scholarly journals Upscaling the interplay between diffusion and polynomial drifts through a composite thin strip with periodic microstructure

Meccanica ◽  
2020 ◽  
Vol 55 (11) ◽  
pp. 2159-2178
Author(s):  
Emilio N. M. Cirillo ◽  
Ida de Bonis ◽  
Adrian Muntean ◽  
Omar Richardson
Keyword(s):  
Transport Coefficients ◽  
Finite Thickness ◽  
Effective Diffusion ◽  
Scale Up ◽  
Chemical Species ◽  
Characteristic Size ◽  
Diffusion Problem ◽  
Thin Strip ◽  
Dispersion Matrix ◽  
Drift Model

Abstract We study the upscaling of a system of many interacting particles through a heterogenous thin elongated obstacle as modeled via a two-dimensional diffusion problem with a one-directional nonlinear convective drift. Assuming that the obstacle can be described well by a thin composite strip with periodically placed microstructures, we aim at deriving the upscaled model equations as well as the effective transport coefficients for suitable scalings in terms of both the inherent thickness at the strip and the typical length scales of the microscopic heterogeneities. Aiming at computable scenarios, we consider that the heterogeneity of the strip is made of an array of periodically arranged impenetrable solid rectangles and identify two scaling regimes what concerns the small asymptotics parameter for the upscaling procedure: the characteristic size of the microstructure is either significantly smaller than the thickness of the thin obstacle or it is of the same order of magnitude. We scale up the diffusion–polynomial drift model and list computable formulas for the effective diffusion and drift tensorial coefficients for both scaling regimes. Our upscaling procedure combines ideas of two-scale asymptotics homogenization with dimension reduction arguments. Consequences of these results for the construction of more general transmission boundary conditions are discussed. We illustrate numerically the concentration profile of the chemical species passing through the upscaled strip in the finite thickness regime and point out that trapping of concentration inside the strip is likely to occur in at least two conceptually different transport situations: (i) full diffusion/dispersion matrix and nonlinear horizontal drift, and (ii) diagonal diffusion matrix and oblique nonlinear drift.

Flaw Tolerance in a Thin Strip Under Tension

2005 ◽  
Vol 72 (5) ◽  
pp. 732-737 ◽  
Author(s):  
Huajian Gao ◽  
Shaohua Chen
Keyword(s):  
Large Scale ◽  
Characteristic Size ◽  
Thin Strip ◽  
Dimensionless Number ◽  
Singular Stress ◽  
Center Crack ◽  
Flaw Tolerance ◽  
Singular Stress Field ◽  
Fracture Size ◽  
Scale Yielding

Recent studies on hard and tough biological materials have led to a concept called flaw tolerance which is defined as a state of material in which pre-existing cracks do not propagate even as the material is stretched to failure near its limiting strength. In this process, the material around the crack fails not by crack propagation, but by uniform rupture at the limiting strength. At the failure point, the classical singular stress field is replaced by a uniform stress distribution with no stress concentration near the crack tip. This concept provides an important analogy between the known phenomena and concepts in fracture mechanics, such as notch insensitivity, fracture size effects and large scale yielding or bridging, and new studies on failure mechanisms in nanostructures and biological systems. In this paper, we discuss the essential concept for the model problem of an interior center crack and two symmetric edge cracks in a thin strip under tension. A simple analysis based on the Griffith model and the Dugdale-Barenblatt model is used to show that flaw tolerance is achieved when the dimensionless number Λft=ΓE∕(S2H) is on the order of 1, where Γ is the fracture energy, E is the Young’s modulus, S is the strength, and H is the characteristic size of the material. The concept of flaw tolerance emphasizes the capability of a material to tolerate cracklike flaws of all sizes.

Mass Transport of Multicomponents Solute in Bentonite Clay

2000 ◽  
Vol 663 ◽  
Author(s):  
Y. Ichikawa ◽  
K. Kawamura ◽  
M. Nakano ◽  
K. Kitayama ◽  
N. Saito ◽  
...  
Keyword(s):  
Md Simulation ◽  
Chemical Species ◽  
Bentonite Clay ◽  
Diffusion Problem ◽  
Radioactive Waste Disposal ◽  
Inhomogeneous Material ◽  
Solute Diffusion ◽  
Diffusion Behavior ◽  
Molecular Behavior ◽  
High Level

ABSTRACTA fundamental concept combining a molecular behavior and macro-continuum phenomenon is presented for a multicomponent solute diffusion problem in bentonite clay, which is a key component of the Engineering Barrier System (EBS) of high-level radioactive waste disposal (HLRW). Bentonite is a micro-inhomogeneous material. Properties of the saturated bentonite are characterized by the constituent clay mineral (montmorillonite) and water, namely montmorillonite hydrate. We analyze its molecular behavior by applying a molecular dynamics (MD) simulation to inquire into the physicochemical properties such as diffusivity of chemical species. For extending the microscopic characteristics of constituent materials to a macroscopic diffusion behavior of the micro-inhomogeneous material we apply a homogenization analysis (HA).

Effect of Extended Defects on the Enhanced Diffusion of Phosphorus Implanted Silicon

1999 ◽  
Vol 568 ◽  
Author(s):  
P. H. Keys ◽  
J. H. Li ◽  
E. Heitman ◽  
P. A. Packan ◽  
M. E. Law ◽  
...  
Keyword(s):  
Species Interactions ◽  
Secondary Ion Mass Spectrometry ◽  
Ion Beam ◽  
Effective Diffusion ◽  
Chemical Species ◽  
High Dose ◽  
Extended Defects ◽  
Near Surface ◽  
Enhanced Diffusion ◽  
Marker Layer

ABSTRACTExtended defects resulting from ion implantation are believed to act in some cases as a driving force behind transient enhanced diffusion (TED). We use secondary ion mass spectrometry (SIMS) to study the diffusion enhancements of an underlying boron doped spike after creating implant damage in the near surface region. Diffusion enhancements are compared for silicon implants and phosphorus implants to distinguish between factors related to chemical species interactions versus those related to ion beam damage. Transmission electron microscopy (TEM) is used to investigate the existence and dissolution of extended defects. {311} extended defects are clearly visible in self-implanted samples but absent in phosphorus doped samples. The extended defects resulting from phosphorus implantation are small (20Å to 60Å diameter) “dot” defects barely resolvable by conventional TEM. methods. Despite the marked differences in defect morphology, diffusion enhancements in the boron marker layer are observable for both species. Results comparing the TED of a buried marker layer after P+ and Si+ show a larger overall effective diffusion length results after high dose (1x1014 cm−2) phosphorus implants. Visible defects in phosphorus implanted silicon are not the only source of TED, suggesting the existence of sub-microscopic phosphorus interstitial clusters (PIC). This provides important insight into the affect of phosphorus on TED.

scholarly journals Continuous or Batch Solid-Liquid Extraction of Antioxidant Compounds from Seeds of Sterculia apetala Plant and Kinetic Release Study

Molecules ◽  
2018 ◽  
Vol 23 (7) ◽  
pp. 1759 ◽  
Author(s):  
Federica Mosca ◽  
Gádor Hidalgo ◽  
Juliana Villasante ◽  
María Almajano
Keyword(s):  
Diffusion Rate ◽  
Effective Diffusion ◽  
Antioxidant Properties ◽  
Chemical Species ◽  
Liquid Extraction ◽  
Process Time ◽  
Total Phenolic ◽  
Antioxidant Compounds ◽  
Solid Liquid Extraction ◽  
Solid Liquid

This work has been intended to investigate the antioxidant properties of compounds extracted from seeds of Sterculia apetala (a plant from Central America) in order to add further results to the relatively poor existing literature on the beneficial properties of this plant. Different extraction methodologies were used such as batch or continuous extraction conditions using water or ethanol 50% as solvents. The kinetic study has allowed estimation of the effective diffusion coefficients in a continuous solid-liquid extraction, highlighting the strict dependence of the diffusion rate and temperature and kind of solvent, showing the highest diffusion rate with ethanol 50% at 60 °C. The comparison between different techniques and two solvents led to the selection of water as the best extraction solvent while batch mechanically-agitated extraction was the most efficient mode, with the benefits of use of an environmental-friendly solvent and reduction in process time to achieve a high amount of extracted phenolic compounds. The analysis techniques used were ABTS and Folin-Ciocalteau methods to investigate the antioxidant activity and quantify the Total Phenolic Content (TPC) respectively. Also, different fatty acids were extracted from Sterculia apetala seeds and analysed by Gas Chromatography in order to quantify other interesting chemical species besides antioxidants.

scholarly journals Effects of kinetic sorptive exchange on solute transport in open-channel flow

2001 ◽  
Vol 446 ◽  
pp. 321-345 ◽  
Author(s):  
CHIU-ON NG ◽  
T. L. YIP
Keyword(s):  
Channel Flow ◽  
Water Distribution ◽  
Open Channel ◽  
Transport Coefficients ◽  
Chemical Species ◽  
Open Channel Flow ◽  
Suspended Sediments ◽  
Sediment Concentration ◽  
Sorption Kinetics ◽  
Bulk Solid

A theory is presented for the transport in open-channel flow of a chemical species under the influence of kinetic sorptive exchange between phases that are dissolved in water and sorbed onto suspended sediments. The asymptotic method of homogenization is followed to deduce effective transport equations for both phases. The transport coefficients for the solute are shown to be functions of the local sediment concentration and therefore vary with space and time. The three important controlling parameters are the suspension number, the bulk solid–water distribution ratio and the sorption kinetics parameter. It is illustrated with a numerical example that when values of these parameters are sufficiently high, the advection and dispersion of the solute cloud can be dominated by the sorption effects. The concentration distribution can exhibit an appreciable deviation from Gaussianity soon after discharge, which develops into a long tailing as the solute cloud gradually moves ahead of the sediment cloud.

Other Important (and Some Lesser Known) Strategies of Rate Enhancement

2001 ◽  
Author(s):  
L. K. Doraiswamy
Keyword(s):  
Supercritical Fluids ◽  
Scale Up ◽  
Chemical Species ◽  
Industrial Applications ◽  
Electronic Energy ◽  
Photochemical Reactions ◽  
Membrane Reactors ◽  
Rate Enhancement ◽  
The Many ◽  
Excitation Processes

The literature contains examples of several strategies of rate enhancement not covered in the previous chapters. Many of these are essentially strategies for individual reactions with little general appeal. On the other hand, a few are very important, and several others combine two or more strategies. Of these, photochemical and micellar enhancements are as important as the strategies considered earlier in this part. However, in photochemical enhancement, recent studies have shown that the basis of scale-up used so far is questionable (Cassano et al., 1995), and designs based on newer concepts are still in their infancy. In micellar catalysis, despite the advances made, there are few industrial applications. As a result, these are included in this chapter on other strategies. Hydrotropes and supercritical fluids, although “old” with respect to other uses, are emerging as strong contenders for rate enhancement and ease of processing. Hence these two strategies are considered at some length in this chapter. Also included are the use of microwaves and several combinatorial strategies such as PTC with electrochemical, enzymatic, or sonochemical techniques; the use of supercritical fluids in similar combinations; enzymatic reactions in micelles; and PTC reactions in supercritical fluids or membrane reactors. Interaction of light with a chemical species can initiate or enhance a chemical reaction. Reactions of this type are known as photochemical reactions. Of the many distinctive features of photochemistry, the following is particularly noteworthy: in thermal excitation processes, all three forms of energy, electronic, transational, and rotational, are raised to higher levels. In contrast, photoexcitation raises only the electronic energy level which leads to higher selectivity, as exemplified by the photochlorination of the methyl group of toluene without any ring chlorination. Further, photochemical reactions are ecologically clean and require much less aggressive methods than conventional syntheses. Examples of reactions initiated or enhanced by light are many, and a small number are in industrial use, particularly in the production of halogenated hydrocarbons, alkane sulfates, and fine organic chemicals, including vitamins and fragrances. But the potential is enormous.

Transforming Municipal Solid Waste (MSW) Into Fuel via the Gasification/Pyrolysis Process

2010 ◽  
Author(s):  
Eilhann Kwon ◽  
Kelly J. Westby ◽  
Marco J. Castaldi
Keyword(s):  
Municipal Solid Waste ◽  
Solid Waste ◽  
Residence Time ◽  
Scale Up ◽  
Chemical Species ◽  
Steam Gasification ◽  
Drop Tube ◽  
Pyrolysis Oil ◽  
Pyrolysis Process ◽  
Syngas Production

Municipal solid waste (MSW) gasification/pyrolysis enhancement using CO2 as gasification medium has been studied to understand the performance under various reaction conditions. MSW gasification/pyrolysis has been characterized thermo-gravimetrically under various atmospheres covering the gasification/pyrolysis process, which has been used as a basis for scale-up experimental work using a flow-through reactor (FTR) and drop tube reactor (DTR) (0.5 g/min of sample, 4–5 sec residence time, 500°C-1000°C). For example, FTR has been used to carry out the fast pyrolysis process having a nominal heating rate of 800°C/min. Oils produced from the FTR have been condensed and analyzed with GC/MS. Among identified chemical species in the pyrolysis sample, the 10 most abundant compounds (benzene, toluene, styrene, limonene, 2,3-dimethyl-1-heptene, benzoic acid, ethylbenzene, indole, xylene, and d-allose) in the pyrolysis oil sample were determined and quantified. These 10 abundant chemical species are substantially reduced in the presence of CO2. This leads to a substantial increase of C1–5 hydrocarbons in gaseous (non-condensable) products and a reduction of pyrolysis oil (∼20%) as well. In addition, MSW samples have been tested in the DTR at a temperature range from 500°C and 1000°C under various atmospheres with CO2 concentrations of 0% and 30%. The release of all chemical species from the DTR was determined using μ-GC. For example, CO (∼30%), H2 (∼25%), and CH4 (∼10%) under the presence of CO2 were generated and introducing CO2 into the gasification process substantially enhanced syngas production. Finally, steam gasification using different ratios of biomass to polyethylene has been explored to better understand the enhanced steam gasification of MSW that is mostly composed of biomass and polymer. Overall thermal degradation trend is the similar, but steam gasification of MSW needs a relatively long residence time and high temperature as compared to biomass.

Prediction of divertor heat flux width for ITER Pre-Fusion Power Operation using BOUT++ transport code

2021 ◽  
Author(s):  
Xiaoxue He ◽  
Xueqiao Xu ◽  
Zeyu Li ◽  
Ben Zhu ◽  
Yue Liu
Keyword(s):  
Heat Flux ◽  
Thermal Diffusivity ◽  
Transport Coefficients ◽  
Poloidal Magnetic Field ◽  
Fusion Power ◽  
Drift Model ◽  
Transport Code ◽  
Initial Plasma ◽  
Power Operation ◽  
Major Radius

Abstract Prediction of divertor heat flux width is performed for the first and the second Pre-Fusion Power Operation (PFPO) phases specified in the new ITER Research Plan using BOUT++ transport code [Li N.M. et al 2018 Comput. Phys. Commun. 228 69–82]. The initial plasma profiles inside the separatrix are taken from CORSICA scenario studies. Transport coefficients in transport code are calculated by inverting the plasma profiles inside the separatrix and are assumed to be constants in the scrape-off-layer (SOL). An anomalous thermal diffusivity scan is performed with E×B and magnetic drifts. The results in two scenarios identify two distinct regimes: a drift dominant regime when diffusivity is smaller than the respective critical diffusivity χc and a turbulence dominant regime when diffusivity is larger than it. The Goldston heuristic drift model and the ITPA multi-machine experimental scaling yield a lower limit of the width λq. From transport simulations, we obtain the critical diffusivity χc = 0.5 m2⁄ s in 5MA/1.77T PFPO-1 scenario and χc = 0.3 m2⁄ s in 7.5MA/2.65T PFPO-2 scenario. Separatrix temperature and collisionality also have a significant impact on the heat flux width in the drift dominant regime. The investigation clearly yields a scaling for critical thermal diffusivity χc ∝ A½ ⁄ ((Z(1+Z)½ Bp 2)) using ITER scenarios with fixed safety factor q95, major radius R, aspect ratio R/a, and the separatrix temperature T, as well as established the connection with CFETR and C-Mod discharges. This scaling implies that for a given tokamak device with q95, R, R/a, and T fixed, a reduction of poloidal magnetic field by a factor of 3 leads to a 9 times higher critical value of thermal diffusivity χc, possibly yielding a transition from turbulence to drift dominant regime.

SIZE EFFECTS ON THE EFFICIENCY OF NEUTRON SHIELDING IN NANOCOMPOSITES — A FULL-RANGE ANALYSIS

2013 ◽  
Vol 12 (03) ◽  
pp. 1350015 ◽  
Author(s):  
LILY SCHREMPP-KOOPS
Keyword(s):  
Semiclassical Approximation ◽  
Full Range ◽  
Scaling Law ◽  
Filler Particle ◽  
Scale Up ◽  
Characteristic Size ◽  
Range Analysis ◽  
Neutron Shielding ◽  
Aerospace Applications ◽  
Filler Particles

Multiphase composites composed of a continuous hydrogenous (polymeric) phase and of neutron absorbing filler particles are attractive candidate materials for the design of light-weight neutron shields. While the characteristic size of the inclusions is traditionally in the micrometer range, we argue that the shielding performance of the composite is significantly enhanced for decreasing filler particle size. Within a semiclassical approximation scheme we analytically determine the corresponding scaling law valid for inclusions from the nanometer scale up to macroscopic sizes and recover meaningful limiting cases. We find that amongst polymer composites, the physical benchmark for optimized shielding at minimal weight penalty is essentially reached, as soon as the size of the filler particles drops within the nanometer range. We demonstrate that our results are in agreement with recent experimental findings and comment on the emerging potential for aeronautic and aerospace applications.

Droplet combustion in a stream of oxidant

1975 ◽  
Vol 347 (1649) ◽  
pp. 195-212 ◽  
Keyword(s):  
Transport Coefficients ◽  
Outer Region ◽  
Chemical Species ◽  
Constant Density ◽  
Stagnation Region ◽  
Density Zero ◽  
Boundary Layer Region ◽  
Layer Region ◽  
Zero Viscosity ◽  
Convection Dominated

The burning of a fuel droplet in a stream of oxidant at high Peclet number is investigated as a small perturbation from a convection dominated situation. By making the assumptions of constant density, zero viscosity and uniform values for specific heat and transport coefficients, we focus atten­tion on the production and transfer of heat and chemical species. The situa­tion is analysed in (i) an outer region away from the droplet, (ii) a boundary layer region near the droplet, (iii) a rear stagnation region and (iv) a down­stream wake region. The appropriate governing equations are obtained and the solution illustrated numerically. The structure of the intense reaction zone and also the force experienced by the droplet are also investi­gated. The results are discussed in the light of previous studies of droplet burning in a stream of oxidant.

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