AGGREGATION AND BREAKAGE OF SOLID PARTICLES IN SUSPENSIONS AGITATED IN A VIBRATING MIXER: A FRACTAL APPROACH

A lumped discrete population balance model has been selected for the verification of the experimental data. Solid aggregates of chalk suspended in vigorously mixed suspension were treated as fractal objects with a mass fractal dimension taken as 2.02. A specially written computer program has been used for determining the evolution of population of aggregates during the course of mixing. The PSD (particle size distribution) results obtained by numerical calculation for fractal and non-fractal approaches have been compared, showing a better fit in the case of the fractal model. The aggregation and breakage rate coefficients were correlated as a function of the average energy dissipation rate in the vibrating mixer.     

AGGREGATION AND BREAKAGE OF SOLID PARTICLES IN SUSPENSIONS AGITATED IN A VIBRATING MIXER: A FRACTAL APPROACH

A lumped discrete population balance model has been selected for the verification of the experimental data. Solid aggregates of chalk suspended in vigorously mixed suspension were treated as fractal objects with a mass fractal dimension taken as 2.02. A specially written computer program has been used for determining the evolution of population of aggregates during the course of mixing. The PSD (particle size distribution) results obtained by numerical calculation for fractal and non-fractal approaches have been compared, showing a better fit in the case of the fractal model. The aggregation and breakage rate coefficients were correlated as a function of the average energy dissipation rate in the vibrating mixer.     

A mathematical model of the batch sieving procedure

A mathematical model is developed to describe the batch sieving procedure, for example for a set of sieves on a test sieving engine. This model allows one to evaluate the size distributions on each sieve surface after a sieving time t from the feed size distribution. The solution of the resulting system of ordinary differential equations is written down, the shape of an introduced sieving function is discussed and the theory is illustrated by an example. It is also shown how to generate the presented model to the case of technical continuous screening.     

Drying of Solid Furl Particlbs in Hot Gases

Drying of solid fuel particles in hot gases ( 50-200c) is studied both theoretically and experimentally. The measurements are carried out by using a thermobalance reactor constructed for drying and pyrolysis studies of particles up to 30 mm by diameter. The model is based on the solution of the conservation equations for mass and energy. The drying is considered to consist of three successive periods: a short initial heating period, period of constant rate of drying and period of falling rate of drying. It is assumed that the particle moisture distribution is uniform during the constant rate of drying. Shrinking core model is assumed for the falling rate period. esides fuel particles, the model is applicable also for other solid particle drying processes. Model calculations are compared to measurements for wood chips. The model can predict the efFect of the main parameters reasonably well. These main parameters affecting the drying rate are: particle size, particle shape, initial particle moisture content, gas temperature and gas moisture content, emperature of the reactor walls and slip velocity. The irregular shape of practical fuel particles can approximately be simulated as one-dimensional case ( plate, cylinder, sphere) by using an equivalent volumc to surface area ratio.     

Kinetics of High-Temperature Oxidation of Inorganic Nonmetallic Materials

A series of new formulae have been developed for describing the kinetics of solid–gas reactions with an emphasis on diffusion control. Compared with traditional methods, these new equations can be used to treat not only sphere samples but also cylinder, cuboid, and cube samples. Different from the traditional methods, all the parameters in our formulae have a clear physical meaning; as a result, they are easy to use and convenient for theoretical discussion. Based on these equations, one may further estimate the influence of the sample shape on the kinetic behavior. It is shown that the calculation errors based on our new models are less than those of traditional models such as the Jander, the Ginstling–Brounshtein as well as the parabolic model. Besides, a new concept of "characteristic oxidation time" has been suggested to measure the oxidation resistance of various materials, which might be useful for evaluating the possible applications of different inorganic nonmetallic materials.     

Experimental study on mechanical filtration through tobacco columns: Influence of cut-filler shape and size distribution on filtration efficiencies

Tobacco columns are extreme examples of heterogenous packed beds, which have various cut-filler shapes and a wide range of size distribution. The behavior of mechanical filtration through tobacco columns has been investigated by using polystyrene latex (PSL) standard particles to compare the actual filtration efficiency with the predicted filtration efficiency calculated by theoretical equations for spherical packed beds. The influence of cut-filler shape and the range of cut-filler size distribution on filtration efficiency have been examined. The effect of diffusion in tobacco columns was lower and the effect of interception and inertia were higher than in spherical packed beds. These results show that a partially faster flow could have occurred in tobacco columns. It means that it is difficult to utilize the theoretical equations for spherical packed beds to heterogenous packed beds as proposed. Filtration efficiency through tobacco columns had a relationship with the factor that shows cut-filler shape and size distribution (r = 0.894, p < 0.05) and the factor that shows cut-filler size distribution (r = 0.683, p < 0.15). The factor showing cut-filler shape and size distribution was expected to be an effective factor of filtration efficiency for heterogenous packed beds. From these experiments, empirical equations that can be applied to tobacco columns have been proposed, and the prediction accuracy during burning was validated. It has been found that the prediction accuracy was precise, revealing the importance of taking the influence of cut-filler shape and size distribution into account in the filtration equations.

Copyright © 2016 American Association for Aerosol Research     

Numerical investigation of the influence of kinetics and shape factor on barium sulfate precipitation in a continuous stirred tank

The effect of kinetics and shape factor on barium sulfate precipitation in a continuous stirred tank has been investigated numerically through solving the standard momentum and mass transport equations in combination with the moment equations for crystal population balance. The numerical method was validated with the literature data. The simulated results include the distribution of the local supersaturation ratio in the reactor, the mean crystal size, and the coefficient of variation. The simulation results show that the value of shape factor used in the model affected greatly the mean crystal size and the moments of the crystal size distribution. The influence of the kinetic expressions on the simulation is also analyzed. It is important to investigate the relationship of the shape factor with the precipitator type and other operation conditions to obtain reliable simulation results and suitable kinetic equations of crystal nucleation and growth rates.     

Drying of Solid Furl Particlbs in Hot Gases

ABSTRACT

Drying of solid fuel particles in hot gases ( 50–200c) is studied both theoretically and experimentally. The measurements are carried out by using a thermobalance reactor constructed for drying and pyrolysis studies of particles up to 30 mm by diameter. The model is based on the solution of the conservation equations for mass and energy. The drying is considered to consist of three successive periods: a short initial heating period, period of constant rate of drying and period of falling rate of drying. It is assumed that the particle moisture distribution is uniform during the constant rate of drying. Shrinking core model is assumed for the falling rate period. esides fuel particles, the model is applicable also for other solid particle drying processes. Model calculations are compared to measurements for wood chips. The model can predict the efFect of the main parameters reasonably well. These main parameters affecting the drying rate are: particle size, particle shape, initial particle moisture content, gas temperature and gas moisture content, emperature of the reactor walls and slip velocity. The irregular shape of practical fuel particles can approximately be simulated as one-dimensional case ( plate, cylinder, sphere) by using an equivalent volumc to surface area ratio.     

Determination of glycerol by oxidation with periodic acid

Summary An acidimetric procedure for the determination of glycerol following oxidation with periodic acid has been described. This procedure has been successfully applied to C. P. grade glycerin, spent soap lyes, soap lye crudes, half crudes, saponification crudes, evaporator salt, and mixtures of glycerol with trimethylene glycol and polyglycerols. Factors that influence the determination, such as size of sample, presence of salt and the presence of organic compounds containing hydroxyl groups, have been discussed.     

THE EFFECT OF RADIAL DISTRIBUTION OF VOIDAGE ON THE BURNING RATE OF A CARBON SPHERE IN A FLUIDIZED BED

The local void around a sphere in a packed bed or in the emulsion phase of a fluidized bed has been calculated theoretically; and measured as a function of the radial distance from the centre of the sphere. Effects of this distribution on the burning rate and Sherwood number have been investigated for two types of bed e.g. where inerts are of the same size as the carbon particle and where the inerts are smaller than the carbon particle. Even though the present analysis studies the effect on the diffusive component of the mass transfer alone, the results suggest that the distribution of voidage will yield Sherwood numbers higher than that calculated from the constant voidage assumption. The voidage distribution explains the increase in burning rate of carbon with increasing size of the inerts.     

Classification mechanism of the chute, a liquid-phase remover of fines in the micrometre range from a batch of porous particles

A simple and effective classification method, the ‘chute’, has been developed for the liquid-phase removal of fines from a batch of porous (catalyst) particles in the micrometre range. The chute is a continuous sedimentation fractionator, working in the gravitational field. Equations based on the sedimentation of particles were derived for the particle size distribution density function at a given position on the chute as a function of the initial size distribution density function. The particle size distribution on the chute appears to be only a function of the physical constants of the fluid, the particles and the dimensions of the chute. To verify the model equations, experiments with the chute were carried out at different suspension flows and chute angles. It was found that the experimental particle size distribution density functions at various positions on the chute were predicted reasonably well. Due to local disturbances near the bottom of the chute, the experimental curves exhibit a less sharp cut-off in the particle size distribution density function than was predicted by the model equations.     

Effect of dispersions of CSD in continuous MSMPR crystallizers

A general model is proposed to predict the crystal size distribution from multistage MSMPR Crystallizers taking into account shape factor, birth size and growth rate dispersions. Two cases, namely nucleation in the first crystallizer and the same process in all crystallizers have been considered. The developed equations can be solved easily by the Monte Carlo technique. The model represents an extension of the earlier work of Sen Gupta and Dutta.     

苯丙酮酸钠反应结晶过程的数学模拟

建立了苯丙酮酸钠反应结晶过程的数学模型,研究了在苯丙酮酸醚萃取液中滴加稀碱溶液的反应结晶过程;对该过程涉及的湍流扩散宏观返混及界面化学反应进行分析,提出了一种简化、有效的混合模型;并考虑了结晶的团聚和破碎作用;运用离散化的粒数平衡方程可求解得到ＣＳＤ（晶体粒度分布）。该模型得到了实验数据的支持,为进一步的过程优化提供了依据。     

New Approach to Solve a Model for the Effective Solid Stress Distribution in Conical Spouted Beds

Charbel et al. (1999) have investigated the flow stability in conical spouted beds by modeling the effective solid stress distribution in the annular region as a function of the failure state under which the spout‐annulus interface is formed. However, due to the complexity in solving the momentum balance equations for the solid phase, the model application has been restricted to one case. This work is aimed at developing a new methodology to solve this set of algebraic differential equations, using optimization techniques to determine the model parameter. This methodology has improved the model solution extending its application for any other case.     

A polydispersed particle system representation of the porosity for non-saturated cementitious materials

In this paper, the porosity of cementitious materials is described in terms of pore size distribution by means of a 3-dimensional overlapping sphere system with polydispersivity in size. On the basis of results established by Lu and Torquato [B. Lu, S. Torquato, Nearest-surface distribution functions for polydispersed particle systems, Phys. Rev. A 45(8) (1992) 5530-5544] and Torquato [S. Torquato, Random Heterogeneous Media: Microstructure and Macroscopic Properties. Springer-Verlag: New York, 2001] providing relations for nearest-neighbor distribution functions, the volume fraction of pores having a radius larger than a prescribed value is explicitly expressed. By adopting an appropriate size distribution function for the sphere system, it is shown that the pore size distribution of cementitious materials as detected for instance by mercury intrusion porosimetry (MIP), which generally points out several pore classes, can be well approached. On the basis of this porosity representation, the evaluation of the capillary pressure in function of the saturation degree is provided. The model is then applied to the simulation of the saturation degree versus relative humidity adsorption curves. The impact of the pore size distribution, the temperature and the thickness of the adsorbed water layer on these parameters are assessed and analyzed for three model materials having different pore characteristics.     

Calibration for measured crystal size distribution

The crystal size distribution (CSD) measured by laser diffraction technique is obtained by assuming spherical crystals. If crystals are non-spheres, calibration is responsible for the true crystal size, particle number concentration and population density. In this paper, CSD calibration equations have been deduced. It was shown that when shape factors are size-independent, the weight percent of particles is not affected by crystal shape and calibration is just a horizontal shift of measured CSD. Calibration was taken for plate-like crystals of cefazolin sodium and rod-like crystals of l-threonine. The effect of CSD calibration on crystal growth kinetics has been investigated in l-threonine-water evaporation crystallization system.     

Diffusion-controlled mass transfer to or from spheres with concentration-dependent diffusivity

Analytical solutions for the growth of an isolated sphere from zero initial size have been derived with diffusivity an explicit function of concentration. Numerical methods have also been developed to treat either growth or dissolution with concentration-dependent diffusivity. Diffusivity is here taken to be an exponential function of concentration but several other forms have been studied. The predictions of the two methods show the same asymptotic behaviour (rate of change in size and concentration distribution) for growing spheres and this is considered to validate the numerical procedures. When appropriately normalized the change in size of a sphere can be described by a constant property model. However, the equivalent diffusivity is equal to the expected average over the appropriate concentration range only for very low solubility; the equivalent diffusivity can be estimated for higher solubilities.     

An improved stagewise model of countercurrent flow liquid—liquid contactors

An improved stagewise model has been developed to represent more accurately the physical processes occurring in a liquid—liquid extraction column. The influence of drop size distribution is more realistically represented in this model. The model equations have been solved numerically with a range of parameter values in order to predict the extent of the influence of drop size distribution on extraction rates. Drop size distributions, measured in a turbine-agitated column section and inserted into the model equations, gave predictions of a considerable influence of size distribution on extraction column performance.     

Correlation-based multi-shape granulometry with application in porous silicon nanomaterial characterization

Image-based granulometry measures the size distribution of objects in an image of granular material. Usually, algorithms based on mathematical morphology or edge detection are used for this task. We propose an entirely new approach, using cross correlations with kernels of different shapes and sizes. We use pyramidal structure to accelerate the multi-scale searching. The local maxima of cross correlations are the primary candidates for the centers of the objects. These candidate objects are filtered using criteria based on their correlations and intersection areas with other objects. Our technique spatially localizes each object with its shape, size and rotation angle. This allows us to measure many different statistics (besides the traditional objects size distribution) e.g. the shape and spatial distribution of the objects. Experiments show that the new algorithm is greatly robust to noise and can detect even very faint and noisy objects. We use the new algorithm to extract quantitative structural characteristics of Scanning Electron Microscopy (SEM) images of porous silicon layer. The new algorithm computes the size, shape and spatial distribution of the pores. We relate these quantitative results to the fabrication process and discuss the rectangle porous silicon formation mechanism. The new algorithm is a reliable tool for the SEM image processing.     

分子动力学模拟研究盐离子对十二烷基硫酸钠胶束溶液中亲水亲油协调机制的影响

The presence of salt has a profound effect on the size, shape and structure of sodium dodecyl sulfate (SDS) micelles. There have been a great number of experiments on SDS micelles in the presence and absence of salt to study this complex problem. Unfortunately, it is not clear yet how electrolyte ions influence the structure of micelles. By describing the compromise between dominant mechanisms, a simplified atomic model of SDS in presence of salt has been developed and the molecular dynamics (MD) simulations of two series of systems with different concentrations of salt and charges of ion have been performed. Polydispersity of micelle size is founded at relatively high concentration of SDS and low charge of cation. Although the counter-ion pairs with head groups are formed, the transition of micelle shape is not observed because the charge of cation is not enough to neutralize the polar of micelle surface.