Theoretical and Numerical Results for a Chemorepulsion Model with Non-constant Diffusion Coefficients

2020 ◽  
pp. 53-90
Author(s):  
Francisco Guillén-González ◽  
María Ángeles Rodríguez-Bellido ◽  
Diego Armando Rueda-Gómez
Keyword(s):  
Diffusion Coefficients ◽  
Numerical Results ◽  
Constant Diffusion

Refinement in the Mathematical and Numerical Treatment of the Internal Oxidation of Alloys

2005 ◽  
Vol 237-240 ◽  
pp. 1157-1162 ◽  
Author(s):  
Wiktor Miszuris ◽  
Andreas Öchsner
Keyword(s):  
Boundary Conditions ◽  
Internal Oxidation ◽  
Diffusion Coefficients ◽  
Finite Dimension ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Numerical Treatment ◽  
Constant Diffusion ◽  
Finite Difference Solution ◽  
Oxide Particles

When oxygen dissolves from atmosphere and diffuses into an alloy during oxidation, the less noble alloy components may react to form oxide particles within the metal. This process is termed internal oxidation. Classical approaches to describe this phenomenon were derived under many strong simplifications such as constant diffusion coefficients, certain boundary conditions and semi-infinite sample. The presented general approach is based on the finite difference solution of the general diffusion equations coupled through the stoichiometry of reaction between oxygen and the considered element. The main enhancement is the consideration of concentration dependent diffusion coefficients, concentration dependent source terms and arbitrary time-dependent boundary conditions formulated as a concentration, a flux or mixed conditions. Furthermore, finite dimension of the specimen is incorporated. This general treatment also allows for the incorporation of the energy balance.

scholarly journals Thermal Annealing of InGaN/GaN Strained-Layer Quantum Well

1999 ◽  
Vol 4 (S1) ◽  
pp. 642-647
Author(s):  
Michael C.Y. Chan ◽  
Kwok-On Tsang ◽  
E. Herbert Li ◽  
Steven P. Denbaars
Keyword(s):  
Optical Properties ◽  
Band Structure ◽  
Quantum Well ◽  
Thermal Annealing ◽  
Diffusion Coefficients ◽  
Green Light ◽  
Optical Gain ◽  
Quantum Well Structures ◽  
Strained Layer ◽  
Constant Diffusion

Quantum well (QW) material engineering has attracted a considerable amount of interest from many people because of its ability to produce a number of optoelectronic devices. QW composition intermixing is a thermal induced interdiffusion of the constituent atoms through the hetero-interface. The intermixing process is an attractive way to achieve the modification of the QW band structure. It is known that the band structure is a fundamental determinant for such electronic and optical properties of materials as the optical gain, the refractive index and the absorption. During the process, the as-grown square-QW compositional profile is modified to a graded profile, thereby altering the confinement profile and the subband structure in the QW. The blue-shifting of the wavelength in the intermixed QW structure is found in this process.In recent years, III-nitride semiconductors have attracted much attention. This is mainly due to their large bandgap range from 1.89eV (wurtzite InN) to 3.44eV (wurtzite GaN). InGaN/GaN quantum well structures have been used to achieve high lumens blue and green light emitting diodes. Such structures also facilitate the production of full colour LED displays by complementing the colour spectrum of available LEDs.In this paper, the effects of thermal annealing on the strained-layer InGaN/GaN QW will be presented. The effects of intermixing on the confinement potential of InGaN/GaN QWs have been theoretically analysed, with sublattices interdiffusion as the basis. This process is described by Fick’s law, with constant diffusion coefficients in both the well and the barrier layers. The diffusion coefficients depend on the annealing temperature, time and the activation energy of constituent atoms. The optical properties of intermixed InGaN/GaN QW structure of different interdiffusion rates have been theoretically analyzed for applications of novel optical devices. The photoluminescence studies and the intermixed QW modeling have been used to understand the effects of intermixing.

QUASI-REGULAR DIRICHLET FORMS ON FREE RIEMANNIAN PATH SPACES

2009 ◽  
Vol 12 (02) ◽  
pp. 251-267 ◽  
Author(s):  
FENG-YU WANG ◽  
BO WU
Keyword(s):  
Large Class ◽  
Free Path ◽  
Riemannian Manifolds ◽  
Diffusion Coefficients ◽  
Dirichlet Forms ◽  
Integration By Parts ◽  
Constant Diffusion ◽  
Integration By Parts Formula ◽  
Noncompact Riemannian Manifolds ◽  
Initial Distributions

The integration by parts formula on free path spaces over noncompact Riemannian manifolds is established for initial distributions with densities in [Formula: see text]. As an application, a large class of Dirichlet forms with (unbounded and non-constant) diffusion coefficients are constructed on free Riemannian path spaces, which are quasi-regular under mild curvature conditions.

Numerical Determination of Intrinsic Diffusion in Fe-Cr-Al Systems

2010 ◽  
Vol 297-301 ◽  
pp. 948-953
Author(s):  
Bartłomiej Wierzba ◽  
Olivier Politano ◽  
Sébastien Chevalier ◽  
Marek Danielewski
Keyword(s):  
Concentration Profile ◽  
Diffusion Coefficients ◽  
Numerical Results ◽  
Multicomponent Systems ◽  
Numerical Determination ◽  
Intrinsic Diffusion ◽  
Aluminide Coatings ◽  
Interdiffusion Process

The intrinsic diffusion coefficients in diffusion aluminide coatings based on Fe-30Cr were determined at 1000oC. The diffusion fluxes were given by the Nernst Planck formulae and the Darken method for multicomponent systems was applied. This paper summarizes some numerical results to determine the composition dependent diffusivities in Fe-Cr-Al systems. The method presented in this study to obtain average intrinsic diffusion coefficients is as an alternative to the Dayananda method. Our method based on empirical parameters allowed us to predict the concentration profile during the interdiffusion process.

Study of Analyte Diffusion into a Silicone-Clad Fiber-Optic Chemical Sensor by Evanescent Wave Spectroscopy

1995 ◽  
Vol 49 (11) ◽  
pp. 1636-1645 ◽  
Author(s):  
Dianna S. Blair ◽  
Lloyd W. Burgess ◽  
Anatol M. Brodsky
Keyword(s):  
Diffusion Coefficients ◽  
Evanescent Wave ◽  
Near Infrared ◽  
Chemical Sensor ◽  
Optical Element ◽  
Constant Diffusion ◽  
Infrared Spectral ◽  
Diffusion Rates ◽  
Two Parameter ◽  
Infrared Data

The diffusion rates of various polar and nonpolar analytes in dimethylsiloxane were examined with the use of a commercially available 200-μm silica-core/300-μm silicone-clad fiber as the optical element for evanescent wave spectroscopy in the near-infrared spectral region. An analytical solution to Fick's second law was used to model the time-dependent analyte concentration at the core/cladding interface. Successful fit of the analytical solutions to infrared data verifies the assumption of constant diffusion coefficients that is necessary to solve the equation. Transport rates of polar analytes in silicone can be estimated with the use of a single-parameter model that results in diffusion coefficients of 3.2 × 10−1, 1.6 × 10−1, 8.1 × 10−7, and 3.9 × 10−7 cm2/s for methanol, ethanol, 2-propanol, and n-butanol, respectively. Estimating the transport of larger nonpolar analytes in the silicone cladding requires a two-parameter model that includes a diffusion coefficient and an interfacial conductance term. For pentane, hexane, heptane, and cyclohexane the resultant diffusion coefficients and interfacial conductance parameters are 6.9 × 10−7, 4.6 × 10−7, 4.4 × 10−7, and 2.3 × 10−7 cm2/s and 2500, 2000, 2000, and 600 μm−1, respectively.

scholarly journals Moisture diffusion coefficient estimation in peas drying by means of a modified Hawlader and Uddin method

2018 ◽  
Author(s):  
Carlos Martínez-Vera ◽  
Mario Vizcarra-Mendoza
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Diffusion Coefficients ◽  
Moisture Diffusion ◽  
Moisture Diffusivity ◽  
Second Step ◽  
Drying Process ◽  
Moisture Diffusion Coefficient ◽  
Coefficient Estimation ◽  
Constant Diffusion

The aim of the present work is to determine the moisture diffusion coefficient in peas applying, in a first step, a methodology previously published in the literature by Uddin et al.[1] for determining constant diffusion coefficients taking in account the volume reduction associated to the drying process. Then, in a second step, refine it by means of an optimization step. The optimization step is justified because the methodology of Uddin et al. is based in a solution of the diffusion equation that is not mathematically valid for the drying-shrinking problem. Keywords: : moisture diffusivity; drying-shrinking; peas drying 

Sign in / Sign up

Export Citation Format

Share Document