Diffusion Width Research Articles

Decaying turbulence: What happens when the correlation length varies spatially in two adjacent zones

We have imagined a numerical experiment to explore the onset of turbulent intermittency associated with a spatial perturbation of the correlation length. We place two isotropic regions, with different integral scales, inside a volume where the turbulent kinetic energy is initially uniform and leave them to interact and evolve in time. The different length scales produce different decay rates in the two regions. Since the smaller-scale region decays faster, a transient turbulent energy gradient is generated at the interface between the two regions. The transient is characterized by three phases in which the kinetic energy gradient across the interface grows, peaks and then slowly decays. The transient lifetime is almost proportional to the initial ratio of the correlation lengths. The direct numerical simulations also show that the interface width grows in time. The velocity moments inside this interaction zone are seen to depart from their initial isotropic values and, with a certain lag, the anisotropy is seen to spread to small scales. The longitudinal derivative moments also become anisotropic after a few eddy turnover times. This anisotropic behaviour is different from that observed in sheared homogeneous turbulent flows, where high transverse derivative moments are generated, but longitudinal moments almost maintain the isotropic turbulence values. Apart from the behaviour of the energy gradient transients, the results also show the timescaling of the interface diffusion width, and data on the anisotropy of the large and small scales, observed through one-point statistics determined inside the intermittency sublayer, which is associated with the interaction zone.

Determination of the parameters of grain-boundary diffusion and segregation of Co in W using an improved model of grain-boundary diffusion

Based on the recently proposed model of grain-boundary diffusion, the available research data on grain-boundary diffusion of Co in W, and on emission Mossbauer studies of grain boundaries in polycrystalline W have been analyzed in detail. Using joint processing of primary data for tracer analysis and Mossbauer studies, all the parameters of grain-boundary diffusion of Co in W have been determined: the coefficient of grain-boundary segregation, coefficient of grain-boundary diffusion, and the diffusion width of the grain boundary.

A 3D Compressible Flow Model for Weak Rotating Waves in Vaneless Diffusers—Part II: Detailed Results

A 3D compressible flow model was presented in Part I of the paper to study the occurrence of weak rotating waves in vaneless diffusers of centrifugal compressors. In this paper, detailed results on the influences of flow and diffuser geometry parameters, including inlet Mach number, inlet distortion, wave number, diffuser outlet-to-inlet radius ratio, diffuser width to inlet radius ratio, and impeller backswept angle, on the rotating waves are presented. It was found that inlet spanwise distortion of radial velocity has little effects on diffuser stability, but rotating wave speed increases with the distortion. The speed also increases with inlet Mach number, so does diffuser instability. Impeller backswept improves diffuser stability and this effect increases with diffuser radius ratio. Multiple resonances were found when impeller backswept is coupled to inlet distortion of radial velocity. These resonances may have similar stabilities but with different wave speeds, suggesting that two rotating waves with different rotating speeds may occur at the same time. Diffuser width was found to have little effects on stability and on wave speed if the same maximum and same minimum values of inlet distortion of radial velocity are kept, but have some effects if the values are not kept. A comparison was also made between the present model predictions and results in open literatures, and good agreement with the experimental results than previous 2D models was achieved.

Effect of Cu and Ag solute segregation on βSn grain boundary diffusivity

We investigate the effect of various amounts of Ag and Cu solute atoms on the self-diffusivity of Sn in the (101) symmetric tilt βSn grain boundary. Using molecular dynamics simulations over a temperature range of 300 K to 450 K, we show that both Ag and Cu decrease the grain boundary self-diffusivity of Sn as the amount of solute in the interface increases. Additionally, the presence of Ag at the grain boundary interface causes a greater reduction in the self-diffusivity of Sn when compared to Cu. We also analyze the solute effect on the diffusive width of the interface and find that low concentrations of both Ag and Cu shrink the width relative to the pure βSn interface. However, adding Cu in excess density greater than 5 × 10−3 atoms/Å2 causes the interface to expand to values almost twice the original width, possibly caused by the larger cohesive energy of Cu-Sn versus Sn-Sn.

On the theory of grain-boundary diffusion in nanostructured materials under conditions of saturation of the subboundary region by the diffusant

In this work, which is the continuation of our previous work (Phys. Met. Metallogr. 109 (6), 329–336 (2010)), we give an extension of the theory of the coefficient of grain-boundary diffusion for the case of relatively large annealing times, when the width of the saturated subboundary zone exceeds the characteristic scale of decreasing coefficient of diffusion but no overlap of diffusion zones occurs in the bulk of nanograins. An analysis of the diffusion problem in this case leads to solutions that in form are analogous to the solution of the problem of one-dimensional diffusion along grain boundaries, corresponding to the C regime of annealing in conventional polycrystals but with time-dependent effective parameters (the grain-boundary diffusion width and the grain-boundary diffusion coefficient). It has been shown that the allowance for the existence of a subboundary region of enhanced diffusion leads to a decrease in the depth of the diffusant penetration along the boundary and to a simultaneous increase in the average sheet concentration. Estimates of these diffusion characteristics for nanocrystalline copper are given. Results of numerical calculations of the diffusion problem are presented, which make it possible to establish the field of the applicability of the approach suggested.

Effect of vaneless diffuser width on the overall performance of a centrifugal compressor

Seven different vaneless diffuser designs varying in diffuser width are studied experimentally. One design is the basic design with the diffuser width and impeller exit and tip clearance width ratio of 1.0. The other six diffusers have width ratios of 0.903, 0.854, and 0.806. Three of the narrower diffusers have the width reduced from the shroud, and three from the hub and the shroud, divided evenly. The total-to-total efficiency and pressure ratio over the whole compressor are studied. It is possible to increase the efficiency of the compressor stage by reducing the diffuser width. The efficiency is increased over a wide operating range area at three different rotational speeds. The pressure ratios are increased at the design and low rotational speeds, but decreased at the high rotational speed. The shroud pinch seems to be more beneficial to the performance, while the hub pinch seems to have only a minor effect. The best design is the one with the width ratio of 0.854, with width reduction only at the shroud. A major finding is the experimental confirmation that the pinch influences the performance of the impeller, reducing the work input at the higher rotational speed.

The Effect of Half Vane Diffuser on the Noise Generated from a Centrifugal Fan

In this paper an experimental study is conducted to investigate the influence of a half vane diffuser on the noise behavior of a centrifugal fan, used in a vacuum cleaner. The diffuser vane height h/b is varied as follows: 0 (vaneless), 0.2, 0.4, 0.6, 0.8 and 1.0 (full vane) at two diffuser inlet radii R3/R2 = 1.03 and 1.07. The experiments were carried out on a high speed centrifugal fan. The sound pressure level (SPL) and pressure rise of the centrifugal fan were measured in a semi-anechoic chamber. The fan flow coefficient was in the range of 0.02 to 0.14, and the rotational speed of the impeller varied from 20,000 to 35,000 rpm. The experimental result shows that by using a half vane diffuser, the sound pressure levels are respectively reduced by 5.5 dB(A) and 3.5 dB(A) at R3/R2 = 1.03 and 1.07. Meanwhile, the half vane diffuser improves the fan performance and extends the flow range. The optimal value of the half vane height is about 0.6 times of the diffuser width.

A quantitative and thermodynamically consistent phase-field interpolation function for multi-phase systems

The aimed properties of the interpolation functions used in quantitative phase-field models for two-phase systems do not extend to multi-phase systems. Therefore, a new type of interpolation functions is introduced that has a zero slope at the equilibrium values of the non-conserved field variables representing the different phases and allows for a thermodynamically consistent interpolation of the free energies. The interpolation functions are applicable for multi-phase-field and multi-order-parameter representations and can be combined with existing quantitative approaches for alloys. A model for polycrystalline, multi-component and multi-phase systems is formulated using the new interpolation functions that accounts in a straightforward way for composition-dependent expressions of the bulk Gibbs energies and diffusion mobilities, and interfacial free energies and mobilities. The numerical accuracy of the approach is analyzed for coarsening and diffusion-controlled parabolic growth in Cu–Sn systems as a function of R/ℓ, with R grain size and ℓ diffuse interface width.

Secondary ion mass spectrometry study of photorefractive-damage-resistant locally Er/Mg-doped near-stoichiometric Ti:Mg:Er:LiNbO3 strip waveguides

Secondary-ion mass spectrometry (SIMS) was used to study the profile characteristics and diffusion properties of Mg, Ti, and Er ions in photorefractive-damage-resistant locally Er/Mg-diffused near-stoichiometric (NS) Ti:Mg:Er:LiNbO3 strip waveguides fabricated on two Z-cut initially congruent, undoped LiNbO3 substrates in sequence by local Er doping at 1100 °C or 1130 °C in air, Mg/Ti pre-diffusion at 1100 °C in wet O2, and post Li-rich vapor transport equilibration (VTE) treatment at 1100 °C. For comparison, a SIMS study was also carried out on the waveguides fabricated without the post-VTE treatment. In order to compensate for the refractive index decrease arising from both the Mg doping and the post-VTE treatment, and hence to get a positive net index increment profile in the Ti-diffused layer, a thicker Ti-film of around 170 nm was coated. Nevertheless, SIMS results show that the Ti diffusion reservoir, as well as the Er and Mg reservoirs, was exhausted. From the SIMS profiles, characteristic diffusion parameters such as the 1/e diffusion width (for Ti only) and depth, diffusivity, and surface concentration of the Mg, Ti, and Er ions are obtained. It is interesting that the Mg distribution in the NS waveguide layer is desirably homogeneous with a concentration [(1.7–2.0) ± 0.3 mol%] higher than the optical damage concentration threshold. The Ti profile follows a sum of two error functions along the lateral direction of NS waveguides with a diffusion width of (12–13) ± 0.5 μm, and a Gaussian function in the depth direction with a 1/e depth of (5.1–6.0) ± 0.2 μm. The Er profile follows also a Gaussian function with a 1/e depth of (3.7–4.4) ± 0.3 μm. In the NS waveguide layer, the mean diffusivity is (7.1 ± 2.2) to (8.3 ± 2.8) μm2/h for Mg, (3.5 ± 0.3) to (4.5 ± 0.4) μm2/h in the lateral direction and (0.54 ± 0.04) to (1.13 ± 0.08) μm2/h in the depth direction for Ti, and (4.1 ± 0.4) to (5.5 ± 0.5) × 10−2 μm2/h for Er. The effects of Li outward diffusion in the initial Er doping procedure, and the Mg codiffusion and post-VTE treatment on the mean Mg, Ti, and Er diffusivities are discussed in comparison with the previously reported results on single Mg, Ti, or Er diffusion and Mg/Ti codiffusion in a pure or homogeneously MgO-doped congruent LiNbO3 crystal. Finally, the keys to the success of the fabrication procedure adopted are discussed.

Lateral diffusion estimation in fully depleted thick CCD using flat field image analysis

Abstract In thick fully depleted CCDs charge carrier transport from the back window to the gates is accompanied by charge diffusion. Lateral diffusion smooths out density variations of the incoming photon flux by redistributing charges spatially. This creates short range positive correlations in recorded amplitudes. Pixel-to-pixel amplitude variations can also be caused by pixel size and quantum efficiency variations. Pixel size variations result in short range negative correlations. Our study shows that the characteristic diffusion width can be extracted from flat field data. The study was performed on fully depleted, thick CCDs produced in a technology study for the Large Synoptic Survey Telescope (LSST). Data were taken in the laboratory at bias voltages between −5 and −40 V. To increase statistical accuracy, images taken in identical conditions were co-added after base line subtraction and master files were produced. A flat field image simulator was developed for statistical comparison of simulated and measured images. Results on diffusion, pixel response variations, data features, analysis and modeling techniques are presented and discussed.

Uphill diffusion, zero-flux planes and transient chemical solitary waves in garnet

Diffusion profiles in minerals are increasingly used to determine the duration of geological events. For this purpose, the distinction between growth and diffusion zoning is critical; it requires the understanding of complex features associated with multicomponent diffusion. Seed-overgrowth interdiffusion experiments carried out in the range 1,050–1,250°C at 1.3 GPa have been designed to quantify and better understand Fe–Mg–Ca interdiffusion in garnet. Some of the diffusion profiles measured by analytical transmission electron microscope show characteristic features of multicomponent diffusion such as uphill diffusion, chemical solitary waves, zero-flux planes and complex diffusion paths. We implemented three different methods to calculate the interdiffusion coefficients of the D matrix from the experimental penetration curves and determined that with Ca as the dependent component, the crossed coefficients of the D matrix are negative. Experiments and numerical simulations indicate that: (1) uphill diffusion in garnet can be observed indifferently on the three components Fe, Mg and Ca, (2) it takes the form of complementary depletion/repletion waves and (3) chemical waves occur preferentially on initially flat concentration profiles. Derived D matrices are used to simulate the fate of chemical waves in time, in finite crystals. These examples show that the flow of atoms in multicomponent systems is not necessarily unidirectional for all components; it can change both in space along the diffusion profile and in time. Moving zero-flux planes in finite crystals are transitory features that allow flux reversals of atoms in the diffusion zone. Interdiffusion coefficients of the D matrices are also analyzed in terms of eigenvalues and eigenvectors. This analysis and the experimental results show that depending on the composition of the diffusion couple, (1) the shape of chemical waves and diffusion paths changes; (2) the width of the diffusion zone for each component may or may not be identical; and (3) the width of diffusion calculated at a given D and duration may greatly vary. D matrices were retrieved from thirteen sets of diffusion profiles. Data were cast in Arrhenius relations. Linear regressions of the data yield activation energies equal to 368, 148, 394, 152 kJ mol−1 at 1 bar and frequency factors Do equal to 2.37 × 10−6, −4.46 × 10−16, −1.31 × 10−5, 9.85 × 10−15 m2 s−1 for $$ \tilde{D}_{FeFe}^{Ca} $$ , $$ \tilde{D}_{FeMg}^{Ca} $$ , $$ \tilde{D}_{MgFe}^{Ca} $$ , $$ \tilde{D}_{MgMg}^{Ca} $$ , respectively. These values can be used to calculate interdiffusion coefficients in Fe–Mg–Ca garnets and determine the duration of geological events in high temperature metamorphic or magmatic garnets.

Novel Technique for Determination of Actual Pixel Size in Dense Arrays of Infrared Detectors

A novel technique is proposed for determining the actual pixel size in dense arrays of infrared detectors. The technique is based on probing individual pixels in an array and analyzing the parasitic bipolar transistor formed between them to determine the lateral diffusion width and, hence, the actual pixel diameter. The actual pixel diameter can then be used to separate the area-dependent dark current from the periphery-dependent dark current. The result shows that, in the present arrays, the dark current is dominated by the periphery current, unless the pixels are so close to each other that their depletion regions overlap.

An experimental investigation of the flow field between two radial plates

The flow field in a radial diffuser downstream of a radial impeller is highly complex, as the flow is turbulent, unsteady, viscous, and three-dimensional. Depending on the initial conditions at the diffuser inlet, the flow may separate from one or both walls of the diffuser. The objective of this experimental investigation of flow characteristics in a radial vaneless diffuser of a centrifugal blower is to enhance the performance of centrifugal compressors over a wide operating range. Numerical and experimental investigations of rotating stall effects on compressors and blowers have been conducted over the past four decades to achieve this objective. The flow characteristics in a radial diffuser were measured while changing the impeller speed and keeping other parameters such as diffuser radius and width ratio constant. The velocity and pressure distributions in the diffuser were measured along a radial path using a miniature X-wire probe and dynamic as well as static pressure transducers. The axisymmetrical radial and tangential mean velocity distributions and their statistics, as well as pressure distributions, are reported. Some of the results presented in this paper agree with those from earlier work on this subject. For example, the flow angle α (measured at half the diffuser width and from the diffuser inlet to its outlet) did not exceed 65°. This means that α < αc, although a recirculation region was present on the diffuser shroud wall. The critical flow angle αc required to initiate self-excited flow oscillations has been generally reported to be about 78°. Current data also indicate that the flow exiting the impeller is skewed, as revealed by the triple velocity product correlations. The current data are valuable for vaneless diffuser numerical model developers, since there are very limited similar data available in the open literature. The current data support the opinion that the flow separation is not enough to trigger or initiate stall at the diffuser.

Study of electric characteristics and diffusion effects of 2-methyl-9,10-di(2-naphthyl)anthracene doped with cesium fluoride by admittance spectroscopy

In this work, the admittance spectroscopy studies show that doping cesium fluoride (CsF) into 2-methyl-9,10-di(2-naphthyl)anthracene (MADN) can greatly decrease the resistance of MADN and raises the Fermi level from deep level to only 0.1 eV below the lowest unoccupied molecular orbital, resulting in enhancing the electron injection. In addition, the diffusion width of CsF from doped MADN layer into tris(8-quinolinolato)aluminium is clearly observed by capacitance-frequency measurement and is about 9.4 nm. Moreover, the diffusion width is significant to be affected by external thermal.

A Generalization of the Local Projection Stabilization for Convection-Diffusion-Reaction Equations

We introduce a generalization of the local projection stabilization for steady scalar convection-diffusion-reaction equations which allows us to use local projection spaces defined on overlapping sets. This enables us to define the local projection method without the need of a mesh refinement or an enrichment of the finite element space and increases the robustness of the local projection method with respect to the choice of the stabilization parameter. The stabilization term is slightly modified, which leads to an optimal estimate of the consistency error even if the stabilization parameters scale correctly with respect to convection, diffusion, and mesh width. We prove that the bilinear form corresponding to the method satisfies an inf-sup condition with respect to the SUPG norm and establish an optimal error estimate in this norm. The theoretical considerations are illustrated by numerical results.

Electrochemical intercalation of O2− in CuAlO2 single crystal and photoelectrochemical properties

The delafossite CuAlO2 single crystal, prepared by the flux method, is a low mobility p-type semiconductor with a hole mobility of 1.2 × 10−5 cm−2 V−1 s−1. The chronoamperometry showed an electrochemical O2− insertion with a diffusion coefficient D 303K of 3.3 × 10−18 cm2 s−1. The thermal variation of D in the range 293–353 K gave an enthalpy of diffusion (ΔH) of 44.7 kJ mol−1. CuAlO2 is photoactive, and the Mott–Schottky plot indicates a flat band potential of +0.42 V vs saturated calomel electrode and a holes density (N A) of 1016 cm−3. The photocurrent spectra have been analyzed by using the Gartner model from which the absorption coefficients and diffusion lengths were determined. An optical transition at 1.66 eV, indirectly allowed, has been obtained. The spectral photoresponse provides a high absorption at 480 nm. The low quantum yield (η) is attributed to a small depletion length (440 nm) and a hole diffusion width (271 nm) compared to a very large penetration depth (12 µm).

Layout Optimization of ESD Protection Diodes for High-Frequency I/Os

Layout options for CMOS ESD diodes' p-n junction geometry and metal routing are investigated in this paper. Experiments are performed using 90- and 180-nm technologies. Using the figures of merit ICP/C and R ON * C, it is shown that twin-well stripe diodes with nonminimum diffusion width and high-level broadside routing are optimum for gigahertz-frequency I/Os. In addition, the suitability of ESD diodes formed with the isolated P-well/deep N-well diffusions available in triple-well technologies is evaluated for high-speed I/O applications.

Optimal Design and Operation for a No-Moving-Parts-Valve (NMPV) Micro-Pump with a Diffuser Width of 500 µm

A no-moving-parts-valve (NMPV) with a diffuser width of D = 500 microns was investigated in this study by numerical simulations at Reynolds numbers, ReD, ranging from 20 to 75, and expansion valve angles ranging from 30° < θ1 < 57° and 110° < θ2 < 120°. The Dp,i value, 1.02 < Dp,i < 1.14, is larger within the proposed range of the expansion valve angles. A flow channel structure with a depth of 500 micron is manufactured using yellow light lithography in this study. From prior analyses and experiments, it is found that piezoelectric films work better at a buzz driving frequency of f < 30Hz and the best operating frequency is at a driving frequency of f = 10Hz because it produces the largest net flow. In addition, the expansion angles θ1 = 30° and θ2 = 120° are the best expansion angles because they produce the largest net flow. These related results are very helpful for the actual design of no-moving-parts-valve micro-pump.

Rigorous upscaling of the reactive flow with finite kinetics and under dominant Péclet number

We consider the evolution of a reactive soluble substance introduced into the Poiseuille flow in a slit channel. The reactive transport happens in presence of dominant Peclet and Damkohler numbers. We suppose Peclet numbers corresponding to Taylor’s dispersion regime. The two main results of the paper are the following. First, using the anisotropic perturbation technique, we derive rigorously an effective model for the enhanced diffusion. It contains memory effects and contributions to the effective diffusion and effective advection velocity, due to the flow and chemistry reaction regime. Error estimates for the approximation of the physical solution by the upscaled one are presented in the energy norms. Presence of an initial time boundary layer allows only a global error estimate in L2 with respect to space and time. We use the Laplace’s transform in time to get optimal estimates. Second, we explicit the retardation and memory effects of the adsorption/desorption reactions on the dispersive characteristics and show their importance. The chemistry influences directly the characteristic diffusion width.

An optimization approach to the estimation of effective drug diffusivity: From a planar disc into a finite external volume

In this paper we propose a new mathematical model based on optimal fitting for estimating effective diffusion coefficients of a drug from a delivery device of 2D disc geometry to an external finite volume. In this model, we assume that the diffusion process occurs within the boundary layer of the external fluid, while outside the layer the drug concentration is uniform because of the convection-domination. An analytical solution to the corresponding diffusion equation with appropriate initial and boundary conditions is derived using the technique of separation of variables. A formula for the ratio of the mass released in the time interval $[0,t]$ for any $t>0$ and the total mass released in infinite time is also obtained. Furthermore, we extend this model to one for problems with two different effective diffusion coefficients, in order to handle the phenomenon of 'initial burst'. The latter model contains more than one unknown parameter and thus an optimization process is proposed for determining the effective diffusion coefficient, critical time and width of the effective boundary layer. These models were tested using experimental data of the diffusion of prednisolone 2-hemisuccinate sodium salt from porous poly(2-hydroxyethylmethacrylate) hydrogel based discs. The numerical results show that the usefulness and accuracy of these models.