A wavelet-based adaptive technique for adsorption problems involving steep gradients

A general, fast wavelet-based adaptive collocation method is formulated for heat and mass transfer problems involving a steep moving profile of the dependent variable. The technique of grid adaptation is based on sparse point representation (SPR). The method is applied and tested for the case of a gas–solid non-catalytic reaction in a porous solid at high Thiele modulus. Accurate and convergent steep profiles are obtained for Thiele modulus as large as 100 for the case of slab and found to match the analytical solution.

A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.

Approximate analytical solutions for porous catalysts with nonuniform activity

Using a novel finite integral transform technique, the problem of diffusion and chemical reaction in a porous catalyst with general activity profile is investigated theoretically. Analytical expressions for the effectiveness factor are obtained for pth order and Michaelis-Menten kinetics. Perturbation methods are employed to provide useful asymptotic solutions for large or small values of Thiele modulus and Biot number.

Oxidation of toluene in waste gas streams using mesoporous Ti-hexagonal mesoporous silica

Various mesoporous catalysts with titanium loadings between 0.5 and 4 Ti wt. % and surface areas between 600 and 1,600 m(2)/g were synthesized using the molecular designed dispersion technique. These catalysts were tested using toluene oxidation in a fixed bed reactor at temperatures between 300 and 550degreesC. The reaction products were found to be CO2 and CO with selectivity towards CO2 above 80% for all catalysts. The catalytic activity of the catalysts increases with titanium loading. The total conversion at 550degreesC was not affected by the textural porosity, but increased textural porosity did significantly reduce the ignition temperature by up to 50degreesC. The Thiele modulus was calculated to be much less than one for all these materials indicating that the reaction rate is not diffusion, limited.

Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas-solid and fluid-solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection-diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection-diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov-Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor-corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus. (C) 2001 Elsevier Science Ltd. All rights reserved.

Study of the surface hardness and modulus of elasticity of conventional and microwave-cured acrylic resins

The aim of this study was to evaluate the following acrylic resins: Clássico®, QC-20® and Lucitone®, recommended specifically for thermal polymerization, and Acron MC® and VIPI-WAVE®, made for polymerization by microwave energy. The resins were evaluated regarding their surface nanohardness and modulus of elasticity, while varying the polymerization time recommended by the manufacturer. They were also compared as to the presence of water absorbed by the samples. The technique used was nanoindentation, using the Nano Indenter XP®, MTS. According to an intra-group analysis, when using the polymerization time recommended by the manufacturer, a variation of 0.14 to 0.23 GPa for nanohardness and 2.61 to 3.73 GPa for modulus of elasticity was observed for the thermally polymerized resins. The variation for the resins made for polymerization by microwave energy was 0.15 to 0.22 GPa for nanohardness and 2.94 to 3.73 GPa for modulus of elasticity. The conclusion was that the Classico® resin presented higher nanohardness and higher modulus of elasticity values when compared to those of the same group, while Acron MC® presented the highest values for the same characteristics when compared to those of the same group. The water absorption evaluation showed that all the thermal polymerization resins, except for Lucitone®, presented significant nanohardness differences when submitted to dehydration or rehydration, while only Acron MC® presented no significant differences when submitted to a double polymerization time. Regarding the modulus of elasticity, it was observed that all the tested materials and products, except for Lucitone®, showed a significant increase in modulus of elasticity when submitted to a lack of hydration.

Using the ultrasound and instrumented indentation techniques to measure the elastic modulus of engineering materials

Currently, the acoustic and nanoindentation techniques are two of the most used techniques for material elastic modulus measurement. In this article fundamental principles and limitations of both techniques are shown and discussed. Last advances in nanoindentation technique are also reviewed. An experimental study in ceramic, metallic, composite and single crystals was also done. Results shown that ultrasonic technique is capable to provide results in agreement with those reported in literature. However, ultrasonic technique does not allow measuring the elastic modulus of some small samples and single crystals. On the other hand, the nanoindentation technique estimates the elastic modulus values in reasonable agreement with those measured by acoustic methods, particularly in amorphous materials, while in some policristaline materials some deviation from expected values was obtained.

Effects of elastic indenter deformation on spherical instrumented indentation tests: the reduced elastic modulus

Although the Hertz theory is not applicable in the analysis of the indentation of elastic-plastic materials, it is common practice to incorporate the concept of indenter/specimen combined modulus to consider indenter deformation. The appropriateness was assessed of the use of reduced modulus to incorporate the effect of indenter deformation in the analysis of the indentation with spherical indenters. The analysis based on finite element simulations considered four values of the ratio of the indented material elastic modulus to that of the diamond indenter, E/E(i) (0, 0.04, 0.19, 0.39), four values of the ratio of the elastic reduced modulus to the initial yield strength, E(r)/Y (0, 10, 20, 100), and two values of the ratio of the indenter radius to maximum total displacement, R/delta(max) (3, 10). Indenter deformation effects are better accounted for by the reduced modulus if the indented material behaves entirely elastically. In this case, identical load-displacement (P - delta) curves are obtained with rigid and elastic spherical indenters for the same elastic reduced modulus. Changes in the ratio E/E(i), from 0 to 0.39, resulted in variations lower than 5% for the load dimensionless functions, lower than 3% in the contact area, A(c), and lower than 5% in the ratio H/E(r). However, deformations of the elastic indenter made the actual radius of contact change, even in the indentation of elastic materials. Even though the load dimensionless functions showed only a little increase with the ratio E/E(i), the hardening coefficient and the yield strength could be slightly overestimated when algorithms based on rigid indenters are used. For the unloading curves, the ratio delta(e)/delta(max), where delta(e) is the point corresponding to zero load of a straight line with slope S from the point (P(max), delta(max)), varied less than 5% with the ratio E/E(i). Similarly, the relationship between reduced modulus and the unloading indentation curve, expressed by Sneddon`s equation, did not reveal the necessity of correction with the ratio E/E(i). The most affected parameter in the indentation curve, as a consequence of the indentation deformation, was the ratio between the residual indentation depth after complete unloading and the maximum indenter displacement, delta(r)/delta(max) (up to 26%), but this variation did not significantly decrease the capability to estimate hardness and elastic modulus based on the ratio of the residual indentation depth to maximum indentation depth, h(r)/h(max). In general, the results confirm the convenience of the use of the reduced modulus in the spherical instrumented indentation tests.

Stochastic stability analysis for the constant-modulus algorithm

We derive an easy-to-compute approximate bound for the range of step-sizes for which the constant-modulus algorithm (CMA) will remain stable if initialized close to a minimum of the CM cost function. Our model highlights the influence, of the signal constellation used in the transmission system: for smaller variation in the modulus of the transmitted symbols, the algorithm will be more robust, and the steady-state misadjustment will be smaller. The theoretical results are validated through several simulations, for long and short filters and channels.

Evaluation of elastic modulus and hardness of thin films by nanoindentation

Simple equations are proposed for determining elastic modulus and hardness properties of thin films on substrates from nanoindentation experiments. An empirical formulation relates the modulus E and hardness H of the film/substrate bilayer to corresponding material properties of the constituent materials via a power-law relation. Geometrical dependence of E and H is wholly contained in the power-law exponents, expressed here as sigmoidal functions of indenter penetration relative to film thickness. The formulation may be inverted to enable deconvolution of film properties from data on the film/substrate bilayers. Berkovich nanoindentation data for dense oxide and nitride films on silicon substrates are used to validate the equations and to demonstrate the film property deconvolution. Additional data for less dense nitride films are used to illustrate the extent to which film properties may depend on the method of fabrication.

Axial Young's modulus prediction of single-walled carbon nanotube arrays with diameters from nanometer to meter scales

Based on a self-similar array model, we systematically investigated the axial Young's modulus (Y-axis) of single-walled carbon nanotube (SWNT) arrays with diameters from nanometer to meter scales by an analytical approach. The results show that the Y-axis of SWNT arrays decreases dramatically with the increases of their hierarchy number (s) and is not sensitive to the specific size and constitution when s is the same, and the specific Young's modulus Y-axis(s) is independent of the packing configuration of SWNTs. Our calculations also show that the Y-axis of SWNT arrays with diameters of several micrometers is close to that of commercial high performance carbon fibers (CFs), but the Y-axis(s) of SWNT arrays is much better than that of high performance CFs. (C) 2005 American Institute of Physics.

Thiele massage as a therapeutic option for women with chronic pelvic pain caused by tenderness of pelvic floor muscles

Aims and objectives Musculoskeletal system has been found to be involved in genesis and perpetuation of chronic pelvic pain (CPP) and has strong evidences that up to 80% of women with CPP present dysfunction of the musculoskeletal system. In this study, we report a series of women with CPP caused by tenderness of pelvic floor muscles successfully treated with Thiele massage. Methods Were included in this study six women with CPP caused by tenderness of the levator ani muscle that underwent transvaginal massage using the Thiele technique, over a period of 5 minutes repeated once a week for 4 weeks. After 1 month, the women returned for follow-up. Results The median tenderness score for the six women evaluated was 3 at the first evaluation and 0 after 1 month of follow-up (P < 0.01). The mean Visual Analogue Scale and McGill Pain Index scores were 8.1 and 34, respectively, at the first evaluation, and 1.5 and 16.6 at follow-up (P < 0.01). Conclusion Thiele massage appears to be very helpful for women with CPP caused by tenderness of the levator ani muscle. However, these results are preliminary and a larger number of women are necessary to obtain more conclusive results.

Polymerization stress, shrinkage and elastic modulus of current low-shrinkage restorative composites

Objective. To compare currently available low-shrinkage composites with others regarding polymerization stress, volumetric shrinkage (total and post-gel), shrinkage rate and elastic modulus. Methods. Seven BisGMA-based composites (Durafill/DU, Filtek Z250/FZ, Heliomolar/HM, Aelite LS Posterior/AP, Point 4/P4, Filtek Supreme/SU, ELS/EL), a silorane-based (Filtek LS, LS), a urethane-based (Venus Diamond, VD) and one based on a dimethacrylate-derivative of dimer acid (N`Durance, ND) were tested. Polymerization stress was determined in 1-mm high specimens inserted between two PMMA rods attached to a universal testing machine. Total volumetric shrinkage was measured using a mercury dilatometer. Maximum shrinkage rate was used as a parameter of the reaction speed. Post-gel shrinkage was measured using strain-gages. Elastic modulus was obtained by three-point bending. Data were submitted to one-way ANOVA/Tukey test (p = 0.05), except for elastic modulus (Kruskal-Wallis). Results. Composites ranked differently for total and post-gel shrinkage. Among the materials considered as ""low-shrinkage"" by the respective manufacturers, LS, EL and VD presented low post-gel shrinkage, while AP and ND presented relatively high values. Polymerization stress showed a strong correlation with post-gel shrinkage except for LS, which presented high stress. Elastic modulus and shrinkage rate showed weak relationships with polymerization stress. Significance. Not all low-shrinkage composites demonstrated reduced polymerization shrinkage. Also, in order to effectively reduce polymerization stress, a low post-gel shrinkage must be associated to a relatively low elastic modulus. (C) 2010 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Elastic modulus of posts and the risk of root fracture

The definition of an optimal elastic modulus for a post is controversial. This work hypothesized that the influence of the posts` elastic modulus on dentin stress concentration is dependent on the load direction. The objective was to evaluate, using finite element analysis, the maximum principal stress (sigma(max)) on the root, using posts with different elastic modulus submitted to different loading directions. Nine 3D models were built, representing the dentin root, gutta-percha, a conical post and the cortical bone. The softwares used were: MSC.PATRAN2005r2 (preprocessing) and MSC.Marc2005r2 (processing). Load of 100 N was applied, varying the directions (0 degrees, 45 degrees and 90 degrees) in relation to the post`s long axis. The magnitude and direction of the sigma(max) were recorded. At the 45 degrees and 90 degrees loading, the highest values of sigma(max) were recorded for the lowest modulus posts, on the cervical region, with a direction that suggests debonding of the post. For the 0 degrees loading, the highest values of sigma(max) were recorded for higher modulus posts, on the apical region, and the circumferential direction suggests vertical root fracture. The hypothesis was accepted: the effect of the elastic modulus on the magnitude and direction of the sigma(max) generated on the root was dependent on the loading direction.