Ideal Diffusion Research Articles

Convergence–confinement analysis of a bolt-supported tunnel using the homogenization method

The behaviour of tunnels reinforced with radially disposed fully grouted bolts is investigated in this paper. Perfect bonding and ideal diffusion of bolt tension are assumed, so that the bolt tension can be assimilated to an equivalent uniaxial stress tensor. An analytical model of the convergence–confinement type is proposed that accounts for the delayed action of bolts due to ground decompression prior to bolt installation. This factor leads to nonsimultaneous yielding, and more generally, a different stress history for each constituent, requiring special treatments in the incremental elastoplasticity calculations. Nonetheless, the resulting model remains sufficiently simple, and an analytical solution is still accessible. Charts are provided to allow for parametric studies and quick preliminary designs. Comparisons with 3D numerical calculations show that the model gives precise results if the correct convergence at the moment of bolt installation is used as an "external" input parameter, validating the homogenization approach. An approximate methodology based on previous works is proposed to determine this parameter to render the proposed model "self-sufficient." Its predictions are again compared to 3D numerical computations, and the results are found to be sufficiently accurate for practical applications.Key words: reinforcement, anisotropy, analytical, lining, yield, elastoplasticity.

Vienna-Type DMA of High Resolution and High Flow Rate

A variant of the Vienna DMA (Winklmayr et al. 1991; Reischl et al. 1997) with inner and outer electrode radii of 25 and 33 mm, and a conventional trumpet inlet diameter of 97 mm has been tested. It incorporates a reduced pressure drop sheath gas exhaust system that enables reaching flow rates approaching 4000 L/min. Several new additional flow features are included to delay the transition to turbulent conditions. A cylindrical geometry with a DMA length L of 97 mm (distance between the aerosol inlet and outlet slits) is seen to keep the flow laminar up to the highest Reynolds number achieved, though showing slight signs of flow quality deterioration at about Re = 20,000. An equally long DMA with an inner electrode shaped as a 5° cone caped by a spherical dome remains stable up to the highest Reynolds number achieved. It is expected to continue this trend to considerably higher flow rates. Both these long configurations exhibit line widths close to the ideal Brownian diffusion limit, reaching FWHH of 4% fo...

Current voltage modeling of current limiting mechanisms in HgCdTe focal plane array photodetectors

An automated iterative nonlinear fitting program has been developed to model current-voltage (I–V) data measured on HgCdTe infrared (IR) detector diodes. This model includes the ideal diode diffusion, generation-recombination, band-to-band tunneling, trap-assisted tunneling (TAT), and avalanche breakdown as potential current limiting mechanisms in an IR detector diode. The modeling presented herein allows one to easily distinguish, and more importantly to quantitatively compare, the amount of influence each current limiting mechanism has on various detectors’ I–V characteristics. Longer cutoff wavelength detectors often exhibit significant current limitations due to tunneling processes. The temperature dependence of these tunneling characteristics is thoroughly investigated for two diodes.

Preparation and characterization of Al 2O 3 hollow fiber membranes

α-Al 2O 3 hollow fibers were prepared by a phase-inversion method combined with the reaction bonded aluminum oxide (RBAO) process. Next, γ-Al 2O 3 membranes, which were fabricated by a sol–gel process, were cast on the outer surface of the hollow fiber supports. Scanning electron microscopy (SEM), transmission electron microscopy (TEM), thermogravimetric analysis (TGA), X-ray diffraction (XRD), nitrogen isothermal absorption measurements and gas permeability testing were used to characterize the supports and γ-Al 2O 3 membranes. The results showed that the mechanical strength of hollow fiber supports is better than that of non-RBAO hollow fiber, and their porosity and mean pore size were 50.1% and 0.88 μm, respectively. SEM images of γ-Al 2O 3 membranes showed that the membranes were defect-free. The most concentrative pore diameter and the specific surface area of γ-Al 2O 3 membranes were about 4.5 nm and 228.9 m 2/g, respectively. Gas permeability tests suggested that the γ-Al 2O 3 membranes possessed gas selectivity, and the separation factor for N 2/Ar are 1.133 at 0.3 MPa and 1.139 at 0.4 MPa, respectively, which is slightly smaller than the value expected from the ideal Kundsen diffusion ( α = 1.194).

Electrical transport and low frequency noise characteristics of Au/n-GaAs Schottky diodes containing InAs quantum dots

Au/n-GaAs Schottky diodes, containing layers of InAs quantum dots (QDs), are investigated by measuring the forward current–voltage characteristics in the temperature range of 77–300 K and low frequency noise at room temperature. The zero-bias barrier height decreases and the ideality factor increases with decreasing temperature, and the ideality factor was found to follow the T0-effect. The departure from the ideal thermionic-emission diffusion model was interpreted in terms of inhomogeneous Schottky contact with a Gaussian distribution of barrier heights. The excess current at small biases, observed in diodes containing layers of InAs QDs, was attributed to small patches of reduced barrier height. In the diode without QDs, the noise intensity SI shows 1/f behaviour and is proportional to I2F, which is explained by modulation of the barrier height due to trapping processes in interface states. In diodes containing InAs QDs, SI shows 1/fγ (with γ < 1) behaviour and is proportional to I2F in the high current range, which is explained by generation of band tail states with exponential energy distribution in the GaAs layer due to the QD formation. In the low current range, SI increases faster than I2F due to contribution to the noise of patches of reduced barrier height.

Preparation of ZrO 2–Al 2O 3 composite membranes by sol–gel process and their characterization

ZrO 2–Al 2O 3 composite membranes with 50 mol% zirconia were prepared by sol–gel process on the porous ceramic tube. X-ray diffraction (XRD), fourier transform infrared spectroscopy (FT-IR), nitrogen isothermal absorption measurement and gas permeability test were used to characterize the membranes. It was identified by XRD that, from 700 to 1100 °C, the composite membranes existed in only tetragonal ZrO 2, and neither monoclinic ZrO 2 nor alpha Al 2O 3 appeared. The thermal stability of the composite membranes was improved greatly, compared to that of pure Al 2O 3 or ZrO 2 membranes. Scanning electron microscopy (SEM) images showed that the membranes were defect-free. The most concentrative pore diameter of the composite membranes determined was about 4.3 nm. Gas permeability test suggest that the composite membranes possessed gas selectivity, and the separation factors for N 2/Ar were 1.119 at 0.3 MPa and 1.140 at 0.5 MPa, respectively, which were slightly smaller than the value expected from the ideal Kundsen diffusion ( α=1.194).

Gloss and goniocolorimetry of printed materials

AbstractAngular distribution of reflectance spectra and of colorimetric parameters for printed papers (varnished and not) and foils, clear and metallized, were measured by goniospectrophotometry, with a photomultiplier for visible region, or a spectrocolorimeter as a detector, keeping the light source in a fixed position, −45° anormally. All reflectance spectra were related to near‐Lambertian BaSO4 powder white standard, relative to which the color coordinates were calculated. The photometric cosine law holds for an ideal diffuser; consequently, all color parameters are significantly perturbed by gloss in a large region, several 10's of degrees around the specular angle. The reflectance peak in the specular angle region of glossy material can be well approximated by the Lorentz function, especially in the vicinity of the specular angle. Lightness, chroma, and hue angle in the gloss angle region suffer as a result of high changes and extremes depending on the gloss of the material tested. This is what complicates color measurements and full determination or definition of the complex appearance of printed materials. The change of chroma with varnishing of glossless materials was clearly elucidated. It was found that “bottom color gloss” considerably influences the appearance of printed metallized foils or other prints on high glossy substrates. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 335–342, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10177

Fluorescence pattern photobleaching recovery for samples with multi-component diffusion

The translational mobility of proteins and lipids in phospholipid bilayers is often not well described as ideal self diffusion. One of the best methods for characterizing such non-ideal diffusion is to use fluorescence pattern photobleaching recovery. In this method, the spatial gradient of the monitoring and bleaching intensity is created by using epi-fluorescence and an expanded Gaussian-shaped laser beam which passes though a Ronchi ruling placed at the back image plane of a microscope. A difficulty arises when the fluorescence recovery from the exchange of slowly diffusing molecules between illuminated and non-illuminated stripes temporally overlaps with the recovery from the exchange of more rapidly diffusing molecules through the gradient produced by the broad Gaussian shape of the illumination. In the work presented here, a general theory is developed that describes the shape of the resulting fluorescence recovery curve for these typical experimental conditions. Approximate expressions amenable to non-linear curve fitting are also given. The new theoretical formalism has been demonstrated on data for the translational mobility of a fluorescent lipid probe in phospholipid bilayers deposited on planar-fused silica substrates.

Ideal and non-ideal diffusion through polymers

Ideal and non-ideal diffusion through polymers

Application of the numerical model describing analyte permeation through hollow fiber membranes into vacuum for determination of permeation parameters of organic compounds in a silicone membrane

Permeation parameters of several organic compounds were determined with a numerical simulation model developed earlier. Diffusivities were determined by calculating permeation curves at various diffusivity values and searching for a value of diffusivity that gave the best correlation of the theoretical curve with the experimental permeation curves. The method also allows determination of error in diffusivity calculation. Error is mainly caused by scattering of experimental data and adding organic interaction with a polymer into the character of a permeation curve. Gas phase distribution ratios were determined from literature data, and permeation selectivities were derived from comparison of experimental data measured by Membrane Inlet Mass Spectrometry (MIMS) and direct inlet measurements. Finding the highest concentration in gas and liquid phase at which the signal still behaves linearly allows estimation of the highest point of linear partitioning. The highest concentration at which diffusivity still remains constant can be estimated by finding the point at which the errors caused by the scattering of the experimental data and the contribution of organic interaction with a polymer into character of a permeation curve are equal. The model was postulated to be applicable over a concentration range in which membrane transport obeys ideal diffusion law, and there is linear sample/membrane partitioning. Calculated membrane diffusivities, water diffusivities, and water/membrane distribution ratios from literature sources were used to simulate permeation fluxes of organic compounds from aqueous phase as a function of the sample flow rate. Comparison of the simulated results showed generally good agreement with the experimental ones, and the expected behavior of permeating flux as a function of sample flow rate was observed.

Ideal and non-ideal diffusion through polymers: Application to pervaporation

Using the approach developed in a previous paper, we integrate the generalised Stefan–Maxwell (SM) diffusion equations for a unique species in both Lagrangian and Cartesian coordinates. The dusty gas membrane model is considered. Two activity–concentration relationships are used: the Flory–Huggins equation and the Freundlich relationship. The ethyl acetate (EA)/PDMS system follows the Flory–Huggins equation and the computed interaction parameter allows to predict quantitatively the non-dimensional EA flux through a PDMS membrane when the Lagrangian coordinates are utilised. The prediction is less satisfactory when integrating the SM equation in the Cartesian coordinates. The system EA/PDMS can be qualified as an ideal system in diffusion. The water/ethanol/PVA-based membrane at 60°C system follows Freundlich’s equation at equilibrium. The bad fitting of the experimental water flux versus volume fraction of water at the feed side of the membrane suggests that this system cannot be described by the dusty gas/Stefan–Maxwell theory even when the Lagrangian coordinates are used. This type of system, defined here as non-ideal, obeys theories of the free volume type, as quoted in a recent paper.

Absence of Diffusion Through the Fractal Boundary of Two Media

We consider ideal gas diffusion through a fractal boundary between two homogeneous media. This boundary is modeled by a spatially self-similar system of folds of the interface surface between the media. This surface can have a finite volume, which is then identified with the physical volume of the boundary layer. We show that the effective diffusion coefficient of ideal molecules vanishes in this layer.

Characterisation of the barrier properties of different paint systems: Part I. Experimental set-up and ideal Fickian diffusion

The water uptake of a commercial alkyd paint system is studied using the impedance spectroscopy technique. The first part of the paper is devoted to establish the experimental setup to accurately measure capacitance values in the pF range, characteristic of the studied system. It was concluded that electrochemical instrumentation is not adequate to perform this task. The second part of the paper discusses the water uptake of the paint system under two different immersion conditions: deionized water and 5% NaCl solution. This analysis leads to the conclusion that the diffusion process seems to follow the ideal-Fickian behaviour in both systems, the corresponding diffusion coefficients were calculated.

Liquid Junction Potential in Potentiometric Titrations. 5. Deduction of the Potential Functions for E.M.F. Cells with Complex Formation and with Liquid Junctions of the Type AY|AY+ BYz(B) + HY + AyL.

Equations were derived, in a general form, for the calculation of the total cell e.m.f. for cells containing liquid junctions of constant ionic medium type, where formation of strong complexes takes place. The total cell e.m.f. is: EJ = E0J + (g/zJ) log cJfJTS2 + ED + EDf Here, (A+, Y-) is the ionic medium, J is the potential-determining ion, Bz(B)+ is the central metal ion, ED is the ideal diffusion potential (Henderson term), EDf is the contribution of the activity coefficients to the diffusion potential, AyL is the ligand. fJTS2 denotes the activity coefficients in the terminal solution TS2. The concentration of a chosen ion of the ionic medium, C, should be in the range 0.5 < or = C < or = 3 mol dm-3. The charge of the metal ion Bz(B)+ should be < or = 3. The total potential anomalies in the cells are delta EJ = (g/zJ) log fJTS2 + ED + EDf

Experimental Study of Hydrogen Diffusion Behaviors in Stress Fields

Abstract Hydrogen diffusion behavior in a given stress field was studied for two high-strength, low-alloy (HSLA) steels using the electrochemical method. In unidirectional tensile stress fields, the apparent diffusion coefficient increased with increases in the linear stress gradient parallel to the direction of diffusion. Steady flux (J∞) increased similarly. The ideal diffusion coefficient (D0) increased with the stress gradient. D0 and J∞ decreased when the direction of diffusion was opposite to the stress gradient. Experimental results were consistent with the theoretical solution.

Gas separation properties of aromatic polyetherimides from 1,4-bis(3,4-dicarboxyphenoxy)benzene dianhydride and 3,5-diaminobenzic acid or its esters

The gas transport properties of a series polyetherimides, which were prepared from 1,4-bis(3,4-dicarboxyphenoxy)benzene dianhydride (HQDPA) with 1,3-phenylenediamine or 3,5-diaminobenzic acid (DBA) or its esters are reported. The effects of carboxylic group (-COOH) and carboxylic ether groups (-COOR), at five positions of 1,3-phenylenediamine moiety, on H-2, CO2, O-2, and N-2 permeability, diffusivity, and solubility of the polyetherimides were investigated. The gas permeability, diffusion, and solubility coefficients of the polyetherimides containing COOR are bigger than those of HQDPA-PDA, but the ideal separation factors and ideal diffusivity selectivity factors are much smaller than that of HQDPA-PDA because COOR decreases chain segmental packing efficiency and increases chain segmental mobility. The permeability coefficients of HQDPA-DBA to H-2, CO2, and O-2 are bigger than those of HQDPA-PDA; the ideal separation factors for gas pairs H-2/N-2, CO2/N-2, and O-2/N-2 are also much bigger than those of HQDPA-PDA. Both the diffusion coefficients of CO2 and O-2 and the ideal diffusivity selectivity factors for CO2/N-2 and O-2/N-2 are bigger than those of HQDPA-PDA because COOH decreases both chain segmental packing efficiency and chain segmental mobility. The copolyimides, which were prepared from 3,5-diaminobenzic acid and 3,5-diaminobenzic esters, have both high permeability and high permselectivity. (C) 1997 John Wiley & Sons, Inc.

Gas separation properties of aromatic polyetherimides from 1,4‐bis(3,4‐dicarboxyphenoxy)benzene dianhydride and 3,5‐diaminobenzic acid or its esters

The gas transport properties of a series polyetherimides, which were prepared from 1,4-bis(3,4-dicarboxyphenoxy)benzene dianhydride (HQDPA) with 1,3-phenylenediamine or 3,5-diaminobenzic acid (DBA) or its esters are reported. The effects of carboxylic group (—COOH) and carboxylic ether groups (—COOR), at five positions of 1,3-phenylenediamine moiety, on H2 CO2, O2, and N2 permeability, diffusivity, and solubility of the polyetherimides were investigated. The gas permeability, diffusion, and solubility coefficients of the polyetherimides containing COOR are bigger than those of HQDPA-PDA, but the ideal separation factors and ideal diffusivity selectivity factors are much smaller than that of HQDPA-PDA because COOR decreases chain segmental packing efficiency and increases chain segmental mobility. The permeability coefficients of HQDPA-DBA to H2, CO2, and O2 are bigger than those of HQDPA-PDA; the ideal separation factors for gas pairs H2/N2, CO2/N2, and O2/N2 are also much bigger than those of HQDPA-PDA. Both the diffusion coefficients of CO2 and O2 and the ideal diffusivity selectivity factors for CO2/N2 and O2/N2 are bigger than those of HQDPA-PDA because COOH decreases both chain segmental packing efficiency and chain segmental mobility. The copolyimides, which were prepared from 3,5-diaminobenzic acid and 3,5-diaminobenzic esters, have both high permeability and high permselectivity. © 1997 John Wiley & Sons, Inc.

Diffusion of six surgical endoscopic procedures in the Netherlands. Stimulating and restraining factors

The diffusion of six surgical endoscopic procedures in the Netherlands was investigated. Questionnaires were sent to 138 laparoscopic surgeons. They were asked which of the following laparoscopic procedures they had adopted in their hospital: cholecystectomy, appendicectomy, Nissen fundoplication, inguinal hernia repair, large bowel resection and thoracoscopic procedures. Furthermore, they were asked to indicate the influence of 13 pre-defined factors: ‘budget’, ‘competition’, ‘conference’, ‘extra benefit’, ‘media’, ‘nature of the technology’, ‘patient demand’, ‘planning/logistics’, ‘reimbursement’, ‘service industry’, ‘support industry’, ‘surgical technique’ and ‘training/course’ on the adoption of those procedures. The adoption rates for the procedures were: 100%, 69%, 19%, 43%, 19% and 52%, respectively. In general, factors were assessed more positively by adopters than by non-adopters. Significant differences were mainly found for ‘extra benefit’, ‘nature of the technology’, ‘surgical technique’ and ‘conference’. The surgeon's perception of the additional benefits of an endoscopic technique and, to a lesser degree, of its technical aspects were the most important factors in deciding whether or not to adopt a procedure. In an ideal diffusion model, a description is given of when and how the 13 factors can influence the diffusion of an endoscopic procedure in the desired direction. In this model, the extra benefit of a new procedure must be proven before other factors are allowed to influence the diffusion.

The plasma transport equations derived by multiple time-scale expansions. II. An application

A multiple time scale derivative expansion scheme has been employed to reveal some aspects of Taylor’s relaxation theory, which states that a ‘‘slightly imperfect’’ plasma relaxes under the conservation of the overall magnetic helicity K toward a state of minimum magnetic energy. The purpose of this paper is to investigate the time evolution of K on the ideal magnetohydrodynamic (IMHD), the MHD-collision (CMHD), and resistive diffusion (RDMHD) time scales. On the ideal MHD time scale, it is found, just as expected, that K is an invariant of motion for each single flux tube. On the MHD-collision time scale Taylor’s conjecture is explicitly proven, namely that only the overall K is an invariant of motion. Finally for the resistive diffusion time scale, it is found that the time derivative is proportional to the resistivity, however, with additional terms arising from the MHD fluctuation spectrum.

Prediction of oxygen transport parameters of plastic packaging materials from transient state measurements

It was the objective of this research project to find reliable methods which allow the prediction of steady state oxygen transmission from transient state measurements. Therefore, two models were tested, one using nonlinear regression analysis in combination with an equation describing the transient state, the other using a partial pressure pulse instead of a constant change in partial pressure. The applicability of both methods in combination with a standard oxygen transmission rate test equipment has been checked for different monolayers and multilayers. With the help of these methods the test procedure can be shortened. More detailed information of the permeation process is given by the fundamental diffusion and solubility coefficients which are calculated with the methods. Both models are valid only for ideal diffusion. Some factors are described that lead to deviations from ideal conditions and influence the results.