Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Growth regime map for liquid-bound granules: further development and experimental validation

An attempt was made to quantify the boundaries and validate the granule growth regime map for liquid-bound granules recently proposed by Iveson and Litster (AlChE J. 44 (1998) 1510). This regime map postulates that the type of granule growth behaviour is a function of only two dimensionless groups: the amount of granule deformation during collision (characterised by a Stokes deformation number, St(def)) and the maximum granule pore saturation, s(max). The results of experiments performed with a range of materials (glass ballotini, iron ore fines, copper chalcopyrite powder and a sodium sulphate and cellulose mixture) using both drum and high shear mixer granulators were examined. The drum granulation results gave good agreement with the proposed regime map. The boundary between crumb and steady growth occurs at St(def) of order 0.1 and the boundary between steady and induction growth occurs at St(def) of order 0.001. The nucleation only boundary occurs at pore saturations that increase from 70% to 80% with decreasing St(def). However, the high shear mixer results all had St(def) numbers which were too large. This is most likely to be because the chopper tip-speed is an over-estimate of the average impact velocity granules experience and possibly also due to the dynamic yield strength of the materials being significantly greater than the yield strengths measured at low strain rates. Hence, the map is only a useful tool for comparing the granulation behaviour of different materials in the same device. Until we have a better understanding of the flow patterns and impact velocities in granulators, it cannot be used to compare different types of equipment. Theoretical considerations also revealed that several of the regime boundaries are also functions of additional parameters not explicitly contained on the map, such as binder viscosity. (C) 2001 Elsevier Science B.V. All rights reserved.

Nucleation, growth and breakage phenomena in agitated wet granulation processes: a review

Wet agglomeration processes have traditionally been considered an empirical art, with great difficulties in predicting and explaining observed behaviour. Industry has faced a range of problems including large recycle ratios, poor product quality control, surging and even the total failure of scale up from laboratory to full scale production. However, in recent years there has been a rapid advancement in our understanding of the fundamental processes that control granulation behaviour and product properties. This review critically evaluates the current understanding of the three key areas of wet granulation processes: wetting and nucleation, consolidation and growth, and breakage and attrition. Particular emphasis is placed on the fact that there now exist theoretical models which predict or explain the majority of experimentally observed behaviour. Provided that the correct material properties and operating parameters are known, it is now possible to make useful predictions about how a material will granulate. The challenge that now faces us is to transfer these theoretical developments into industrial practice. Standard, reliable methods need to be developed to measure the formulation properties that control granulation behaviour, such as contact angle and dynamic yield strength. There also needs to be a better understanding of the flow patterns, mixing behaviour and impact velocities in different types of granulation equipment. (C) 2001 Elsevier Science B.V. All rights reserved.

The mechanisms of combustion and continuous reactions during mechanical alloying

Some materials exhibit a combustion event during mechanical alloying, which results in the rapid transformation of reactants into products, while others show a slow transformation of reactants into products, In this paper, the continuous W + C --> WC reaction is compared to the Ti + C --> TiC combustion reaction. Rietveld refinement of X-ray diffraction patterns is used to show that these particular reactions proceed through different pathways, determined by crystallographic factors of the reactants. When a crystallographic relationship exists between the reactants and the products, such as that between W and WC, the product forms slowly over a period of time. In contrast, insertion of C into the Ti structure is associated with atomic rearrangements within the crowded lattice planes and the subsequent catastrophic failure of the reactant lattices results in combustion to form TiC. (C) 2001 Academic Press.

Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

An inverse design of an open, head/neck RF coil for MRI

Radio-frequency (RF) coils are a necessary component of magnetic resonance imaging (MRI) systems. When used in transmit operation, they act to generate a homogeneous RF magnetic field within a volume of interest and when in receive operation, they act to receive the nuclear magnetic resonance signal from the RF-excited specimen. This paper outlines a procedure for the design of open RF coils using the time-harmonic inverse method. This method entails the calculation of an ideal current density on a multipaned planar surface that would generate a specified magnetic field within the volume of interest. Because of the averaging effect of the regularization technique in the matrix solution, the specified magnetic field is shaped within an iterative procedure until the generated magnetic field matches the desired magnetic field. The stream-function technique is used to ascertain conductor positions and a method of moments package is then used to finalize the design. An open head/neck coil was designed to operate in a clinical 2T MRI system and the presented results prove the efficacy of this design methodology.

Thunderstorms - their importance in wind engineering (a case for the next generation wind tunnel)

This paper attempts a state-of-the-art summary of research into thunderstorm wind fields from an engineering perspective. The characteristics of thunderstorms and the two extreme wind events-tornadoes and downbursts-spawn by thunderstorms are described. The significant differences from traditional boundary layer flows are highlighted. The importance of thunderstorm gusts in the worldwide database of extreme wind events is established. Physical simulations of tornadoes and downbursts are described and discussed leading to the recommendation that Wind Engineering needs to focus more resources on the fundamental issue - What is the flow structure in the strongest winds? © 2002 Published by Elsevier Science Ltd.

Cloud-point extraction and preconcentration of cyanobacterial toxins (microcystins) from natural waters using a cationic surfactant

A new cloud-point extraction and preconcentration method, using a cationic, surfactant, Aliquat-336 (tricaprylyl-methy;ammonium chloride), his-been developed for the determination of cyanobacterial toxins, microcystins, in natural waters. Sodium sulfate was used to induce phase separation at 25 degreesC. The phase behavior of Aliquat-336 with respect to concentration of Na2SO4 was studied. The cloud-point system revealed a very high phase volume ratio compared to other established systems of nonionic, anionic, and cationic surfactants: At pH 6-7, it showed an outstanding selectivity in ahalyte extraction for anionic species. Only MC-LR and MC-YR, which are known to be predominantly anionic, were extracted (with averaged recoveries of 113.9 +/- 9% and 87.1 +/- 7%, respectively). MC-RR, which is likely to be amphoteric at the above pH range, was. not cle tectable in.the extract. Coupled to HPLC/UV separation and detection, the cloud-point extraction method (with 2.5 mM Aliquat-336 and 75 mM Na2SO4 at 25 degreesC) offered detection limits of 150 +/- 7 and 470 +/- 72 pg/mL for MC-LR and MC-YR, respectively, in 25 mL of deionized water. Repeatability of the method was 7.6% for MC-LR and 7.3% for MC-YR: The cloud-point extraction process can be. completed within 10-15 min with no cleanup steps required. Applicability of the new method to the determination of microcystins in real samples was demonstrated using natural surface waters, collected from a local river and a local duck pond spiked with realistic. concentrations of microcystins. Effects of salinity and organic matter (TOC) content in the water sample on the extraction efficiency were also studied.

Transformation processes, pathways, and possible sources of distinctive polychlorinated dibenzo-p-dioxin signatures in sink environments

In recent years, studies on environmental samples with unusual dibenzo-p-dioxin (PCDD) congener profiles were reported from a range of countries. These profiles, characterized by a dominance of octachlorinated dibenzodioxin (OCDD) and relatively low in dibenzofuran (PCDF) concentrations, could not be attributed to known sources or formation processes. In the present study, the processes that result in these unusual profiles were assessed using the concentrations and isomer signatures of PCDDs from dated estuarine sediment cores in Queensland, Australia. Increases in relative concentrations of lower chlorinated PODS and a relative decrease of OCDD were correlated with time of sediment deposition. Preferred lateral, anaerobic dechlorination of OCDD represents a likely pathway for these changes. In Queensland sediments, these transformations result in a distinct dominance of isomers fully chlorinated in the 1,4,6,9-positions (1,4-patterns), and similar 1,4-patterns were observed in sediments from elsewhere. Consequently, these environmental samples may not reflect the signatures of the original source, and a reevaluation of source inputs was undertaken. Natural formation of PCDDs, which has previously been suggested, is discussed; however, based on the present results and literature comparisons, we propose an alternative scenario. This scenario hypothesizes that an anthropogenic PCDD precursor input (e.g. pentachlorophenol) results in the contamination. These results and hypothesis imply further investigations are warrented into possible anthropogenic sources in areas where natural PCDD formation has been suggested.

Who does not gain weight? Prevalence and predictors of weight maintenance in young women

OBJECTIVE: To investigate the prevalence and predictors of weight maintenance over time in a large sample of young Australian women. DESIGN: This population study examined baseline and 4y follow-up data from the cohort of young women participating in the Australian Longitudinal Study on Women's Health. SUBJECTS: A total of 8726 young women aged 18 - 23y at baseline. MEASURES: Height, weight and body mass index (BMI); physical activity; time spent sitting; selected eating behaviours (eg dieting, disordered eating, takeaway food consumption); cigarette smoking, alcohol consumption; parity; and socio-demographic characteristics. RESULTS: Only 44% of the women reported their BMI at follow-up to be within 5% of their baseline BMI (maintainers); 41% had gained weight and 15% had lost weight. Weight maintainers were more likely to be in managerial or professional occupations; to have never married; to be currently studying; and not to be mothers. Controlling for sociodemographic factors, weight maintainers were more likely to be in a healthy weight range at baseline, and to report that they spent less time sitting, and consumed less takeaway food, than women who gained weight. CONCLUSIONS: Fewer than half the young women in this community sample maintained their weight over this 4y period in their early twenties. Findings of widespread weight gain, particularly among those already overweight, suggest that early adulthood, which is a time of significant life changes for many women, may be an important time for implementing strategies to promote maintenance of healthy weight. Strategies which encourage decreased sitting time and less takeaway food consumption may be effective for encouraging weight maintenance at this life stage.

Growth and compaction behaviour of copper concentrate granules in a rotating drum

In order to understand the growth and compaction behaviour of chalcopyrite (copper concentrate), batch granulation tests were carried out using a rotating drum. The granule growth exhibited induction-type behaviour, as defined by Iveson and Litster [AIChE J. 44 (1998) 15 10]. There were two consecutive stages during granulation: the induction stage, during which the granules are gradually being compacted and little or no growth occurs, and the rapid growth stage, which starts when the granules have become surface wet and are rapidly growing. In agreement with earlier findings. an increased amount of binder liquid shortened the induction time. The compaction behaviour was also investigated. A displaced volume method was adopted to determine the porosity of the granules. It was shown that this technique had a limitation as it was unable to detect the reduction of the volumes of the granule pores after the granules had become surface wet. Due to this, some of the measurements were not suited for fitting a three-parameter empirical model. Attempts were made to determine whether the rapid growth stage started with the pore saturation exceeding a certain critical value, but due to the scatter in the porosity measurements and the fact that some of the measurements could not be used, it was not possible to determine a critical pore saturation, However, the porosity measurements clearly demonstrated that the porosity of the granules decreased during the induction stage of an experiment and that when rapid growth occurred, the granules had a pore saturation was around 0.85. This value was slightly lower than unity, which is most likely due to trapped air bubbles. (C) 2002 Published by Elsevier Science B.V.

Percolation Phenomena in Micropore Adsorption: Influence on Single and Multicomponent Adsorption Equilibria

A novel and simple method for determination of micropore network connectivity of activated carbon using liquid phase adsorption is presented in this paper. The method is applied to three different commercial carbons with eight different liquid phase adsorptives as probes. The effect of the pore network connectivity on the prediction of multicomponent adsorption equilibria was also studied. For this purpose, the Ideal Adsorbed Solution Theory (IAST) was used in conjuction with the modified DR single component isotherm. The results of comparison with experimental data show that incorporation of the connectivity, and consideration of percolation processes associated with the different molecular sizes of the adsorptives in the mixture, can improve the performance of the IAST in predicting multicomponent adsorption equilibria.