Elastic moduli of model random three-dimensional closed-cell cellular solids

Most cellular solids are random materials, while practically all theoretical structure-property results are for periodic models. To be able to generate theoretical results for random models, the finite element method (FEM) was used to study the elastic properties of solids with a closed-cell cellular structure. We have computed the density (rho) and microstructure dependence of the Young's modulus (E) and Poisson's ratio (PR) for several different isotropic random models based on Voronoi tessellations and level-cut Gaussian random fields. The effect of partially open cells is also considered. The results, which are best described by a power law E infinity rho (n) (1<n<2), show the influence of randomness and isotropy on the properties of closed-cell cellular materials, and are found to be in good agreement with experimental data. (C) 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations. (C) 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:504-520, 2001.

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.

Application of heterogeneous vacancy solution theory to characterization of microporous solids

The vacancy solution theory of adsorption is re-formulated here through the mass-action law, and placed in a convenient framework permitting the development of thermodynamic ally consistent isotherms. It is shown that both the multisite Langmuir model and the classical vacancy solution theory expression are special cases of the more general approach when the Flory-Huggins activity coefficient model is used, with the former being the thermodynamically consistent result. The improved vacancy solution theory approach is further extended here to heterogeneous adsorbents by considering the pore-width dependent potential along with a pore size distribution. However, application of the model to numerous hydrocarbons as well as other adsorptives on microporous activated carbons shows that the multisite model has difficulty in the presence of a pore size distribution, because pores of different sizes can have different numbers of adsorbed layers and therefore different site occupancies. On the other hand, use of the classical vacancy solution theory expression for the local isotherm leads to good simultaneous fit of the data, while yielding a site diameter of about 0.257 nm, consistent with that expected for the potential well in aromatic rings on carbon pore surfaces. It is argued that the classical approach is successful because the Flory-Huggins term effectively represents adsorbate interactions in disguise. When used together with the ideal adsorbed solution theory the heterogeneous vacancy solution theory successfully predicts binary adsorption equilibria, and is found to perform better than the multisite Langmuir as well as the heterogeneous Langmuir model. (C) 2001 Elsevier Science Ltd. All rights reserved.

Turbulent flow around a rotating stepped cylinder

Direct numerical simulation (DNS) of turbulent flow around a rotating cylinder with two backward-facing steps axisymmetrically mounted in the circumferential direction was performed and compared with DNS of plane backward-facing step flow (PBSF) of Le [J. Fluid Mech. 330, 349 (1997)]. The original motivation of this work stemmed from the efforts to design a simple device which can generate flows of high turbulence intensity at low cost for corrosion researchers. It turned out that the current flow shows flow structures quite similar to those of PBSF downstream of the step, even though configurations of the two flows are totally different from one another. The stepped cylinder appears to be a cost-effective tool in the generation of flow structures similar to those of PBSF. (C) 2002 American Institute of Physics.

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.

Mass transfer correlations for rotating drum bioreactors

Evaporative cooling is extremely important for large-scale operation of rotating drum bioreactors (RDBs). Outlet water vapour concentrations were measured for a RDB containing wet wheat bran with the aim of determining the mass transfer coefficient for evaporation from the bran bed to the headspace. Mass transfer was expressed as the mass transfer coefficient times the area for transfer per unit volume of void space in the drum. Values of ka' were determined under combinations of aeration superficial velocities ranging from 0.006 to 0.017 ms(-1) and rotation rates ranging from 0 to 9 rpm. Mass transfer coefficients were evaluated using a variety of residence time distributions (RTDs) for flow in the gas phase including plug flow and well-mixed and a Central Jet RTD based on RTD studies. If plug flow is assumed, the degree of holdup at low effective Peclet (Pe(eff)) numbers gives an apparent under-estimate of ka' compared with empirical correlations. Values of ka' calculated using the Central Jet RTD agree well with values of ka' from literature correlations. There was a linear relationship between ka' and effective Peclet number: ka' = 2.32 x 10(-3) Pe(eff). (C) 2002 Elsevier Science B.V. All rights reserved.

Porous solids from layered clays by combined pillaring and templating approaches

The pore structure formation in bentonite, pillared with a mixed sol of silicon and titanium hydroxides and treated subsequently with quaternary ammonium surfactants, is investigated. The surfactant micelles act as a template, similar to their role in MCM41 synthesis. Because both the surfactant micelles and the sol particles are positively charged, it is greatly favorable for them to form meso-phase assembles in the galleries between the clay layers that bear negative charges. Besides, the sol particles do not bond the clay layers strongly as other kinds of pillar precursors do, so that the treatment with surfactants can result in radical structure changes in sol-pillared clays. This allows us to tailor the pore structure of these porous clays by choice of surfactant. The surfactant treatment also results in profound increases in porosity and improvement in thermal stability. Therefore, the product porous clays have great potential to be Used to deal with large molecules or at high operating temperatures. We also found that titanium in these samples is highly dispersed in the silica matrix rather than existing in the form of small particles of pure titania. Such highly dispersed Ti active centers may offer excellent activities for catalytic oxidation reactions such as alkanes into alcohols and ketones.

A mathematical model of concentrate solids content for the wet drum magnetic separator

Low concentrate density from wet drum magnetic separators in dense medium circuits can cause operating difficulties due to inability to obtain the required circulating medium density and, indirectly, high medium solids losses. The literature is almost silent on the processes controlling concentrate density. However, the common name for the region through which concentrate is discharged-the squeeze pan gap-implies that some extrusion process is thought to be at work. There is no model of magnetics recovery in a wet drum magnetic separator, which includes as inputs all significant machine and operating variables. A series of trials, in both factorial experiments and in single variable experiments, was done using a purpose built rig which featured a small industrial scale (700 mm lip length, 900 turn diameter) wet drum magnetic separator. A substantial data set of 191 trials was generated in this work. The results of the factorial experiments were used to identify the variables having a significant effect on magnetics recovery. It is proposed, based both on the experimental observations of the present work and on observations reported in the literature, that the process controlling magnetic separator concentrate density is one of drainage. Such a process should be able to be defined by an initial moisture, a drainage rate and a drainage time, the latter being defined by the volumetric flowrate and the volume within the drainage zone. The magnetics can be characterised by an experimentally derived ultimate drainage moisture. A model based on these concepts and containing adjustable parameters was developed. This model was then fitted to a randomly chosen 80% of the data, and validated by application to the remaining 20%. The model is shown to be a good fit to data over concentrate solids content values from 40% solids to 80% solids and for both magnetite and ferrosilicon feeds. (C) 2003 Elsevier Science B.V. All rights reserved.

Horizontal rotating cylinder - A compact apparatus for studying the effect of water wetting on carbon dioxide corrosion of mild steel

Water wetting is a crucial issue in carbon dioxide (CO.) corrosion of multiphase flow pipelines made from mild steel. This study demonstrates the use of a novel benchtop apparatus, a horizontal rotating cylinder, to study the effect of water wetting on CO2 corrosion of mild steel in two-phase flow. The setup is similar to a standard rotating cylinder except for its horizontal orientation and the presence of two phases-typically water and oil. The apparatus has been tested by using mass-transfer measurements and CO2 corrosion measurements in single-phase water flow. CO2 corrosion measurements were subsequently performed using a water/hexane mixture with water cuts varying between 5% and 50%. While the metal surface was primarily hydrophilic under stagnant. conditions, a variety of dynamic water wetting situations was encountered as the water cut and fluid velocity were altered. Threshold velocities were identified at various water cuts when the surface became oil-wet and corrosion stopped.

Numerical investigation of turbulent flow around a rotating stepped cylinder for corrosion study

Direct numerical simulation has been carried out for turbulent flow set up by a rotating cylinder with two backward-facing steps axisymmetrically mounted in the circumferential direction. This flow geometry creates a qualitatively similar flow pattern as observed near, a sudden, pipe expansion or a plane backward-facing step, characterized by flow separation and reattachment. A region of intense turbulence intensity and high wall-shear-stress fluctuations is formed in,the recirculating I region downstream of the step, where high mass-transfer capacity was also experimentally observed. Since, corrosion is frequently mass-transfer., controlled, our findings, put forward this apparatus as useful tool for future corrosion research.

Effect of lifter design on drying performance in rotary dryers

Lifter use in dryers improves mass transfer by increasing the amount of surface area available for transfer and also by increasing the velocity of gas over the particle surface. An even cross-sectional distribution of particles in a dryer improves the efficiency of operation by ensuring that evaporation from falling particles is taking place for the maximum fraction of the rotation period of the drier. Studies on lifter design to improve the cross-sectional particle distribution were performed on angled lifters. A single lifter was used and the mass-transfer rate examined as a function of angular lifter displacement. Analysis of the mass transfer characteristics of single lifters allowed performance comparisons and recommendations for lifter design.