Binary Particle Systems Research Articles

Dynamic response of well-mixed binary particulate systems subjected to low magnitude vibration

The dynamic response of well-mixed binary mixtures subjected to low magnitude vibration was investigated using a newly developed non-invasive method. An apparent mass, defined as a ratio of the base force to base acceleration, was measured when applying a sweep vibration that ranged from 10 to 2000 Hz. The method could operate more rapidly, conveniently and non-destructively for a wider range of particle packing states, including a natural packed bed, compared to previous methods. The apparent mass data exhibited several significant peaks due to the bed harmonic resonance. The first peak frequency gave the longitudinal elastic modulus of the bed via the velocity of longitudinal stress wave propagation. For loosely packed mixture beds, the mixing fraction dependence upon the elastic modulus was found to be describable by the two-phase series model. In addition, the particle packing dependence upon the elastic modulus agreed reasonably well with the fourth power scaling law in spite of the wide size distribution. Comparison of the two-phase series model and experimental data for a range of particle packing fractions was made in terms of the coefficient of the scaling law.

The removal of hydrogen sulfide with manganic sorbent in a high-temperature fluidized-bed reactor

The removal of hydrogen sulfide (H2S) from simulated gas was carried out in a batch type fluidized-bed reactor using natural manganese ore (NMO), which consists of several metal oxides (MnOx: 51.85%, FeOy: 3.86%, CaO: 0.11%). The H2S breakthrough curves were obtained by changing temperature, gas velocity, initial H2S concentration, and aspect ratio. Moreover, the effects of the particle size and the particle-mixing fraction on H2S removal were investigated in a binary system of different particle size. From this study, H2S removal efficiency increased with increasing temperature but decreased with increasing excess gas velocity. The breakthrough time for H2S decreased as the gas velocity increased, which leads to reducing gas-solid contacting due to gas bypassing in a fluidized bed reactor. Improvement of H2S removal efficiency in continuous process can be expected from the results of the binary particle system with different size in a batch experiment. The NMO could be considered as a potential sorbent in H2S removal.

Particle mixing in bubbling fluidized beds of binary particle systems

The mixing and segregation behavior of spherical solids between 20 and 40 mm in diameter in a bubbling fluidized bed of quartz sand was investigated. The experimental system used is a cold-air fluidized bed of 0.45×0.45 m bed area and about 0.5 m bed height. Binary systems “particle/sand” were studied using two different sizes of sand (Geldart B–D) and varying the fluidization velocity and the size, density and volumetric fraction of the large solids. Time average segregation patterns of the solid mixtures were obtained from single particle trajectories measured by a newly developed experimental procedure. The method utilizes the interactions between a magnetic field imposed on the fluidized bed chamber and a single metal covered tracer particle, which is moving inside the fluidized bed. The technique proposed is generally suitable to locate metallic spheres in three dimensions inside non-transparent and non-metallic media at rates of about 50 samples per second. Experimental results presented within this paper indicate that segregation of large flotsam particles is apparent in bubbling fluidized bed systems particularly at low superficial velocities, in coarse particle systems and for low densities of the flotsam particles.

CFD modeling of gas‐fluidized beds with a bimodal particle mixture

AbstractA computational fluid dynamics model was developed for gas‐solid fluidized beds containing a mixture of two particle species. To calculate stresses of the solid phase, the kinetic theory of granular flow was extended to consider a binary mixture of smooth, nearly elastic, spheres. The developed model was simulated to demonstrate key features of binary mixture fluidization. Bed expansion with a binary mixture of different size particles, but with identical densities, was much higher than that of a system consisting of mono‐sized particles of the same mean size as the bimodal mixture. Minimum fluidization velocity for the binary particle system was significantly lowered. The mixing behavior of the binary mixture of particles, characterized by the mixing index, increased with increasing superficial gas velocity. For a binary mixture of particles of larger size with lower density and smaller size with higher density, larger, lighter particles segregated to the top of the fluid bed, while smaller, heavier particles segregated to the bottom. With increasing fluidization velocity, this segregation pattern reversed and “inversion” occurred. The drag and gravity force difference between small, heavy particles and large, light particles was dominant at low gas velocities. With an increase in gas velocity, however, the gradients in granular temperature and pressure became dominant terms in the equations for the relative force and thus velocity between two different particle species.

Detection and Analysis of Aerosol Particles by Laser-Induced Breakdown Spectroscopy

Laser-induced breakdown spectroscopy (LIBS) was evaluated as a means for quantitative analysis of the size, mass, and composition of individual micron-to submicron-sized aerosol particles over a range of well-characterized experimental conditions. Conditional data analysis was used to identify LIBS spectra that correspond to discrete aerosol particles under low aerosol particle loadings. The size distributions of monodisperse particle source flows were measured using the LIBS technique for calcium- and magnesium-based aerosols. The resulting size distributions were in good agreement with independently measured size distribution data. A lower size detection limit of 175 nm was determined for the calcium- and magnesium-based particles, which corresponds to a detectable mass of approximately 3 femtograms. In addition, the accuracy of the LIBS technique for the interference-free analysis of different particle types was verified using a binary aerosol system of calcium-based and chromium particles.

二成分系流動層内の気泡と粗大粒子挙動の可視化

Fluidized-bed combustion systems are composed of many kinds of particles with a variety of sizes, e.g. coal, sand, RDF, limestone etc. In such a binary system of particles, the segregation, if occurs, may harm the combustion, mixing and heat transfer in the bed, depending on the particle movement. The particle movement or circulation in the fluidized-bed depends on many factors, such as the density ratio, size ratio, shape of particle, fluidization velocity. Owing to the difficulty of flow visualization, such particle movement has not been fully understood so far. This paper describes large-particle movement obtained by the flow visualization using neutron radiography. Tracer particles mixed into the fluidized particles indicated clearly bubbles and the cloud behavior around the bubble. Image processing, i.e. PIV and PTV, gives rather clear understanding on the interaction between the large particle, emulsion and/or cloud behavior in the bed.

Hydrodynamics of a spouted bed with an impermeable draft tube for binary particle systems

A spouted bed with an impermeable draft tube was employed to obtain fundamental data of binary mixtures of glass beads for both the operating conditions and the design factors. These data were compared with those for the coarser particle system only. From this view point, minimum spouting velocity, pressure drop, hold-up of solid particles within a draft tube, upward gas flow rate within the annulus and solids circulation rate were determined by changing the total gas flow rate and mass fraction of finer particles as operating parameters and by changing distance of entrainment zone and draft tube diameter as geometric parameters.

Diffusion in binary suspensions of charged colloids

The dependence of diffusion coefficient in the binary suspension system of charged spherical colloidal particles on the colloid diameter and surface potential was investigated experimentally. A ratio of the diffusion coefficient in the binary system to that in free water was less than unity. This means that the diffusion of a charged colloidal particle is slowed down through the friction induced on the colloidal particle by the electrostatic interaction in the binary system. The ratio was calculated by generalized Langevin equation, and it was found that the calculated ratio agreed well with the experimental ratio. Diffusion behavior of a charged colloidal particle through quartz powder was also studied in the binary suspension system. A decrease in the effective diffusion coefficient, in comparison with that in monodispersed system, was observed.

Minimum Spouting Velocity of Binary Particle Systems in a Spouted Bed with a Draft Tube.

ドラフトチューブ付き噴流層の安定操作に関して, ガラスビーズを用いた大・小二成分系の最小噴流化速度が3つの定義に基づいて算出された.その場合, それらに与える小粒子混合割合やエントレメント区間の影響が検討され, さらに大粒子のみの場合とも比較され.その結果, 安定な噴流化操作は, 最小の安定噴流化速度以上での流速で行う必要があること, また大粒子群中への小粒子の少量の混入によって, 最小の安定噴流化速度が著しく減少することが認められた.

Dependence of Compaction Efficiency in Dry Pressing on the Particle Size Distribution

The compact densification with pressing pressure (compaction efficiency) was determined to be sensitive to the particle size distribution. For the three types of alumina powders used in this research, the compaction efficiency increased with increasing particle size. It has been demonstrated that if the compact density versus log (pressure) has a linear relationship for any two types of powders, so do the blends of the two powders. A model is proposed which can predict the compaction efficiency of a binary particle system based on the Furnas particle packing model and consider the packing efficiency as a function of forming pressure. The composition of the binary mixture at which the highest density is obtained under high pressures is also the composition having the largest compaction efficiency. When coarse particles were added to this composition, the compaction efficiency slowly decreased, and when fine particles were added, the compaction efficiency rapidly decreased. For a continuous particle size distribution, the highest compaction efficiency is related to the average value of ‐log (porefraction).

The formation of nanostructured materials by consolidating ultrafine amorphous alloy particles prepared by chemical reduction

Amorphous (Fe, Co, Ni)-B binary and ternary alloy particles of diameter 20–50 nm can be prepared by chemical reduction using KBH 4 as a reduction agent. In the FeB binary system, structure and chemical concentration of particles depend on the mixing molar ration of KBH 4 to Fe 2+ ions M R. The structure is amorphous for M R⩾ 10.0 and with decreasing M R a crystalline α-phase is precipitated in an amorphous matrix. The B concentration in the amorphous phase is about 33 at.% for M R⩾ 9.0 and about 25 at.% for M R ⪕ 8.0 . The amorphous alloy particles in (Fe, Ni, Co)-B binary and ternary systems are consolidated to a cylindrical shape at various temperatures. The structure of hot-pressed compacts is amorphous for pressing temperatures below the crystallization temperature. T x. These crystalline phases are confirmed to have a nanometer-scale structure. It is concluded that these particles should form a fully dense amorphous bulk or a crystalline bulk consisting of nanometer-scale mixed phase.

Polydisperse fluidization—I. Basic equations

Momentum equations governing the vertical distribution of particles of different sizes and densities in homogeneous fluidized bed are formulated. The particles are presumed to be large enough for the interparticle exchange by pulsating momentum and energy to be carried out mostly through direct collisions. Two main assumptions of principal nature are used: (i) the dispersion of concentrational fluctuations is though of as the composed of contributions due to separate particulate species, and (ii) the random velocity of any particle is supposed to be proportional to the same random function of time with a coefficient being inversely proportional to the square root of the particle mass. The equations for continua modelling particles of different types are presentd in an entirely closed form, by analogy with those of the kinetic theory of multicomponent gases. By way of example, fluidization of binary particulate systems is considered, in which case properties of a macroscopically homogeneous state of a binary bed of ideal mixing and a critical velocity that corresponds to particles of one type being replaced by thoe of the other type in the upper part of the bed in an inhomogeneously mixed state are considered. A general calculation procedure needed to find out the particle distribution in a fluidized bed of given composition is exemplified and discussed in detail.

二成分粒子の二次元配列系の全電気抵抗 二成分の抵抗比の影響

In the previous paper, the total electric resistance of a planer binary system of particles was studied from the viewpoint of the combinatorial theory, and it was concluded that the electric path (or percolation path) of the system could be made under a certain condition of the RK-RS relationsihp. (RK: Total electric resistance of the system calculated by applying Kirchfoff's law, RS: Total electric resistance of the system calculated by series-and-parallel method). In the present paper, the problem of the percolation phenomenon of the system was studied in detail. The details of the condition whereby the geometry of the electric path might be governed was referred to. Furthermore, the percolation probabilities(P(p)) of the system which were determined by counting up the number of RK-RS plots in percolation region and non-percolation region were referred to.

電気抵抗値の異なる２成分粒子系の混合のシミュレーション 変形による計算の簡易化

In order to simplify the calculation of the total electric resistance of a binary particle system of two dimensional f·c·c (face centered cubic) structure, we propose a conventional method of transforming a lattice from the f·c·c to the square. This transformation is practiced by the following procedure.At first, an original f·c·c particle system whose total electric resistance should be calculated is rotated in an angle π/4 as shown in Fig. 1(a), (b). Then, with the addition of four triangles to the slant f·c·c system of Fig. 1(b), it is possible to complete the system of Fig. 1(c) whereby the total electric resistance may be easily calculated.The results obtained are summarized as follows;(1) The calculation of the total electric resistance of a f·c·c system can be symplified by using the method of transformation described above.(2) The edge effect of the mixing zone of a f·c·c structure is greater than that of the two dimensional square system.(3) There is a high correlation (correlation coefficient<0.94) between the total electric resistance of the system PQRS and the standard deviation of mixing of the system ABCD (Fig. 1(c)).

電気抵抗法による２成分粒子系ランダムネス推定 サンプリング法

電気抵抗法による２成分粒子系ランダムネス推定 サンプリング法

２成分粒子系の電気抵抗簡易推算法

In this paper, the total electric resistance of a planar binary system of particles is described. To clarify the relationship between Rk (strict value of total electric resistance of the system applying Kirchhoff's law) and Rs (approximate value of total electric resistance of the system), a combinatorial study related to the total number (ns) of different values of Rs is done.

Prediction of complete mixing of liquid-fluidized binary solid particles

In a liquid-fluidized bed consisting of density- and size-different binary solid particles with a given bulk composition, complete mixing may be observed at a liquid velocity less than the terminal velocities of the constituent particles. In such cases a change either in liquid velocity or in bulk composition results in stratification of the bed. A theoretical model to predict relationships between the bulk composition and the critical velocity for complete mixing is developed on the basis of momentum equations for each particle component. The voidage function involved in the equations is independently given from a unit cell model with assumptions of creeping flow around the particle within the fictitious spherical cell and of a potential flow outside the cell. Although the voidage function estimates monocomponent bed expansions to an accuracy comparable to that of the empirical Richardson-Zaki equation, it is not accurate enough when used for predicting the volume fractions of binary particles at complete mixing. The prediction is highly sensitive to monocomponent bed-expansion characteristics, and closer agreements between the predicted and observed results are obtained when experimental expansion data are used in the prediction. Nonetheless, the present model gives correct predictions for totally segregating particle systems. Thus, a segregation map is then illustrated which predicts the mixing state of any given binary particle system and is well comparable with the observed results not only from the present work but also from other existing investigations.

電気抵抗差のある２成分粒子系の混合モデル

Simulation for a mixing model of a binary system of spherical particles with different electric resistance, such as lead and stainless particles, was carried out in a stationary mixer with vertical impeller blades.The simulation model described above was compared with the actual experiment. In the actual experiment, the total electric resistance of the system, R was measured by a DC-tester, and the top and bottom views of the bed were observed. The mixing model in the previous paper based on the assumption that the particles were moved in square orbits, was modified to fit to the actual process. The modification was made by taking into account the contour of orbits, and by introducing the circulating velocity of particles (the following coefficient), phase and frequency in the equation of R.The contour of orbit seemed to be semicircle according to the photographs. The actual value of the following coefficient (the ratio of the domain of rotational movement of particles to that of each orbit) was obtained from the photograph.By considering the fact described above, the following modified equation was proposed.R=l·exp(-k1·t)·Σal·sin2(ωl·t-π/4)+m-n·exp(-k2·t)Where, R: Total electric resistancel, k1, al, m, n, k2: Constantsωl: Angular velocity: Following coefficientst: TimeThe proposed equation showed good agreement with the experimental data.

電気抵抗法による２成分粒子系のランダムネスの推定（並列性について）

In order to minimize or avoid trouble in spot sampling, it is worthwhile to develop a simple method whereby the degree of mixing or parallelism of packing is non-destructively measured.In this report, the mixing process of a binary system of particles with different electric resistance, group A and group B, was treated by the use of a two-dimensional simulation.In order to discuss the change in the total electric resistance of the particle system with the change in the arrangement of the particles in the system, the term “parallelism of packing” defined as inter-row standard deviation was proposed.

電気抵抗の異なる２種の粉粒体の混合シミュレーション

In this report, the mixing mechanism of a binary system of particles with different electric resistance, group A and group B, was treated by the use of a two-dimensional model. Before mixing, the particles of group A and group B were arranged in a parallel circuit, as shown in Fig. 1, (c).Accompanied with the beginning of rotation of impellar blades at an angular velocity ω1-3, the particles belonging to 1, 2, 3 orbits began to move in their orbits at the same velocity as that of impellar blades, while the particles belonging to 4, 5 orbits had less velocities (ω4, ω5) than ω1-3.Together with the rotational motion of particles, the random exchange of positions of particles occurred. Thus, the resulting equation was as follows.R=l×e-kt×|∑ai×sin(ωi×t)|+(m-n×e-kt)where, R: Total electric resistanceai, k, l, m, n: Constantωi: Angular velocityt: Time