. A good agreement has been observed for the variously shaped agglomerates of spheres as well as for the regularly shape particles, over the ranges 0.15<Re<1500, 0.80<d_A/d_n<1.50 and 0.4<c<1.0.     

Numerical analysis of particle mixing in a rotating fluidized bed

This paper describes the numerical analysis of particle mixing in a rotating fluidized bed (RFB). A two-dimensional discrete element method (DEM) and computational fluid dynamics (CFD) coupling model were proposed to analyze the radial particle mixing in the RFB. Spherical polyethylene particles (Geldart group B particles) were used as model particles under the assumptions that they were cohesionless and mono-disperse with their diameter of 0.5 mm.The validity of the proposed model was confirmed by the comparison between the calculated degree of particle mixing and the experimental one, which was obtained by measuring the lightness of the recorded image taken by a high-speed video camera. Effects of the operating parameters (gas velocity, centrifugal acceleration, particle bed height, and vessel radius) on the radial particle mixing rate were numerically analyzed. The radial particle mixing rate was found to be strongly affected by the bubble characteristics, especially by the bubble size. The mathematical model for the rate coefficient of particle mixing as functions of operating parameters was empirically proposed. The radial particle mixing rate in a RFB could be well correlated by the three dimensionless numbers: dimensionless acceleration (Ac), bubble Froude number (Fr_b), and dimensionless radius on the surface of particle bed (β_s).