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.

Engineering the structures of nanoporous clays with micelles of alkyl polyether surfactants

Composite clay nanostructures (CCNs) were observed in intercalating Laponite clay with alumina in the presence of alkyl polyether surfactants which contain hydrophobic alkyl chains and ether groups. Such nanostructured clays are highly porous solids consisting of randomly orientated clay platelets intercalated with alumina nanoparticles. The pores in the product solids are larger than the dimension of the surfactant molecules, ranging from 2 to 10 nm. This suggests that the micelles of the surfactant molecules, rather than the molecules, act as templates in the synthesis. Interestingly, it is found that the size of the framework pores was directly proportional to the amount of the surfactants in terms of moles, but shows no evident dependence on the size of the surfactant molecules. Broad pore size distributions were observed for the product CCNs. This study demonstrates that introducing surfactants in the pillaring process of clays is a powerful strategy for tailoring the pore structures of nanoporous clays. With this new technique, it is possible to design and engineer such composite clay nanostructures with desired pore and surface properties by the proper choice of surfactant amounts and preparation conditions.

Multicomponent supercritical adsorption in microporous activated carbon materials

In this paper, a new technique for predicting multicomponent adsorption equilibria of supercritical fluids in microporous carbons is presented. In difference from adsorption on a surface, which is a function of the fluid-solid interaction only, adsorption in porous media is influenced by the proximity of the pore walls, resulting in the enhancement in adsorption affinity. The degree of this enhancement is different for different adsorbates, and it increases with a decrease in pore size. The theory is applied to a number of carbonaceous systems with good success.

A flexible method for rapid force computation in elliptical magnets

The design of open-access elliptical cross-section magnet systems has recently come under consideration. Obtaining values for the forces generated within these unusual magnets is important to progress the designs towards feasible instruments. This paper presents a novel and flexible method for the rapid computation of forces within elliptical magnets. The method is demonstrated by the analysis of a clinical magnetic resonance imaging magnet of elliptical cross-section and open design. The analysis reveals the non-symmetric nature of the generated Maxwell forces, which are an important consideration, particularly in the design of superconducting systems.

An inverse design method for elliptical MRI magnets

An inverse, current density mapping (CDM) method has been developed for the design of elliptical cross-section MRI magnets. The method provides a rapid prototyping system for unusual magnet designs, as it generates a 3D current density in response to a set of target field and geometric constraints. The emphasis of this work is on the investigation of new elliptical coil structures for clinical MRI magnets. The effect of the elliptical aspect ratio on magnet performance is investigated. Viable designs are generated for symmetric, asymmetric and open architecture elliptical magnets using the new method. Clinically relevant attributes such as reduced stray field and large homogeneous regions relative to total magnet length are included in the design process and investigated in detail. The preliminary magnet designs have several novel features.

A novel target-field method for finite-length magnetic resonance shim coils: I. Zonal shims

This paper presents a new approach for the design of genuinely finite-length shim and gradient coils, intended for use in magnetic resonance imaging equipment. A cylindrical target region is located asymmetrically, at an arbitrary position within a coil of finite length. A desired target field is specified on the surface of that region, and a method is given that enables winding patterns on the surface of the coil to be designed, to produce the desired field at the inner target region. The method uses a minimization technique combined with regularization, to find the current density on the surface of the coil. The method is illustrated for linear, quadratic and cubic magnetic target fields located asymmetrically within a finite-length coil.

Asymmetric zonal shim coils for magnetic resonance applications

A method is presented for the systematic design of asymmetric zonal shim coils for magnetic resonance applications. Fourier-series methods are used to represent the magnetic field inside and outside a circular cylinder of length 2L and radius a. The current density on the cylinder is also represented using Fourier series. Any desired field can be specified in advance on the cylinder's radius, over some nonsymmetric portion pL

Compact clinical MRI magnet design using a multilayer current density approach

In this work, a new method of optimization is successfully applied to the theoretical design of compact, actively shielded, clinical MRI magnets. The problem is formulated as a two-step process in which the desired current densities on multiple, cc-axial surface layers are first calculated by solving Fredholm equations of the first kind. Non-linear optimization methods with inequality constraints are then invoked to fit practical magnet coils to the desired current densities. The current density approach allows rapid prototyping of unusual magnet designs. The emphasis of this work is on the optimal design of short, actively-shielded MRI magnets for whole-body imaging. Details of the hybrid numerical model are presented, and the model is used to investigate compact, symmetric, and asymmetric MRI magnets. Magnet designs are presented for actively-shielded, symmetric magnets of coil length 1.0 m, which is considerably shorter than currently available designs of comparable dsv size. Novel, actively-shielded, asymmetric magnet designs are also presented in which the beginning of a 50-cm dsv is positioned just 11 cm from the end of the coil structure, allowing much improved access to the patient and reduced patient claustrophobia. Magn Reson Med 45:331540, 2001. (C) 2001 Wiley-Liss, Inc.

The stochastic design of force-minimized compact magnets for high-field magnetic resonance imaging applications

New designs for force-minimized compact high-field clinical MRI magnets are described. The design method is a modified simulated annealing (SA) procedure which includes Maxwell forces in the error function to be minimized. This permits an automated force reduction in the magnet designs while controlling the overall dimensions of the system. As SA optimization requires many iterations to achieve a final design, it is important that each iteration in the procedure is rapid. We have therefore developed a rapid force calculation algorithm. Novel designs for short 3- and 4-T clinical MRI systems are presented in which force reduction has been invoked. The final designs provide large homogeneous regions and reduced stray fields in remarkable short magnets. A shielded 4-T design that is approximately 30% shorter than current designs is presented. This novel magnet generates a full 50-cm diameter homogeneous region.

A segmentation-based and partial-volume-compensated method for an accurate measurement of lateral ventricular volumes on T-1-weighted magnetic resonance images

Lateral ventricular volumes based on segmented brain MR images can be significantly underestimated if partial volume effects are not considered. This is because a group of voxels in the neighborhood of lateral ventricles is often mis-classified as gray matter voxels due to partial volume effects. This group of voxels is actually a mixture of ventricular cerebro-spinal fluid and the white matter and therefore, a portion of it should be included as part of the lateral ventricular structure. In this note, we describe an automated method for the measurement of lateral ventricular volumes on segmented brain MR images. Image segmentation was carried in combination of intensity correction and thresholding. The method is featured with a procedure for addressing mis-classified voxels in the surrounding of lateral ventricles. A detailed analysis showed that lateral ventricular volumes could be underestimated by 10 to 30% depending upon the size of the lateral ventricular structure, if mis-classified voxels were not included. Validation of the method was done through comparison with the averaged manually traced volumes. Finally, the merit of the method is demonstrated in the evaluation of the rate of lateral ventricular enlargement. (C) 2001 Elsevier Science Inc. All rights reserved.

Current density mapping approach for design of clinical magnetic resonance imaging magnets

Novel current density mapping (CDM) schemes are developed for the design of new actively shielded, clinical magnetic resonance imaging (MRI) magnets. This is an extended inverse method in which the entire potential solution space for the superconductors has been considered, rather than single current density layers. The solution provides an insight into the required superconducting coil pattern for a desired magnet configuration. This information is then used as an initial set of parameters for the magnet structure, and a previously developed hybrid numerical optimization technique is used to obtain the final geometry of the magnet. The CDM scheme is applied to the design of compact symmetric, asymmetric, and open architecture 1.0-1.5 T MRI magnet systems of novel geometry and utility. A new symmetric 1.0-T system that is just I m in length with a full 50-cm diameter of the active, or sensitive, volume (DSV) is detailed, as well as an asymmetric system in which a 50-cm DSV begins just 14 cm from the end of the coil structure. Finally a 1.0-T open magnet system with a full 50-cm DSV is presented. These new designs provide clinically useful homogeneous regions and have appropriately restricted stray fields but, in some of the designs, the DSV is much closer to the end of the magnet system than in conventional designs. These new designs have the potential to reduce patient claustrophobia and improve physician access to patients undergoing scans. (C) 2002 Wiley Periodicals, Inc.

Ellipsoidal harmonic (Lame) MRI shims

Ellipsoidal harmonics are presented as a basis function set for the design of shim coils for magnetic resonance imaging (MRI) or spectroscopy. MR shim coils may be either superconductive or resistive. Ellipsoidal harmonics form an orthogonal set over an ellipsoid and hence are appropriate in circumstances where the imaging or spectroscopic region of a magnet more closely conforms to an ellipsoid rather than a sphere. This is often the case in practice. The Cartesian form of ellipsoidal harmonics is discussed. A method for the design of streamline coil designs is detailed and patterns for third-order ellipsoidal (Lame) shims wound on a cylindrical surface are presented.

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.

Polymer product engineering utilising oscillatory baffled reactors

The Oscillatory baffled reactor (OBR) can be used to produce particles with controlled size and morphology, in batch or continuous flow. This is due to the effect of the superimposed oscillations that radially mixes fluid but still allows plug-flow (or close to plug flow) behaviour in a continuous system. This mixing, combined with a close to a constant level of turbulence intensity in the reactor, leads to tight droplet and subsequent product particle size distributions. By applying population balance equations together with experimental droplet size distributions, breakage rates of droplets can be determined and this is a useful tool for understanding the product engineering in OBRs. (C) 2002 Elsevier Science B.V All rights reserved.