Breakage behaviour of enzyme granules in a repeated impact test

In many industries, handling or processing of relatively fragile particles takes place and predictions are required whether a significant proportion of the particles will be damaged. These processes have been designed and controlled solely on the basis of particle size and shape. Another parameter that needs to be introduced is particle strength. The stringent environmental laws demand improved particle mechanical quality, which has given rise to the need for a more accurate and fundamental particle strength measurement and its application in modelling and control of particulate processes. Particles need to show good resistance against static and dynamic loads.

The present paper deals with the study of breakage behaviour of different enzyme granules subjected to repeated impacts using a new instrument developed at the Delft University of Technology. The impact test involves bombarding the particles against a flat target repeatedly. The main feature of this new test is its ability to impact a large number of particles against a flat target repeatedly, and generate extremely reproducible results. Testing a large number of particles has the advantage of producing statistically correct results. The repeated impacts provide information on the breakage behaviour of the particles based on their history. In the new impact test enzyme granules can undergo very low impact velocities of the order of 5 m s⁻¹. These low impact velocities lead to attrition and chipping of the granules.

The current paper presents preliminary results on the breakage behaviour of the new impact test and its basic advantages over already existing tests. Furthermore, experiments were performed on enzyme granules, and the breakage mechanisms determined, depending on the change in size and shape of the particles.     

The mechanism model of gas–liquid mass transfer enhancement by fine catalyst particles

In order to present the enhancement of gas–liquid mass transfer by heterogeneous chemical reaction near interface, the mechanism model has been proposed to describe the mass transfer rate for a gas–liquid–solid system containing fine catalyst particles. The composite grid technique has been used to solve the model equations. With this model the effect of particle size, first-order reaction rate constant, distance of particle to gas–liquid interface and residence time of particle near gas–liquid interface on the mass transfer enhancement have been discussed. The particle–particle interaction and slurry apparent viscosity can be considered in the model. The experimental data have been used to verify the model, and the agreement has been found to be satisfied.     

The impact endurance of polycrystalline graphite

Repeated impact tests have been carried out on a wide range of polycrystalline graphites. Two modes of test were employed using centrally impacted rods and discs with the rods supported horizontally at their ends and the discs supported around the circumference. The resulting impact endurance curves for all the different graphites under repeated impacts of constant energy were found to have a substantially common shape in both the disc and the rod tests. The absolute levels of the endurance curves differ considerably and correlate well with other mechanical properties of graphites, in particular the strain energy density at failure in bend. Measurement of impact forces on the single impact failure of graphite rods supports this correlation by showing that the dynamic stresses generated at failure in a single impact are the same as the corresponding static 3-point bend strengths in the same test mode. Measurement of impact forces at energies less than those required to cause failure in a single impact show that the fraction of energy absorbed as specimen strain energy is dependent on specimen size and shape but is not very sensitive to impact energy. A fracture mechanics model based on incremental crack growth and previously used to interpret stress-cycling fatigue data for graphite is proposed to describe also the endurance of polycrystalline graphite under repeated impacts. The model describes available experimental data obtained under both impact and fatigue conditions. On this model, the difference between the two cyclic stressing modes is the rate of crack growth per stress cycle, this being greater under repeated impacts than under fatigue cycles of the same stress amplitude.     

Network model for straining dominated particle entrapment in porous media

A network model has been developed to study and describe formation damage resulting from particle entrapment in porous media by straining or size exclusion. Unlike the previous network models, this model considers the simultaneous entry of a number of particles into the network, as well as the effects of fluid flow on the particle transport path. A systematic study has been carried out on the flow and entrapment of monodispersed particles as well as particles with a size distribution through different networks. The effects of various parameters such as network size, particle size distribution and pore size distribution on the extent of formation damage, manifested by permeability reduction have been discussed in this paper. The model has also been used to determine the degree of prefiltration required to prevent damage to injection wells during water flooding. The model predictions show good agreement with experimental data for several different runs. A single parameter is used to match the exact number of pore volumes required to produce damage to the porous media. This parameter was found to be constant for the two different sandstones studied and for different concentrations of particles in the suspension. The simulation was also performed using the “random walk model” (which does not account for the fluid flow effects on particle flow) for purposes of comparison. The permeability responses predicted by this random walk model show trends that are significantly different from those observed experimentally. The network model developed in this paper has wide application in water flooding and matrix acidizing operations where diverting agents are used.     

Evolution of the Efficiency and Pressure Drop of a Filter Media with Loading

A model for calculating the filtration efficiency and the pressure drop of a fiber filter media in dynamic regime was used and modified to take account of both the fiber and the particle size distributions. Measurements were carried out on two medias employed in industry and two loading aerosols to test the possibilities offered by the model to predict the evolution of both the efficiency and pressure drop characteristics. The results show that the model satisfactorily reflects the variations in efficiency and pressure drop of a media with respect to the loading if its structure is homogeneous and if the deposit of particles takes place within the thickness of the filtering layer. On the other hand, the divergence between the model and practical experience becomes significant as soon as surface filtration regime occurs or when the media has a heterogeneous structure. A test rig was developed to determine the filtering characteristics, such as fractional efficiency and pressure drop in relation to the degree of loading, from aerosols of various particle sizes. This study has highlighted the necessity of taking into account the influence of loading in the methods for testing filters, especially those used in the industry, and demonstrates that the particle size of the test aerosol is a very sensitive parameter.     

CFD investigation of the pipe transport of coarse solids in laminar power law fluids

A numerical parametric study of the laminar pipe transport of coarse particles in non-Newtonian carrier fluids of the power law type has been conducted using an Eulerian-Eulerian computational fluid dynamics (CFD) model. The predicted flow fields have been successfully validated by experimental measurements of particle velocity profiles obtained using a positron emission particle tracking technique, whilst solid-liquid pressure drop has been validated using relevant correlations gleaned from the literature. The study is concerned with nearly-neutrally buoyant particles flowing in a horizontal or vertical pipe. The effects of various parameters on the flow properties of such mixtures have been investigated over a wide range of conditions. The variables studied are: particle diameter (2-9 mm), mean solids concentration (5-40% v/v), mean mixture velocity (25-125 mm s⁻¹), and rheological properties of the carrier fluid (k=0.15-20 Pa sⁿ; n=0.6-0.9). A few additional runs have been conducted for shear thickening fluids, i.e. n>1. Whilst the effects of varying the power law parameters and the mixture flowrate for shear thinning fluids are relatively small over the range of values considered, particle size and solids concentration have a significant bearing on the flow regime, the uniformity of the normalised particle radial distribution and of the normalised velocity profiles of both phases, and the magnitude of the solid-liquid pressure drop. The maximum particle velocity is always significantly less than twice the mean flow velocity for shear thinning fluids, but it can exceed this value in shear thickening fluids. In vertical down-flow, particles are uniformly distributed over the pipe cross-section, and particle diameter and concentration have little effect on the normalised velocity and concentration profiles. Pressure drop, however, is greatly influenced by particle concentration.     

Supercritical antisolvent precipitation from an emulsion: β-Carotene nanoparticle formation

Supercritical antisolvent precipitation of β-carotene from an oil-in-water emulsion in which the solute is dissolved in the droplets that confirm the dispersed phase has been studied, with the objective of producing particles with a mean particle size in the nanometer scale. The aim of the current research work was to confirm the possibility to control the particle size of the carotene + surfactant suspensions obtained with this process, with the initial drop size present in the emulsions. The final products were formed by particles with a mean size below 400 nm in suspension in an aqueous media, which was also the mean droplet size of the emulsion. This result suggests that produced particles are encapsulated in surfactant micelles. The final suspension was then lyophilized and observed by means of a scanning electron microscopy. In order to obtain a better comprehension of the process, a mass transfer model was developed. This model is based on previous observations of the evolution of the organic phase drop and the solute, obtained with a view cell.     

Hydrodynamic studies of an advanced fluidized-bed bioreactor for direct interaction with coal

Fine coal particles fluidized by the upflow of a liquid medium containing a dissolved biocatalyst undergo size reduction as the reaction progresses. Three aspects of the design of such a reactor were examined:

1. (1)the use of force balances to describe pressure drop for the segregated bed;

2. (2) measurement of liquid-phase dispersion coefficients; and

3. (3) fluorescent tagging of particles to track size distribution.

Hydrodynamic data were obtained for a liquid-solid fluidized bed of coal particles in the size range 30–150 μm. Illinois No. 6 coal was ball-milled, sieved into four fractions, and suspended in a 0.1% aqueous solution of Tween 80. A sample with a bimodal particle size distribution centred on 49 and 63 μm was placed in a glass column and fluidization and pressure-drop data were compared with a new model developed to describe particle segregation. Measured liquid-phase dispersion coefficients varied from 0.034 to 0.283 cm² s⁻¹ as the flow varied from 0.005 to 0.0159 cm s⁻¹. A technique was also developed for coating coal particles with a fluorescent paint which may allow direct measurement of the change in the fraction of marked particles of known size along the axis of a fluidized bed.     

Micromechanic modeling and analysis of the flow regimes in horizontal pneumatic conveying

Pneumatic conveying is an important technology for industries to transport bulk materials from one location to another. Different flow regimes have been observed in such transportation processes, but the underlying fundamentals are not clear. This article presents a three‐dimensional (3‐D) numerical study of horizontal pneumatic conveying by a combined approach of discrete element model for particles and computational fluid dynamics for gas. This particle scale, micromechanic approach is verified by comparing the calculated and measured results in terms of particle flow pattern and gas pressure drop. It is shown that flow regimes usually encountered in horizontal pneumatic conveying, including slug flow, stratified flow, dispersed flow and transition flow between slug flow and stratified flow, and the corresponding phase diagram can be reproduced. The forces governing the behavior of particles, such as the particle–particle, particle‐fluid and particle‐wall forces, are then analyzed in detail. It is shown that the roles of these forces vary with flow regimes. A general phase diagram in terms of these forces is proposed to describe the flow regimes in horizontal pneumatic conveying. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Development and verification of coarse-grain CFD-DEM for nonspherical particles in a gas–solid fluidized bed

Computational fluid dynamics coupled with discrete element method (CFD-DEM) has been widely used to understand the complicated fundamentals inside gas–solid fluidized beds. To realize large-scale simulations, CFD-DEM integrated with coarse-grain model (CG CFD-DEM) provides a feasible solution, and has led to a recent upsurge of interest. However, when dealing with large-scale simulations involving irregular-shaped particles such as biomass particles featuring elongated shapes, current CG models cannot function as normal because they are all developed for spherical particles. To address this issue, a CG CFD-DEM for nonspherical particles is proposed in this study, and the morphology of particles is characterized by the super-ellipsoid model. The effectiveness and accuracy of CG CFD-DEM for nonspherical particles are comprehensively evaluated by comparing the hydrodynamic behaviors with the results predicted by traditional CFD-DEM in a gas–solid fluidized bed. It is demonstrated that the proposed model can accurately model gas–solid flow containing nonspherical particles, merely the particle dynamics are somewhat lost due to the scaleup of particle size. Finally, the calculation efficiency of CG CFD-DEM is assessed, and the results show that CG CFD-DEM can largely reduce computational costs mainly by improving the calculation efficiency of DEM. In general, the proposed CG CFD-DEM for nonspherical particles strikes a good balance between efficiency and accuracy, and has shown its prospect as a high-efficiency alternative to traditional CFD-DEM for engineering applications involving nonspherical particles.     

Experimental and modelled efficiencies during the filtration of a liquid aerosol with a fibrous medium

The aim of this study was to determine and model efficiency during the filtration of a liquid aerosol through a fibrous filter. A series of experiments demonstrated that liquid particle filtration is different from solid particle filtration in that a drainage state appears, characterized by a constant pressure drop at the end of filter clogging. Moreover, during filter clogging, the number efficiency presents a minimum level for particles close to 100 nm in diameter (the most penetrating particle size). The results also reveal that during filter clogging there is a decrease in the medium's performance for particles smaller than 100 nm and an increase in efficiency for particles with a diameter >200 nm. Both effects are induced by the amount of liquid collected in the medium. Finally, a model is proposed to describe filter efficiency during clogging with a liquid aerosol.     

液固流化床的混合离析模型

本文从颗粒的微观运动出发，采用随机过程模型描述了定常态下液固流化床内二元颗粒的混合和离析现象。在φ１０４×１５００ｍｍ的流化床内，以水为流化介质，对两种不同大小的同种颗粒二元体系在不同流速、不同组成、不同粒径比情形下进行了测定，确定了模型参数关联式，获得了颗粒沿床层的浓度分布关系。将模型计算值与实验值及文献值作了比较，证实了该模型的可行性     

Prediction of pressure drop with steady state pneumatic conveying of solids in horizontal pipes

Current relationships for determination of the pressure drop with pneumatic conveying of solids in pipes are not of general validity. The theoretical considerations underlying these relationships do not take into account the influence of the rotatory motion of the particles. On the other hand, extremely high rotatory speeds of the particles due to wall collision are observed.Therefore a new concept is presented which takes into account the rotatory motion of the particles. A further aim was to represent the data in the form of nondimensional groups which allow meaningful, physical interpretation of the results obtained.A state diagram for the prediction of pressure drop with pneumatic conveying in the form of sliding particles strands is described.Calculation of power loss per particle and of the force and the moment acting on a particle leads to a nondimensional representation of pressure drop in which a normalized pressure drop is combined with a particle Froude number and a Froude number which contains the particle fall velocity and the pipe diameter. This combination of nondimensional groups defines fully suspended flow.The normalized pressure drop is defined in such a way that it represents the nondimensional slip of the particles, too.Comparison with pressure drop measurements for pneumatic transport in horizontal pipes which included changes in particle size, particles density and pipe diameter confirms the physical significance of the parameters used with regard to the prediction of pressure drop and of particles slip velocity.A simple procedure for the prediction of pressure drop in the full range of steady-state pneumatic conveying is proposed.     

压力脉动法预测硅粉颗粒最小流化速度的实验

应用压力传感器研究了不同筛分粒径的硅粉的流化性质，证实流化床层的压力脉动标准方差σp随着表观气速的增加而线性增大, 根据σp=0的条件即可确定流化床的初始流化气速Umf. 此Umf与传统压降变化法得到的实验结果基本一致. 对测得的不同筛分粒级的硅粉的Umf进行拟合，得到了Umf与相应粒级平均粒径的关联式Umf=0.014e10(d–0.28)–0.012e–10(d–0.28)+0.065. 对双粒级复配混合颗粒体系的σp进行的实验研究发现，其σp介于相关单粒级体系的σp之间，并且粗颗粒组份的比例对σp的影响较大.     

On the prediction of internal particle morphology in suspension polymerization of vinyl chloride. Part I:: The effect of primary particle size distribution

The present study provides a comprehensive investigation on the determination of the primary particle size distribution in the suspension “powder” polymerization of vinyl chloride. The primary particle size distribution inside the polymerizing monomer droplets is determined by the solution of a population balance equation governing the nucleation, growth, and aggregation of the primary particles. The stability of the colloidal primary particles is expressed in terms of the electrostatic and steric stabilization forces. The primary particle stability model includes the effects of agitation, temperature, electrolyte as well as primary and secondary stabilizer concentrations. It also includes both diffusive and shear-induced particle destabilization mechanisms. The proposed stability model is shown to accurately describe existing experimental data on particle number, mean particle size and particle size distribution for both bulk and suspension vinyl chloride polymerizations. The primary particle population balance model can predict the critical monomer conversion at which massive particle aggregation occurs leading to the formation of a continuous network of primary polymer particles inside the polymerizing monomer droplets. A detailed investigation on the predicted critical monomer conversion is carried out including its dependence on the rate of agitation, temperature, electrolyte concentration, as well as the concentrations of the primary and secondary stabilizers.     

Determining particle-size distributions from chord length measurements for different particle morphologies

A recently proposed model to determine particle-size distributions (PSDs) from chord length measurements has been applied to different particle morphologies, namely compact, platelet- and rod-shaped particles. To study these systems, chord length distributions (CLDs) were measured at varying particle size and solids concentration for each compound and were subsequently utilized to determine the system-specific parameters. Each model was successfully applied to its respective compound such that the experimental PSDs and model predictions were in good agreement. Moreover, the effect of other variables such as agitation rate and solvent composition was investigated and found to be negligible for the specific systems tested. Finally, potential model optimizations of the general model construct have been studied. Two variants of the CLD compression step, namely principal component analysis and a geometric model have been considered as surrogate models. However, neither of these approaches yielded superior results than the previously proposed approach.     

Numerical simulation of particle breakage in dry impact pulverizer

A novel method to simultaneously simulate particle motion and its breakage in a dry impact pulverizer was developed. The motion of particles in the pulverizer was calculated using a discrete phase model (DPM)‐computational fluid dynamics (CFD) coupling model. When the particle impacts against a vessel wall, impact stress acting on the particle is calculated from Hertz's theory as a function of the impact velocity. At the same time, the particle strength as a function of the particle size is calculated from Griffith's theory. If the impact stress is larger than the particle strength, the particle is broken and replaced with smaller fragments. The size distribution of the fragments is obtained from a breakage function proposed. The motion of the fragments is calculated again by using the DPM‐CFD coupling model. By repeating the above calculations over the whole particles, the grinding phenomenon can be simulated. The calculated results showed good agreement with the experimental one, and validity of the proposed method was confirmed. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3601–3611, 2013     

Determination of non-spherical particle size distribution from chord length measurements. Part 1: Theoretical analysis

In this paper, extensive theoretical studies are described on two important issues in translating a chord length distribution (CLD) measured by FBRM instrument into its particle size distribution (PSD) including PSD-CLD and CLD-PSD translation models for general non-spherical particles. Analytical solutions to calculate the PSD-CLD models for spherical and ellipsoidal particles are developed. For non-spherical particles, a numerical method is given to calculate the PSD-CLD model. The iterative non-negative least squares (NNLS) method is proposed in the CLD-PSD model, because of its many advantages converting measured CLD into its PSD, such as insensitivity to measurement noise and particle shape. The effectiveness of the proposed methods is validated by extensive simulations.     

Effect of Pore Size and Particle Size Distribution on Granular Bed Filtration and Microfiltration

Abstract

The paper reviews the effect of particle size distribution and pore size distribution on granular bed filter and crossflow microfiltration performance. The experimental results of the granular bed filter with pollen particles in suspension showed that the presence of large particles improved the filter efficiency of smaller particles in suspension. Microfiltration results with bi and tri‐modal latex suspensions showed that the permeate flux and the quality were significantly affected by the particle size and its distribution, especially when the particle size was smaller than the pore size of the membrane. The mathematical model simulation results of granular bed filtration show that media pore size distribution is an important parameter of filtration for the particle removal and pressure drop across the filter.     

Review: An investigation of single particle breakage tests for coal handling system of the gladstone port

Aspects of the literature on single particle breakage test have been reviewed in this article. The test procedures that are commonly used by the researchers in examining and measuring the breakage characteristics of the ore and coal particles are also discussed. It appears that most of the common size distribution function fitting techniques were not suitable for accurate representation of the size distributions obtained from a pendulum breaking process. The single impact test, double impact test (drop weight test, pendulum test) and slow compression test can be used to study the behaviour of the single particle breakage events. The single impact test, slow compression test and drop weight test cannot measure the energy utilization pattern in single particle breakage events, but this can be determined from the pendulum test.The energy utilized for breakage was predominantly dependent upon the size and shape of the specimen, level of input energy and the breakage properties of the specimen. This review highlights that the size distribution curves were linear in the fine particle region and have varying curvature in the coarser region, the gradient of the linear fine particle region of the size distribution curves increases with an increase in the specific comminution energy. The comminution energy increases with input energy at lower levels of input energy but at the higher levels of input energy the comminution energy did not show the same proportional increase. At a given level of input energy, the size distribution resulting from the breakage of the particles by the pendulum apparatus can be represented by a one-parameter family of curves.