Crushing characteristics

A method of measuring the basic characteristics of comminution was developed. These characteristics are expressed by the major comminution functions: crushing probability function, energy function and breakage function. The crushing probability function is the strength distribution of particles of a given size. The energy function is the strength of the particles as a function of their sizes. And finally, the breakage function is the size distribution of the crushed material. The functions are defined mathematically. Several natural minerals were tested by drop tests in order to determine their individual comminution functions. From the tests, several crushing properties of the particulate materials can be derived. The comminution functions given in this paper would be the basic elements in developing mathematical models for various crushing and grinding processes.     

Investigation of lint particle adhesion in offset printing using Weibull statistics

Linting is one of the biggest concerns for the newspaper printing industry. In the offset printing process, lint particles from the paper are removed from the paper surface under the force of the tacky ink, adhere to the printing blanket and disrupt the transfer of ink, causing deterioration in image quality and affecting the pressroom productivity. This paper deals with the bond strength of the lint particles released from the paper substrate and printing blanket surface. The strength distribution of lint particles was characterised in order to study the dynamics of linting. The dynamics was modelled using a system with two first-order rate equations. Weibull statistics were used to describe the particle size distribution of the lint collected after the sheet-fed printing trials. In this investigation, the lint samples were collected by washing the lint from the printing blanket, filtering and performing image analysis to measure the particles. In order to analyse the data, the lint particle size was set as an independent variable. The number of small particles removed is as expected much higher than the number of larger particles. When the ink tack is increased and thus also the force working on the lint particles, then the relative increase in large particles is higher than the number of small particles. The removal rate of particles from the printing blanket is independent of particle size indicating that both the adhesion force between particles and blanket and the removal force due to ink tack is proportional to the particle area.     

A multifractal comminution approach for drilling scaling laws

The drilling comminution is theoretically and experimentally analyzed by a multifractal approach. A generalization of the three classical comminution laws [Rittinger, P.R., 1867. Lehrbuch der Aufbereitungskunde. Berlin; Kick, F., 1885. Das Gesetz der Proportionalen Widerstände. Leipzig; Bond, F.C., Min. Eng. 193 (1952) 484] has been performed to evaluate the energy dissipation in the process and to compute the mass distribution of the particles. A transitional fractal exponent of the fragment size distribution is experimentally demonstrated to exist. As a consequence, a multifractal scaling law for the partial mass of fragments and its physical interpretation is consistently proposed.In addition, we show, both theoretically and experimentally, that the drilling strength is strongly size-dependent and cannot be considered a material constant, as classically supposed. Consequently, a multifractal scaling law for the drilling strength is also proposed.     

Microstructure and phase evolution of micronized ceramic colorants from a pilot plant for inks production

The advent of inkjet printing as digital decoration of ceramic materials has irreversibly modified the industrial decoration technology, imposing companies to change the colorant production process. The inkjet application requires micronized particles in the ultrafine particle size range (smaller than 1 μm). Particles size reduction of ceramic colorants is performed by a high-energy comminution process in wet-operated bead mills, affecting colorants properties. Since a deep knowledge of milling-induced microstructural changes is still lacking, the micronization effects on a set of five industrial ceramic colorants are thoughtfully investigated in this work by simulating the industrial process at a pilot plant. Particle size distribution and energy consumption are monitored during the comminution process. The compositional (including crystallite size and microstrain analysis of the main phases) and morphological variation of four ceramic pigments (yellow zircon, brown spinel, pink malayaite, and green eskolaite) and one dye (blue olivine) is investigated by XRPD (Rietveld method) and SEM analyses. The analytical approach combined with a physical/semiempirical modelling of the colorants elastic features versus the energy demand for particle reduction has yielded details on the nature of the micronization-induced microstructural changes in ceramic colorants. Specifically, the comminution efficiency as well as the crystalline phase stability are related to the intrinsic properties of each colorant. Brittle breakage rather than plastic deformation on comminution are also system dependent. When an euhedral to subhedral crystal habit is maintained a brittle fracture is preserved throughout the comminution progress, while the formation of flake-like particles and particle agglomeration are strong evidences of plastic deformation. The last evidence deals with the material elastic features. Materials with high bulk modulus convert the grinding energy to lattice defects that lead to particle breakage by brittle fractures, while materials with lower bulk modulus convert/dissipate part of the supplied energy in plastic deformations, drastically decreasing the comminution process efficiency.     

The effect of particle shape on simple shear flows

Simple shear flows, (without gravity force and implemented using periodic boundary conditions or in Couette flow configurations with gravity) have been the subject of study using DEM simulation for more than two decades. Earlier studies explored the effect of attributes such as shear rate, particle size and domain scale on the distribution of the particles in the flow, velocity profiles and the stress distributions. These studies were conducted using simple shapes for the particles such as spheres. In recent years, the importance of particle shape on flow has been recognized in a range of industrial application including mixing, comminution, hopper discharge and chute flows. In this paper, we return to the simple shear flows and quantitatively explore the effect of particle shape on velocity, volume fraction, granular temperature and stress distributions across the channel. Particle shape is found to sharply increase the strength of the material making it stronger and harder to shear. The generation of particle spin throughout the flow of non-circular particles leads to high granular temperatures, dilative pressures and lower solid fractions in the core of the flow. For aspect ratios between 0.6 and 0.5, a transition in the effective behaviour of the wall boundary conditions is identified. The connections of shape to spin, to granular temperature, to bulk flow changes are elaborated.     

KINETICS OF HETEROGENEOUS MAGNETIC FLOCCULATION USING A BIVARIATE POPULATION-BALANCE EQUATION

The discrete bivariate population-balance equation is formulated and solved to describe the kinetics of heterogeneous magnetic flocculation of colloidal paramagnetic particles in a uniform magnetic field. The particles are allowed to have various sizes and values of magnetic susceptibility. Computations show the importance of particle size and magnetic susceptibility on the flocculation rate and the transient bivariate (size/magnetic susceptibility) density function. The particle size distribution of certain magnetic-susceptibility particles and the magnetic-susceptibility distribution of certain size particles are calculated as functions of time and initial and operatingconditions. The composition of a floe at any time depends on magnetic, van der Waals, double layer, and hydrodynamic forces among pairs of particles. The magnetic force is a function of the particle size, magnetic susceptibility, and strength of the magnetic field. Results are presented for various initial conditions of particles after ten minutes of flocculation. The results are of significance in understanding the forces among the particles and designing efficient magnetic separation processes.     

Particle size monitoring in dense suspension using ultrasound with an improved model accounting for low‐angle scattering

The inherent ability of ultrasonic wave to propagate in dense and opaque suspensions makes it a desirable method for online measurement of particle size distribution in industrial operations. The ability of ultrasonic attenuation spectroscopy to determine particle size distribution has been extended to dense suspensions of particles lying predominantly in the intermediate wave propagation regime at the measurement frequencies. This was achieved by accounting for the effect of detector size and shift in the frequency spectrum under dense conditions in the theoretical model and deconvolution algorithm, respectively. The proposed modifications enable the application of this technique in various industrial processes requiring in situ and real‐time measurement of particle size distribution such as crystallization, mineral processing and food processing. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

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.     

Microstructural and mechanical evaluation of porous biomorphic silicon carbide for high temperature filtering applications

Biomorphic SiC (bioSiC) is a low cost SiC/Si composite obtained by melt infiltration of carbon preforms obtained from the pyrolysis of cellulose precursors. The porosity and pore size distribution of bioSiC can be tailored for specific applications by adequate selection of the wood precursor. Natural and artificial industrial woods were explored as possible bioSiC precursors. Silicon was removed by chemical etching. Relevant microstructural parameters such as pore size distribution, total porosity, and permeability were characterized. Since the filtration process involves large pressure gradients along the material at high temperatures, mechanical properties of porous bioSiC from the different precursors were evaluated at room temperature and 800 °C. The feasibility of porous bioSiC as a filtration material for high temperature gasification processes is discussed in terms of these properties. MDF-bioSiC is shown to be a promising material for such applications because of its good mechanical properties, interconnected porosity, pore sizes, and permeability.     

Effects of raw material particle size distribution on the characteristics of Scots pine sawdust fuel pellets

In order to study the influence of raw material particle size distribution on the pelletizing process and the physical and thermomechanical characteristics of typical fuel pellets, saw dust of Scots pine was used as raw material for producing pellets in a semi industrial scaled mill (∼ 300 kg h^− 1). The raw materials were screened to a narrow particle size distribution and mixed into four different batches and then pelletized under controlled conditions. Physical pellet characteristics like compression strength, densities, moisture content, moisture absorption and abrasion resistance were determined. In addition, the thermochemical characteristics, i.e. drying and initial pyrolysis, flaming pyrolysis, char combustion and char yield were determined at different experimental conditions by using a laboratory-scaled furnace. The results indicate that the particle size distribution had some effect on current consumption and compression strength but no evident effect on single pellet and bulk density, moisture content, moisture absorption during storage and abrasion resistance. Differences in average total conversion time determined for pellet batches tested under the same combustion conditions was less than 5% and not significant.     

Agglomeration of fine particles subjected to centripetal compaction

Agglomeration is a common phenomenon in many processes. The mechanical properties of agglomerates strongly depend on their structures. This paper presents a numerical study of the agglomeration of fine particles down to 1 μm in size based on the discrete element method. The agglomerates were formed with particles initially generated randomly in a spherical space and then packed under an assumed centripetal force. Agglomerate structure, packing density, coordination number and tensile strength were analysed with particular reference to the effect of particle size associated with the van der Waals attraction. The results showed that both the packing density and coordination number of the agglomerates decay exponentially to their limits as agglomerate size increases. The tensile strength of the agglomerates was calculated from the simulations and shown to decrease with the increase of particle size. The strength was also estimated from the Rumpf model supported by the empirical equations formulated based on the present simulation results. The good agreement between the results from the simulations and the estimation indicates that the equations are useful to facilitate engineering applications.     

Low-temperature fabrication and characterization of porous SiC ceramics using silicone resin as binder

Commercially available silicone resin and silicon carbide (SiC) powders were adopted as the starting materials for the fabrication of porous SiC ceramics. During the heat treatment process, silicone resin experienced an organic–inorganic transformation and acted as the bonding material between SiC particles at a low temperature of 1000 °C. The mean particle size of starting SiC powders and silicone resin content can control the pore size, open porosity and fracture strength. The flexural strength of porous SiC ceramics increases with increasing silicone resin content and decreasing mean particle size of SiC powders. Larger pores can be obtained with coarser starting SiC powders and higher silicone resin content. The fracture surface of porous SiC ceramics was observed.     

Analysis of particle fracture by repeated stressing as damage accumulation

Breakage of particulate materials by repeated low-energy stressing events is an important subject in areas such as particle transport - both mechanical and pneumatic - and comminution. Recently, a mathematical model, based on continuum damage mechanics, has been proposed to describe fracture of particles subjected to repeated loading and has been applied to model breakage of single particles by repeated impacts in a drop weight apparatus. The present paper analyzes the model in greater detail by investigating how its only parameter varies with particle size and shape, demonstrating also its validity to describe repeated impacts of particles against an anvil, such as in drop and air-gun tests. In addition, a model is proposed to describe the size distribution of the progeny under low-energy stressing events.     

The application of the attainable region analysis to comminution

The aim of any comminution circuit is to produce material of a desired particle size distribution (PSD) at a minimum operational cost. Currently, the comminution process is energy intensive and operates at very low efficiency when the input energy is compared to the breakage achieved. The attainable region (AR) technique has been successfully used to solve optimization problems simultaneously with the process synthesis formulation of reactor systems. The AR looks at the fundamental processes of a given system and determines all the possible outputs to which the objective function can be applied and an optimal process solution selected.Particle breakage, separation (classification) and mixing are identified as the three fundamental processes of interest taking place during comminution. Breakage and mixing processes are used in this paper to illustrate the applicability of the AR theory in comminution. We develop a fundamentally based model which is equipment independent to describe breakage. Specific energy is the independent variable and the production of particles with a certain PSD is the objective function. We use geometric construction to represent this PSD as a point in an n-dimensional space in relation to an input specific energy. Output PSDs are dependent on the input PSDs, allowing connectivity of the batch grinding stages to form a pseudo-continuous process.Specific energy is used as the control variable to obtain sharper product PSDs. It is shown that the same net energy consumed in the system can produce different product PSDs. Therefore, this implies that the design of comminution circuits should achieve better control of the specific energy. Once the candidate AR is constructed, operational process targets can be defined more accurately. This establishment of targets permits a measure of the actual process efficiency against a theoretical target. The advantage of the AR method lies in its ability to develop not only the performance of the optimal circuit but also the operational conditions to be used in the optimal process circuit. This also answers the process synthesis question of the type of equipment to be used which is a function of the specific energy.     

Breakage probability of irregularly shaped particles

The investigation of breakage probability by compression of single particles was carried out. The spherical glass particles and irregularly shaped particles of NaCl, sugar, basalt and marble were subjected to a breakage test. The breakage test includes the compression up to breakage of 100 particles to obtain the distribution of the breakage probability depending on the breakage force or compression work. The breakage test was conducted for five particle size fractions from each individual material, at two stressing rates. Thus obtained 50 breakage force distributions and corresponding 50 breakage work distributions were fitted with log-normal distribution function.Usually, the breakage probability distribution can be found by means of stress or energy approach. The first one uses the stress to calculate the breakage probability distribution. The second approach uses the mass-related work done to break the particle. We prefer to use the breakage force and energy as essential variables. The correlation between the force and energy at their breakage points is obtained by integrating the characteristic force–displacement curve, i.e. the constitutive function of elastic–plastic mechanical behavior of the particle. The irregularly shaped particle is approximated by comparatively “large” hemispherical asperities. In terms of elastic–plastic deformation of the contacting asperities with the plate, a transition from elastic to inelastic deformation behavior was considered. Thus, one may apply the model of soft contact behavior of comparatively stiff hemispheres. Based on this model a relationship between the breakage force distributions and corresponding energy distributions was analyzed. Every tested material exhibits a linear relationship between average breakage energy and average breakage force calculated for every size fraction.For future consideration both force and energy distributions were normalized by division by average force or energy, consequently. The relationship between the fit parameters of normalized energy distribution and corresponding fit parameters of normalized force distribution was established. The mean value and standard deviation of normalized force distribution can be found from mean value and standard deviation of normalized energy distribution by means of system of two linear equations. The coefficients of those linear equations remain the same for all of the above tested materials; particle size fractions and stressing rates. As a result the simple transformation algorithm of distributions is developed. According to this algorithm the force distribution can be transformed into energy distribution and vice versa.     

Toughening of polypropylene with calcium carbonate particles

Polypropylene-CaCO₃ composites were prepared on a twin screw extruder with a particle content of 0-32 vol%. The influence of particle size (0.07-1.9 μm) and surface treatment of the particles (with and without stearic acid) on the toughening properties were studied. The matrix molecular weight of the polypropylene was also varied (MFI 0.3-24 dg/min). The experiments included tensile tests, notched Izod impact tests, differential scanning calorimetry (DSC), scanning electron microscopy and rheology experiments. The modulus of the composites increased, while the yield stress was lowered with filler content. This lowering of yield stress was connected to the debonding of the particles from the polypropylene matrix. From DSC experiments it was shown that the particle content had no influence on the melting temperature or crystallinity of the PP phase, also particle size showed no effect on the thermal properties. The impact resistance showed large improvement with particle content. The brittle-to-ductile transition was lowered from 90 to 40 °C with the addition of CaCO₃ particles. Notched Izod fracture energy was increased from 2 up to 40-50 kJ/m². The stearic acid coating on the particle surface showed a large positive effect on the impact strength. This was mainly due to the improved dispersion of the CaCO₃ particles. Aggregates of particles clearly had a detrimental effect on the impact behaviour of the composites. The smaller particle sizes (<0.7 μm) showed coarse morphologies and this lowered the toughening efficiency. The molecular weight of the polypropylene matrix had a profound effect on the toughening properties. A higher molecular mass shifted the brittle-to-ductile transition towards lower temperatures. At the higher filler loads (>20 vol%), however, still problems seem to occur with dispersion, lowering the toughening efficiency. Of all particle types used in this study the stearic acid treated particles of 0.7 μm were found to give the best combination of properties. From the study of the micro-toughening mechanism it was shown that at low strain the particles remain attached to the matrix polymer. At higher strain the particles debond and this leads to a change in stress state at the particle size level. This prevents crazing of the matrix polymer and allows extensive plastic deformation, resulting in large quantities of fracture energy.     

水泥颗粒粒度分布分形维与其胶砂抗压强度的关系研究

为研究水泥颗粒粒度分布分形维与其胶砂抗压强度的关系,利用粒度分布分形维的计算模型分析了有关文献报道的10种水泥颗粒粒度分布分形维值,结果表明:定量表征其分形特征的分形维值在2.325～2.435之间,各水泥颗粒粒度分布具有分形特征;分析了水泥颗粒粒度分布分形维值与水泥3d抗压强度、28d抗压强度的关系,分析表明:化学组成和矿物组成基本相同的条件下,水泥颗粒粒度分布分形维与水泥胶砂的3d、28d抗压强度具有较好的正线性相关关系。     

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.     

Handling properties of cereal materials in the presence of moisture and oil

A powder flow analyzer attached to a Texture Analyser (Stable Micro Systems, UK) was used to compare the flow behaviour of four cereals systems: maize and wheat (in both starch and flour forms), as functions of particle size and distribution, water content and the addition of different types of oil. It was expected that the smaller the particle size the higher the tendency to stick (because of less free volume between the particles), but that was not the case. The results showed that wheat starch used, with bigger particle size than maize starch, had higher cohesion properties and as water content increases the cohesion increases by the same magnitude. This was attributed to the differences in granular shape as well as protein quantity and quality. Caking strength for both starches was influenced by the water content; in particular at 30% water content (w/w), neither cohesion nor caking indices could be measured for wheat starch because of the high stickiness of the particles.Although the two flours had particles of very similar sizes, with differences in the distributions only, maize showed higher cohesion indices compared to wheat flour. These values decreased with increasing water content. The caking property for maize was not significantly affected by water content with values of approximately 100 ± 5. The caking strength increased for wheat flour from 8 to 500 as moisture increased from 12.5 to 30%. This was ascribed to the differences in hydration properties of the two flours. For wheat flour and as the water content increased, gluten started to form and would require more than 30% to form a homogenous, visco-elastic mass.Generally, cohesivity and cake forming ability were affected by water content as well as the physical state of the oil i.e. by the solid/liquid ratios. As water content increases, wheat starch showed the greatest packing and cohesive behaviour, with and without the oil, while maize flour exhibited the weakest packing and cohesive properties.     

Analysis of the relationship between particle size distribution of α-calcium sulfate hemihydrate and compressive strength of set plaster—Using grey model

Particle size distribution (PSD) is one of the important factors associated with the strength property of cementitious materials. However, the relationship between PSD of α-calcium sulfate hemihydrate (α-HH) and compressive strength of set plaster is not well known. The plaster system could be regarded as a grey system and a grey model was developed to explore the relationship. The grey model shows that the compressive strength is derived from the combined action of each particle fraction, which could be divided into two groups. One works with positive effect: the particle fractions of 0-20 μm, 20-50 μm and 90-140 μm. The other works with negative effect: the particle fractions of 50-90 μm and > 140 μm. Variations of the compressive strength with the increment of specific particle fractions, which result from actions of particles on the hydration rate and the characteristics of pore structure, are in general agreement with the results given by the grey model. The availability of the grey model is restricted by the water-hemihydrate weight ratio (W/H) giving standard consistency of α-HH paste. The results indicate that the grey model could provide a potential method to evaluate the relationship.