Parametric solution of the inverse light-scattering problem for individual spherical particles

We analyze the relation between spherical particle parameters (size parameter ? and relative refractive index m ) and light-scattering indicatrix parameters (fringe pitch and visibility) for ?and m ranging from 7 to 88 and from 1.025 to 1.2, respectively. We consider formation of the indicatrix structure under variation of size parameter ? and phase-shift parameter ? =2 ?(m - 1). We show that indicatrix visibility depends basically on the phase-shift parameter whereas fringe pitch depends on the size parameter. An analysis of these dependencies allows us to determine the region in the ? x ? map where particle parameters can be derived unambiguously from indicatrix parameters. We clarify errors in determination of particle characteristics on the basis of the approximating equations that relate particle size and phase shift to indicatrix parameters.     

Kinematic and static hypotheses for constitutive modelling of granulates considering particle rotation

Summary The granular material perceived as a collection of particles is modelled as a Cosserat or multipolar continuum taking into account the effect of material microstructure. The macro-scale constitutive law for a granular material is derived from the micro-scale of two interacting particles. We adopt an approach based on a static hypothesis and establish two relationships: i) macro-to-micro static relationship, and ii) micro-to-macro kinematic relationship. We derive macro-scale constitutive constants for granular materials with idealized isotropic packing structure. The effects of inter-particle stiffness on the macro-scale constitutive constants are discussed. In addition, Green's function for concentrated force and couple is derived to be expressed in terms of inter-particle stiffness. Using the expressions of Green's function, the physical meaning and the effect of the internal characteristic length for granular materials are discussed.     

Granular packings of cohesive elongated particles

We report numerical results of effective attractive forces on the packing properties of two-dimensional elongated grains. In deposits of non-cohesive rods in 2D, the topology of the packing is mainly dominated by the formation of ordered structures of aligned rods. Elongated particles tend to align horizontally and the stress is mainly transmitted from top to bottom, revealing an asymmetric distribution of local stress. However, for deposits of cohesive particles, the preferred horizontal orientation disappears. Very elongated particles with strong attractive forces form extremely loose structures, characterized by an orientation distribution, which tends to a uniform behavior when increasing the Bond number. As a result of these changes, the pressure distribution in the deposits changes qualitatively. The isotropic part of the local stress is notably enhanced with respect to the deviatoric part, which is related to the gravity direction. Consequently, the lateral stress transmission is dominated by the enhanced disorder and leads to a faster pressure saturation with depth.     

Deformation created by the impact of small angular and spherical particles on individual grains

Damage mechanism induced by 25 m, average size, angular and spherical particles impacting the surface of Cu-30% Zn (-brass) was investigated. Particles were impacted to the surface at normal incidence, with a velocity of 12 m/s. The primary characterization tools used were scanning electron microscopy (SEM) and atomic force microscopy (AFM). AFM allowed for the measurement of impact profiles, those of the cut surface and material pile-ups. Deformed volume by the particles was limited to a single grain. The impacts produced were asymmetrical and the chip formation was also highly directional. These asymmetries were the same in a single grain but they varied from grain to grain. Regardless of particle geometry, similar deformation features were observed on the target surface impacted by angular and spherical particles. The direction of the deformation appeared to be imposed by the mechanical response of the deforming grain. Since the deformation induced by a single impact is limited to a single grain, anisotropic mechanical properties of the individual grains observed were attributed to their impact damage morphology.     

Measurement of scattering properties of individual particles with a scanning flow cytometer

A hydrofocusing head with an optical cuvette has been developed for the flow cytometer to generate complete scatter patterns of single particles at scattering angles ranging from 10° to 120°. The scatter signal has been measured as a function of the angle (a flying indicatrix) by the use of particle motion within a scanning system of the flow cytometer by the use of a single photomultiplier. Scattering data measured with the flow cytometer have been compared with those calculated from Mie theory for latex particles. A calculation algorithm has been used to estimate the size and the refractive index of spherical particles from the scattering data measured.     

Surface heat transfer coefficients to stationary spherical particles in an experimental unit for hydrofluidisation freezing of individual foods

Convection heat transfer to spherical particles inside a hydrofluidisation freezing unit was investigated. The unit contained a food tank with a perforated bottom plate to create agitating jets. An aqueous solution of 30% ethanol+20% glucose was used as the refrigeration medium in a temperature range of −20 to 0 °C and flow rates from 5 to 15 l min⁻¹. The lumped capacitance method was applied on cooling profiles of aluminium spheres of 5–50 mm to obtain surface heat transfer coefficients. Coefficients were within a range of 154–1548 W m⁻² °C⁻¹, and depended on diameter, flow rate, refrigeration temperature and fluid agitation level. The agitation due to jets was accounted for by means of an agitation Reynolds number in a Nusselt correlation A large variability of measured surface heat transfer coefficients was observed. This could be attributed to non-constant flow and turbulence fields in the refrigeration medium. The value of the heat transfer coefficient was compared to values determined on strawberries.     

Vacuum heating of spherical alumina particles

Heating of spherical alumina particles by high-intensity laser radiation under vacuum conditions to the melting temperature is investigated with account for the nonuniform distribution of energy sources with respect to the particle volume.B. I. Stepanov Institute of Physics, Academy of Sciences of Belarus, Minsk. Translated fron Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 3–4, pp. 307–312, September–October, 1994.     

Unsteady mass transfer of spherical particles

A one-dimensional problem on unsteady diffusion of a distributed substance through a conventional diffusion boundary layer is formulated and solved. Based on its solution relations are obtained for calculation of the instantaneous and mean mass transfer coefficients for the times corresponding to layer formation. A procedure is proposed for calculation of the mentioned coefficients using the known dimensionless relations derived for the steady process. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 6, pp. 930–935, November–December, 1997.     

Particle shape effects in discrete element modelling of cohesive angular particles

This paper investigates the effect of particle angularity on general granular response concentrating on flow and stress-strain behaviour. A 2D polygon DEM model is developed to a 3D polyhedron model. The effect of particle shape on the response of polygons in simple shear and polyhedra under gravity flow is investigated using regular shapes with rounded vertices. The study concentrates on the angularity rather than aspect ratio by comparing circles, near squares and near equilateral triangles in 2D and spheres, tetrahedra and octahedra in 3D. In summary the more angular the particle the greater the resistance to the forcing load and the flowability is reduced. A mix of spheres and octahedra demonstrates an approximate linear combination of effects.     

Free precipitation of spherical particles in anomalous-viscosity liquids

An experimental study is reported of the motion of solid spherical particles in four concentrated high-polymer solutions in a centrifugal force field. The results are compared with the theoretical dependences given by Tomita, Slattery, and Wasserman.     

Chemical control in precipitation of spherical zirconia particles

Monodisperse spherical zirconia particles are precipitated by hydrolysis of alcoholic solutions of zirconium alkoxides in the presence of long-chain carboxylic acids. The particle size can be finely tuned from 0.1 to 2.5 m by controlling the concentration of zirconium alkoxide, the water/zirconium ratio, the nature of alcohol from ethanol to butanol, the nature of carboxylic acid from caproic to oleic acid and its concentration. The relationships between the induction time before nucleation, the particle size and all the above parameters are tentatively explained on the grounds of the solubility of the carboxy-alkoxide derivatives and their tendency to form micelles. Calcination of precipitated powders between 300 and 600 C produces mixtures of varying composition from cubic to monoclinic phases of small crystallite sizes, and brings out the loss of surface area and organic content. Different conditions of drying powders lead to variously ordered microstructures.     

Simulation of statistical packings of spherical particles

An algorithm has been developed which simulates the process of statistically filling a fixed volume with spherical particles and which allows one to obtain the distributions of the coordination numbers of particles depending on the packing density.Institute of Engineering Chemistry, Ural Branch, Russian Academy of Sciences, Perm. Translated from Inzhenerno-Fizicheski Zhurnal, Vol. 63, No. 1, pp. 69–71, July, 1992.     

Adhesive interaction of elastically deformable spherical particles

Two spherical particles that attract each other by van der Waals volume forces and can undergo deformation as a result of the attraction are considered. Small deformations of such particles can be described by the solution of the Hertz problem. The deformation of particles, in turn, alters the force of attraction between them. It has been established that the relationship between the adhesion and elasticity of the indicated particles is determined by the degree to which these particles deform and that the adhesion force acting between the particles depends on their elasticity, size, and the Hamaker constants.     

Synthesis of nano-sized spherical barium-strontium ferrite particles

Magnetic recording media requires good particle dispersion, a smooth surface, and small interparticle interaction to make an adequate signal-to-noise ratio (SNR). Well dispersed 50-60 nm sized spherical barium-strontium ferrite (S-Ba/Sr-Fe) nanoparticles were successfully prepared with 40 nm sized hematite precursor particles and BaCO/sub 3//SrCO/sub 3/ colloid. The coercivity and saturation magnetizations of S-Ba/Sr-Fe nano-particles were 1568 Oe and 48.6 emu/g, respectively. In order to evaluate magnetic interaction, magnetic tape was prepared using an Eiger mill with binder and organic solvent. /spl Delta/M measurement showed the S-Ba/Sr-Fe nanoparticles in the tape had negative magnetic particle-to-particle interaction.     

亚微米球形ZrO_2颗粒材料的水热法合成及表征

以Zr(NO_3)_4·5H_2O和CO(NH_2)_2为原料,乙醇为溶剂,通过水热法合成亚微米级球形ZrO_2颗粒;用扫描电子显微镜(SEM)、X射线衍射仪(XRD)、傅里叶红外光谱仪(FT-IR)、热重-差热分析仪(TGA-DTA)、紫外-可见光吸收光谱仪(UVVis)对ZrO_2颗粒进行分析表征,研究工艺条件对球形ZrO_2颗粒尺寸和形貌的影响。结果表明:通过水热法合成的球形ZrO_2颗粒粒径分布较窄,添加适量的表面活性剂、无机盐溶液及水对产物的尺寸与形貌具有一定的影响;添加适量水可获得粒径分布更窄的球形ZrO_2颗粒,且热处理对球形ZrO_2颗粒的粒径大小和形状影响不大。     

Preparation of monodispersed spherical barium titanate particles

Spherical barium titanate particles with cubic phase were synthesized by a low-temperature hydrothermal reaction. Firstly, The method of hydrolysis of titanium tetrachloride was used for producing spherical TiO₂ particles (0.45–1.5 μ m) with various concentrations of TiCl₄(0.05–0.2 M) and volume ratios of acetone to water solutions (RH = 0–4). These TiO₂ particles were converted to barium titanate by a hydrothermal conversion in a barium hydroxide solution. The size and morphology of the TiO₂ particles was controlled by the volume ratio of acetone to water (RH ratio) in the mixed solvent. At the RH ratio of 3, the morphology of TiO₂ particles was very uniform and discrete. These TiO₂ particles were in the anatase phase and were converted to the rutile phase when the calcination temperature increased to 700∘C and above. Uniform and spherical barium titanate particles were successfully synthesized from the as-prepared TiO₂ particles by using a hydrothermal reaction in a barium hydroxide solution. The Ba/Ti ratios, reaction temperature, and reaction time did not influence the size and morphology of BaTiO₃ particles, but increased the concentration of unfavorable salts such as Ba(OH)₂ and BaCO₃. The high purity BaTiO₃ particles could be obtained by washing with formic acid to remove the unfavorable salts. The size and morphology of the BaTiO₃ particles remained the same as those of the TiO₂ particles, confirming the in-situ transformation mechanism for the conversion of TiO₂ to BaTiO₃. The as-synthesized particles were cubic phase and transformed to tetragonal phase after calcinations at 1150∘C for 1 h. The mean density of the pellets sintered at 1300∘C for 2 h was 5.86 g/cm³ and accounted for 97.34% of the theoretical density.     

Effect of rotation of the inner cylinder on the equilibrium condition of spherical particles in a turbulent ascending flow in an annular channel

The equilibrium condition of a solid spherical particle in a turbulent flow is considered. A relation between the rotational velocity of the inner cylinder and the critical velocity of the ascending flow in an annular channel is obtained for the range of Reynolds numbers 10³ –5 · · 10⁴.     

Morphology-dependent resonances of nearly spherical particles in random orientation

We use precise T-matrix calculations for prolate and oblate spheroids, Chebyshev particles, and spheres cut by a plane to study the evolution of Lorenz-Mie morphology-dependent resonances (MDRs) with increasing asphericity of nearly spherical particles in random orientation. We show that, in the case of spheroids and Chebyshev particles, the deformation of a sphere by as little as one hundredth of a wavelength essentially annihilates supernarrow MDRs, whereas significantly larger asphericities are needed to suppress broader resonance features. The MDR position and profile are also affected when the deviation of the particle shape is increased from that of a perfect sphere. In the case of a sphere cut by a plane, the supernarrow MDRs are much more resistant to an increase in asphericity and do not change their position and profile. These findings are consistent with the widely accepted physical interpretation of the Lorenz-Mie MDRs.