Variations of particle size and bed voidage distributions in expanded bed during transient operation processes

Changes in bed expansion are frequently encountered during an expanded bed adsorption, such as during the initial bed expansion, feed loading and washing processes. We have here studied the changes of local particle size distribution and bed voidage of an expanded bed in the initial bed expansion process as well as those during the changes in mobile phase viscosity, which imitated feed loading and column washing processes. Using a glass column modified with three side sampling ports and Streamline AC as the solid phase, experimental measurements on a series of operation moments during the transient processes were carried out by sampling the particles from within the column at different axial positions. In the initial bed expansion process, the gradual formation of an axial classification from a settled bed to a stable expanded bed was first displayed. By changing the mobile phase from water to 10% (w/w) glycerol solution or vice versa, the variations in both the particle size distribution and bed voidage corresponding to the increase or decrease of the bed height caused by the changes of the mobile phase viscosity were examined as well. The transient changes of the local particle size distribution and bed voidage first occurred in the bed bottom and then progressed from bottom to top along the axial direction. However, the changes of bed voidage at different axial positions were not unidirectional. That is, by changing the mobile phase to the high-viscosity glycerol solution, a constant increase of the bed voidage was observed in the bed bottom, while a distinct decrease of the bed voidage before its increase was involved at the middle and top positions. This is ascribed to the compression effect caused by the upward movement of the lower part particles.     

Particle number density and velocity distributions in laser plumes

A time-of-flight mass spectrometer with electron impact ionization facility was used in investigations of the laser plume structure. Densities and velocity distributions of positively charged and neutral species were measured 12 cm downstream of the target. Velocities of particles in a plume were measured by the retarding potential method. The combination of a skimmer and declining electric field was used to suppress the influence of charged particles during the measurement of the neutral component parameters. In the case of YBaCuO ceramic laser ablation, a strong variation of the laser-induced plume composition was observed from its head to its tail. It seems to be accounted for by the difference of the starting (phase transition) temperatures of various layers of a plume. Ions detected mainly in the head of a plume were followed by atoms, molecules and clusters in inverse succession to their appearance in the plume under the light intensity increase. The characteristic of the number density dependence upon the laser spot diameter make it clear that most of the molecules BaO and YO are the direct product of ablation. In contrast, the detected clusters with masses up to 2000 amu are the product of condensation in the expanding plume under the conditions of the experiments.     

Particle size effects in X-ray absorption analysis: Formulae for size distributions

New equations have been derived to describe the dependence of X-ray transmitted intensity on particle size in heterogeneous specimens. The formulae include the effect of size distribution, a problem not covered in earlier theoretical work.     

Fluidisation and dispersion behaviour of small high density pellicular expanded bed adsorbents

The fluidisation and dispersion properties of various agarose-based expanded bed matrices--small high density stainless steel cored prototypes and standard commercial types--were studied in 1-cm diameter expanded bed contactors in which fluid entering the column base is locally stirred. In all cases, fluidisation behaviour was poorly predicted from the Richardson-Zaki correlation, with experimentally determined values of the expansion index being considerably higher than the theoretical values. The resons for these discrepancies are discussed in detail and the validity of applying this widely used correlation for characterisation of expanded bed systems is questioned. Residence time distribution studies using acetone tracers, demonstrated that in comparison to existing commercial supports, the small pellicular prototype materials generally possessed far superior hydrodynamic properties, which augurs well for their future employment in expanded bed chromatographic separations.     

Concentration and purification of orotic acid directly from whey with an expanded bed adsorption system

The development of an expanded bed process for the concentration and purification of orotic acid directly from whey is described. Different commercially available adsorbents were tested in series of pilot batch adsorption experiments to determine the most suitable separation system. Best results were achieved using a weak anion-exchange matrix. An elution protocol was established using MgCl2 as eluting agent to recover the adsorbed orotic acid with approximately 85% yield and 10-fold concentration. Purified orotic acid was precipitated under acid conditions with a yield of 95%.     

Particle size distributions of silver nanoparticles at environmentally relevant conditions

Silver nanoparticles (Ag NPs) are becoming increasingly popular as antimicrobial agents in consumer goods with consequent risk to environmental health from discharges. Environmentally relevant fate and transport investigations are limited but essential to gain understanding towards bioavailability and toxicology. In this study, monodisperse 15 nm citrate-stabilised Ag NPs were synthesised, characterised and then fractionated by flow field-flow fractionation (FlFFF) at environmentally relevant conditions (pH 5 or 8, presence of natural organic macromolecules (NOM) and presence of sodium or calcium). At low ionic strength, Ag NPs particle size increased as pH increased from 5 to 8. However, changing the ionic strength from 10⁻³ to 10⁻² M Na increased instability of the Ag NPs, and loss of peak at pH 5 but in the presence of humic substance (HS), a reduction in NP size was seen, most likely due to a reduction in the diffuse layer. The presence of Ca²⁺ ions, at the higher ionic strengths caused complete loss of the solution Ag NPs with or without HS, most likely due to aggregation. At the lower Ca²⁺ ionic strength the Ag NPs were still unstable, but again, in the presence of HS the NPs were largely dispersed. The presence of HS improved stability of Ag NPs under these conditions by forming a surface coating resulting in both steric and charge stabilisation. This work implies that Ag NPs could have long residence times in aquatic systems in the presence of HS potentially resulting in increased bioavailability.     

Low density polyethylene,expanded polystyrene and expanded polypropylene: Strain rate and size effects on mechanical properties

Polymeric foam materials may be used as energy absorbing materials for protection in impact scenarios, and design with these materials requires the mechanical properties of foams across a range of deformation rates, where high deformation rate testing often requires small samples for testing. Owing to their cellular macrostructure, and the large deformations that occur during loading of foams, the measured stress-strain response of a foam material may be influenced by the sample size. In this study, the mechanical properties of three closed-cell polymeric foams (Low Density Polyethylene, Expanded Polystyrene and Expanded Polypropylene) at two different densities were investigated over a range of deformation rates from 0.01 s⁻¹ to 100 s⁻¹. For each foam material, three different nominal sample sizes (10 mm, 17 mm and 35 mm) were tested. On average, the polymeric foam materials exhibited increasing stress with increasing deformation rate, for a given amount of strain.Density variation was identified at the sample level, with smaller samples often exhibiting lower density. Expanded Polystyrene demonstrated the highest variability in sample density and corresponding variability in mechanical response, qualitatively supported by observed variations in the macrostructure of the foam. Expanded Polypropylene exhibited variability in density with sample size, and observable variability in the material macrostructure; however, the dependence of the measured mechanical properties on sample size was modest. Low Density Polyethylene was found to have a relatively consistent cell size at the macrostructure level, and the material density did not vary significantly with sample size. In a similar manner, the dependence of measured mechanical properties on sample size was modest. The effect of sample size was identified to be material specific, and it is recommended that this be assessed using sample-specific density measurements and considering different sized samples when testing foam materials.     

Particle size correlations in brownian agglomeration. Closure hypotheses for product density equations

In a previous paper the authors have demonstrated inaccuracies in the population balance equation, as applied to agglomerating particulate systems, which arise due to an inherent assumption regarding the statistical independence of particle pairs. When this assumption is removed, an intractable hierarchy of product density equations results. In this paper a closure hypothesis for the product density equations is proposed, evaluated against alternatives, and used in an approximate solution to the product density equations. The closure hypothesis is shown to improve significantly upon the population balance equation which is itself the result of the simplest closure.     

The density distributions of the counterions and the coions confined in two similarly charged plates

By using the field-theoretic method, we established a unified systematic formulation of a model of counterions and coions confined in two similarly charged plates, and calculated the density distributions of counterions and coions with various coupling parameters by the two methods: Poisson-Boltzmann (PB) approach and the strong coupling (SC) theory, respectively. We also performed Monte Carlo simulations, and obtained the density distributions of counterions and coions with several different coupling parameters. Comparing our theoretical results with those from Monte Carlo simulation, we find that the PB approach is valid when the coupling parameter Xi is smaller than 1, but, as Xi > or = 1, the results by the PB approach deviate from the corresponding Monte Carlo simulation data, and the deviation gets larger with the coupling parameter increasing. This shows that the PB approach is completely invalid when the coupling parameter is equal to 1 or larger than 1. For the latter case, the development trend of the distribution curve calculated by SC theory agrees with that from Monte Carlo simulation as the coupling parameter increases. This demonstrates that the SC theory can give a qualitative available explanation on the density distribution of the counterions in the system in which the coupling parameters are strictly confined.     

Mathematical modeling and simulation of inulinase adsorption in expanded bed column

A mathematical model for an expanded bed column was developed to predict breakthrough curves for inulinase adsorption on Streamline SP ion-exchange adsorbent, using a crude fermentative broth with cells as the feedstock. The kinetics and mass transfer parameters were estimated using the PSO (particle swarm optimization) heuristic algorithm. The parameters were estimated for each expansion degree (ED) using three breakthrough curves at initial inulinase concentrations of 65.6 U mL⁻¹. In sequence, the model parameters for an ED of 2.5 were validated using the breakthrough curve at an initial concentration of 114.4 U mL⁻¹. The applicability of the validated model in process optimization was investigated, using the model as a process simulator and experimental design methodology to optimize the column and process efficiencies. The results demonstrated the usefulness of this methodology for expanded bed adsorption processes.     

Immobilised metal ion affinity chromatography purification of alcohol dehydrogenase from baker’s yeast using an expanded bed adsorption system

Alcohol dehydrogenase (ADH) from solutions of homogenised packed bakers’ yeast has been successfully purified using immobilised metal-ion affinity chromatography in an expanded bed. Method scouting carried out using pure ADH solutions loaded onto 5-ml HiTrap columns charged with Zn²⁺, Ni²⁺ and Cu²⁺ and eluted using 0–50 mM EDTA gradient found that charging with Zn²⁺ gave the highest recovery and the lowest EDTA concentration required for elution. These results were used to develop a protocol for the expanded bed system and further tested using clarified yeast homogenate loaded onto XK16/20 packed beds (approximately 30 ml) packed with Chelating Sepharose FastFlow matrix in order to determine the optimum elution conditions using EDTA. The ADH was found to elute at 5 mM EDTA and the dynamic and total binding capacities of Streamline chelating for ADH were found to be 235 U/ml and 1075 U/ml matrix, respectively. Expanded bed work based on a step EDTA elution protocol demonstrated that ADH could be successfully eluted from unclarified homogenised bakers’ yeast diluted to 10 mg/ml total protein content with a recovery of 80–100% that was maintained over five consecutive runs with a vigorous clean-in-place procedure between each run.     

Expectation values and density matrices in the Coupled-Cluster theory

A scheme for calculating expectation values in coupled-cluster wave functions is given. The unlinked terms originating from the norm of the wave function are eliminated. Hermiticity and trace conditions for the density matrices are exhibited in such a way as to guarantee their conservation in any reasonable truncation scheme.     

Particle size effects of clusters and crystallites

Size effects of pair distance, cohesive energy, surface stress, and compressibility have been calculated for shell-like structurated particles Y _N ofn complete shells (units Y: rare gases, molecules, ion pairs). The influence of surface definition on size effects has been discussed.     

Particle size and sol stability in metal colloids

Summary It is shown experimentally that the stability of metal sols depends on particle size. Sols with small particles are more stable against electrolyte coagulation than coarser suspensions. It is possible to separate metal particles of different radii by fractionated coagulation. Results are explained from the diminishedvan der Waals attraction between small particles. Consequences for the repeptization of metal sols and for the measurement ofHamaker constants are discussed. It is concluded that the smallness of the particles is a decisive factor for the stability of metal colloids.

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Zusammenfassung Es wird gezeigt, daß die Stabilität von Metallkolloiden von der Teilchengröße abhängig ist. Systeme aus kleinen Teilchen sind bei Elektrolytkoagulation wesentlich stabiler als Systeme mit größeren Teilchen. Durch fraktionierte Flockung werden Kolloidteilchen dem Teilchenradius nach getrennt. Die Erklärung dieser Ergebnisse folgt aus der verringertenvan der Waalsschen Anziehung zwischen kleinen Teilchen. Konsequenzen für die Repeptisierung von Metallkolloiden und für die Bestimmung derHamakerschen Konstante werden diskutiert. Die Stabilität der Metallkolloide wird von der Teilchengröße weitgehend beeinflußt.

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Presented at the 25th Colloid-Meeting in Munich, October 13–15, 1971.     

Anaerobic treatment of low-strength brewery wastewater in expanded granular sludge bed reactor

Anaerobic treatment of low-strength brewery wastewater, with influent total chemical oxygen demand (COD) (CODin) concentrations ranging from 550 to 825 mg/L, was investigated in a pilot-scale 225.5-L expanded granular sludge bed (EGSB) reactor. In an experiment in which the temperature was lowered stepwise from 30 to 12 degrees C, the COD removal efficiency decreased from 73 to 35%, at organic loading rates (OLR) of 11-16.5 g COD/L/d. The applied hydraulic retention time (HRT) and liquid upflow velocity (Vup) were 1.2 h and 5.8 m/h, respectively. Under these conditions, the acidified fraction of the CODin varied from 45 to 90%. In addition to the expected drop in reactor performance, problems with sludge retention were also observed. In a subsequent experiment set at 20 degrees C, COD removal efficiencies exceeding 80% were obtained at an OLR up to 12.6 g COD/L/d, with CODin between 630 and 715 mg/L. The values of HRT and Vup applied were 2.1-1.2 h, and 4.4-7.2 m/h, respectively. The acidified fraction of the CODin was above 90%, but sludge washout was not significant. These results indicate that the EGSB potentials can be further explored for the anaerobic treatment of low-strength brewery wastewater, even at lower temperatures.     

Interpreting magic-number and evaporation effects in cluster size distributions

The Smoluchowski equations describe the coalescence of clusters to form larger clusters. If the kernels or rate constants in these equations are homogeneous, meaning thatK _{j, k} = ² K _jk (wherej andk are cluster sizes), it can be shown that the populationsn _k approachAk ^a e - ^bk for largek and large time, where the constantsa andb depend on the homogeneity parameter. Deviations of observed populations from this formula may be ascribed to magic-number and/or evaporation effects on the kernels. By integrating the Smoluchowski equations numerically for various choices of the kernels, we derive population distributions and show the effects of magic-number clusters and evaporation on the population distribution. Various methods are used to extract the value of, in order to determine the best way to extract the underlying value of from experimental data. Experimental populations for sodium metal clusters are then analyzed according to the same procedure, to extract the homogeneity parameter and explain the patterns in the population distribution.     

Statistical theory of parcticle size distributions in emulsions and suspensions

Summary The particle size distributions in emulsions and suspensions are mostly empirical. Here a rigorous statistical theory of the problem is given, leading to the logarithmic-normal distribution for the sizes of the particle. On the simple physical basis that the disruption of the interface and the evolution of the particle sizes during emulsification are random turbulent processes, the log-normal law is derived by considering the process as aMarkoff chain. An alternate simpler derivation is also presented. The nature of the simplifying assumption involved in the theory is clearly brought out. Some properties of the log-normal curve are given. The statistical analysis in fitting the log-normal distribution to the experimental data with special reference to the distortion of the fractile diagram and the advantages of a theoretical distribution over an empirical one are discussed in detail with suitable examples.

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Zusammenfassung Die Teilchenverteilungen von Emulsionen und Dispersionen sind meist empirisch. Hier wird eine strenge statistische Theorie des Problems gegeben, die zu der logarithmischen Normalverteilung der Teilchengr?\en führt. Auf der einfachen physikalischen Grundlage, da\ Zerbrechen der Oberfl?chen und die Entstehung der Teilchengr?\en w?hrend Emulgierung einem zuf?lligen turbulenten Proze\ zuzuschreiben sind, wird die log-Normalverteilung durch Analyse dieses Prozesses als eineMarkoffsche Kette abgeleitet. Eine einfache alternative Ableitung wird au\erdem gebracht. Die Natur der in die Theorie eingehenden Grundannahmen wird erkl?rt. Einige Eigenschaften der log-Normal-Kurve werden diskutiert. Die statistische Analyse zur Darstellung von Beobachtungsdaten mit Hilfe der log-Normalverteilung, speziell in Bezug auf die Ver?nderung der Kurven für H?ufigkeitsverteilungen sowie die Vorteile einer theoretischen Verteilung gegenüber einer empirischen Kurve, werden an geeigneten Beispielen in allen Einzelheiten dargelegt.

     

神华煤流化床气化带出细粉的粒径分离及分离后细粉的CO_2气化特性研究

按粒径将神华煤流化床气化带出细粉(简称细粉)依次筛分为七个组分。采用工业分析仪、元素分析仪、热重分析仪、X射线粉末衍射仪、物理吸附仪等对各组分细粉的基本物化特性、CO2恒温和程序升温气化行为进行了考察。在此基础上,对气化活性差异及其原因进行初步探索。结果表明,细粉经历部分气化后,由于挥发分的析出,细粉的固定碳含量较原煤高,但较相应半焦低。细粉的粒径分布范围较宽,呈近似"M"形分布。随细粉粒径减小,灰分含量增大,而含碳量减少。CO2恒温气化与程序升温气化获得的气化反应活性顺序一致:均随细粉粒径的减小先逐渐降低而后又逐渐升高。不同细粉气化反应活性的差异与其自身的石墨化程度及灰分含量有关,而在研究实验条件下与孔径结构关系不大。     

Spatial distributions of metastable argon,temperature and electron number density in an inductively coupled argon plasma

Spatially resolved radial distributions of excitation temperature and electron number density in an argon ICP were obtained. The argon excitation temperature and electron number density near the plasma center were found to 7000 K and 5 × 10¹⁵ cm^?3, respectively, at an RF power of 1.5 kW and a carrier argon flow rate 0.65 1 min^?1.Various distributions of the absorbance at the Ar I 811.5 nm line, which has one of the metastable levels as the lower level, were obtained with and without carrier argon flow, where an MIP was used as a light source. Introduction of a large amount of potassium did not influence the distribution of the absorbance. The emission intensities at Ar I 811.5 nm were also measured for comparison.     

约化密度矩阵和蛋白质研究中的原子对势能

讨论为得到在蛋白质折叠和结合研究中所使用的原子对势能,应该建立怎样的物理化学模型和如何应用统计力学．在尽力澄清统计方法背后的物理化学模型的同时,强调了使用平均力势的优点,和应用二阶约化密度矩阵正确计算了平均力势的公式．