Combined Edge and Anisotropy Effects on Fickian Mass Diffusion in Polymer Composites

2004 ◽  
Vol 126 (4) ◽  
pp. 427-435 ◽  
Author(s):  
Levent Aktas ◽  
Youssef K. Hamidi ◽  
M. Cengiz Altan
Keyword(s):  
Experimental Data ◽  
Diffusion Equation ◽  
Polymer Composites ◽  
Diffusion Coefficients ◽  
Anisotropic Diffusion ◽  
Rectangular Domain ◽  
Least Square ◽  
Fickian Diffusion ◽  
Finite Sample ◽  
Time Curve

The common methods used to determine the diffusion coefficients of polymer composites are based on the solution of Fickian diffusion equation in one-dimensional (1D) rectangular domain. However, these diffusivities usually involve errors primarily due to finite sample dimensions and anisotropy introduced by fiber reinforcements. In this study, the solution of transient, three-dimensional (3D) anisotropic Fickian diffusion equation is nondimensionalized using six parameters. The solution is then used to analyze the combined contribution of finite sample dimensions and anisotropy to the errors involved in diffusion constants calculated by 1D methods. The small time solution of the Fickian diffusion equation in 3D domain is used to analyze the slope used in diffusivity calculations. It is shown that the diffusion coefficient calculated by the 1D approach is exact only if the correct slope of percent mass gain versus root square time curve at t=0 is used. However, it has also been shown that depending on the part geometry and degree of anisotropy, there might be considerable differences between the measured slope from the experimental data and the actual slope at t=0. The mismatch between the slopes results in as much as 50% errors in estimates of diffusion coefficients. Using the 3D solution in nondimensional form, the magnitudes of these errors are studied. A least-square curve-fit method, which yields accurate anisotropic diffusion coefficients, is proposed. The method is demonstrated on artificially generated experimental data for a polymer composite containing 50% unidirectional reinforcement. The anisotropic diffusion coefficients used to generate the data are recovered with less than 1% error.

Combined Edge and Anisotropy Effects on Fickian Mass Diffusion in Polymer Composites

2003 ◽  
Author(s):  
Levent Aktas ◽  
Youssef K. Hamidi ◽  
M. Cengiz Altan
Keyword(s):  
Experimental Data ◽  
Diffusion Equation ◽  
Polymer Composites ◽  
Diffusion Coefficients ◽  
Anisotropic Diffusion ◽  
Three Dimensional ◽  
Least Square ◽  
Fickian Diffusion ◽  
Finite Sample ◽  
One Dimensional

The common methods used to determine the diffusion coefficients of polymer composites are based on the solution of Fickian diffusion equation in one-dimensional rectangular domain. However, these diffusivities usually involve errors primarily due to finite sample dimensions and anisotropy introduced by fiber reinforcements. In this study, the solution of transient, three-dimensional anisotropic Fickian diffusion equation is non-dimensionalized using six parameters. The solution is then used to analyze the combined contribution of finite sample dimensions and anisotropy to the errors involved in diffusion constants calculated by one-dimensional methods. The small time solution of the Fickian diffusion equation in three-dimensional domain is used to analyze the slope used in diffusivity calculations. It is shown that the diffusion coefficient calculated by one-dimensional approach is exact only if the correct slope of percent mass gain versus root square time curve at t=0 is used. However, it has also been shown that depending on the part geometry and degree of anisotropy, there might be considerable differences between the measured slope from the experimental data and the actual slope at t=0. The mismatch between the slopes results in as much as 50% errors in estimates of diffusion coefficients. Using the three-dimensional solution in non-dimensional form, the magnitudes of these errors are studied. A least square curve fit method, which yields accurate anisotropic diffusion coefficients, is proposed. The method is demonstrated on artificially generated experimental data for a polymer composite containing 50% unidirectional reinforcement. The anisotropic diffusion coefficients used to generate the data are recovered with less than 1% error.

scholarly journals Anisotropic Diffusion and the Townsend?Huxley Experiment

1973 ◽  
Vol 26 (4) ◽  
pp. 469 ◽  
Author(s):  
JJ Lowke
Keyword(s):  
Experimental Data ◽  
Electric Field ◽  
Electron Mobility ◽  
Diffusion Coefficients ◽  
Applied Electric Field ◽  
Anisotropic Diffusion ◽  
Diffusion Tubes ◽  
New Formula ◽  
The Relationship ◽  
Diffusion Tube

The relationship between current ratios and electron diffusion coefficients for the Townsend-Huxley experiment is reanalysed with the assumption that diffusion can be represented by two coefficients DT and DL for diffusion transverse and parallel respectively to the applied electric field. When the new formula is used to interpret previous experimental data obtained with a diffusion tube of length 2 cm, the derived values of DT/fl become independent of pressure (fl being the electron mobility). For longer diffusion tubes (~ 6 cm), current ratios are insensitive to DL and the results differ insignificantly from those obtained using the formula previously derived on the assumption that diffusion is isotropic.

Transport of Neutral Solute Across Articular Cartilage: The Role of Zonal Diffusivities

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
V. Arbabi ◽  
B. Pouran ◽  
H. Weinans ◽  
A. A. Zadpoor
Keyword(s):  
Experimental Data ◽  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Equilibrium Concentration ◽  
Cartilage Tissue ◽  
Zone Model ◽  
Superficial Zone ◽  
Time Curve ◽  
Order Of Magnitude ◽  
Multizone Model

Transport of solutes through diffusion is an important metabolic mechanism for the avascular cartilage tissue. Three types of interconnected physical phenomena, namely mechanical, electrical, and chemical, are all involved in the physics of transport in cartilage. In this study, we use a carefully designed experimental-computational setup to separate the effects of mechanical and chemical factors from those of electrical charges. Axial diffusion of a neutral solute (Iodixanol) into cartilage was monitored using calibrated microcomputed tomography (micro-CT) images for up to 48 hr. A biphasic-solute computational model was fitted to the experimental data to determine the diffusion coefficients of cartilage. Cartilage was modeled either using one single diffusion coefficient (single-zone model) or using three diffusion coefficients corresponding to superficial, middle, and deep cartilage zones (multizone model). It was observed that the single-zone model cannot capture the entire concentration-time curve and under-predicts the near-equilibrium concentration values, whereas the multizone model could very well match the experimental data. The diffusion coefficient of the superficial zone was found to be at least one order of magnitude larger than that of the middle zone. Since neutral solutes were used, glycosaminoglycan (GAG) content cannot be the primary reason behind such large differences between the diffusion coefficients of the different cartilage zones. It is therefore concluded that other features of the different cartilage zones such as water content and the organization (orientation) of collagen fibers may be enough to cause large differences in diffusion coefficients through the cartilage thickness.

scholarly journals Diffusion in Binary Aqueous Solutions of Alcohols by Molecular Simulation

Processes ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 947 ◽  
Author(s):  
Alexander Klinov ◽  
Ivan Anashkin
Keyword(s):  
Experimental Data ◽  
Aqueous Solutions ◽  
Diffusion Coefficients ◽  
Force Fields ◽  
Fickian Diffusion ◽  
Intermolecular Potential ◽  
Thermodynamic Factor ◽  
Self Diffusion ◽  
Temperature Dependences ◽  
Transport Diffusion

Based on the molecular dynamics method, the calculations for diffusion coefficients were carried out in binary aqueous solutions of three alcohols: ethanol, isopropanol, and tert-butanol. The intermolecular potential TIP4P/2005 was used for water; and five force fields were analyzed for the alcohols. The force fields providing the best accuracy of calculation were identified based on a comparison of the calculated self-diffusion coefficients of pure alcohols with the experimental data for internal (Einstein) diffusion coefficients of alcohols in solutions. The temperature and concentration dependences of the interdiffusion coefficients were determined using Darken’s Equation. Transport (Fickian) diffusion coefficients were calculated using a thermodynamic factor determined by the non-random two-liquid (NRTL) and Willson models. It was demonstrated that for adequate reproduction of the experimental data when calculating the transport diffusion coefficients, the thermodynamic factor has to be 0.64. Simple approximations were obtained, providing satisfactory accuracy in calculating the concentration and temperature dependences of the transport diffusion coefficients in the studied mixtures.

Diffusion of gases in liquids: the constant size bubble method

1969 ◽  
Vol 47 (6) ◽  
pp. 1075-1077 ◽  
Author(s):  
Wing Y. Ng ◽  
John Walkley
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Steady State ◽  
Diffusion Equation ◽  
Diffusion Coefficients ◽  
Steady State Solution ◽  
State Solution ◽  
Constant Size ◽  
Good Agreement ◽  
Diffusion Of Gases

A method is described by which the diffusion of a gas in a liquid is measured by maintaining a bubble of the gas at constant size in the liquid. A steady state solution to the diffusion equation is seen to fit the observed experimental data. The measured diffusion coefficients for nitrogen, oxygen, and carbon dioxide in water at 25 °C are found in good agreement with previously determined values.

A Useful Curve Fitting Method for Concrete Uniaxial Compressive Experiment Data

2011 ◽  
Vol 291-294 ◽  
pp. 1015-1020 ◽  
Author(s):  
Chong Jin ◽  
Hong Wang ◽  
Xiao Zhou Xia
Keyword(s):  
Experimental Data ◽  
Orthogonal Polynomial ◽  
Least Square ◽  
Base Function ◽  
Concrete Material ◽  
Fitting Method ◽  
Orthogonal Base ◽  
The Matrix ◽  
Uniform Function ◽  
Curve Fitting Method

Based on the superiority avoiding the matrix equation to be morbid for those fitting functions constructed by orthogonal base, the Legendre orthogonal polynomial is adopted to fit the experimental data of concrete uniaxial compression stress-strain curves under the frame of least-square. With the help of FORTRAN programming, 3 series of experimental data is fitted. And the fitting effect is very satisfactory when the item number of orthogonal base is not less than 5. What’s more, compared with those piecewise fitting functions, the Legendre orthogonal polynomial fitting function obtained can be introduced into the nonlinear harden-soften character of concrete constitute law more convenient because of its uniform function form and continuous derived feature. And the fitting idea by orthogonal base function will provide a widely road for studying the constitute law of concrete material.

Anisotropic diffusion at the field scale in a 4-year multi-tracer diffusion and retention experiment – I: Insights from the experimental data

2014 ◽  
Vol 125 ◽  
pp. 373-393 ◽  
Author(s):  
Thomas Gimmi ◽  
Olivier X. Leupin ◽  
Jost Eikenberg ◽  
Martin A. Glaus ◽  
Luc R. Van Loon ◽  
...  
Keyword(s):  
Experimental Data ◽  
Anisotropic Diffusion ◽  
Tracer Diffusion ◽  
Field Scale

scholarly journals Material parameter identification using finite elements with time-adaptive higher-order time integration and experimental full-field strain information

2021 ◽  
Author(s):  
Stefan Hartmann ◽  
Rose Rogin Gilbert
Keyword(s):  
Experimental Data ◽  
Finite Elements ◽  
Parameter Identification ◽  
Material Parameter ◽  
Measurement Data ◽  
Least Square ◽  
Image Correlation ◽  
Field Strain ◽  
Material Parameter Identification ◽  
Full Field

AbstractIn this article, we follow a thorough matrix presentation of material parameter identification using a least-square approach, where the model is given by non-linear finite elements, and the experimental data is provided by both force data as well as full-field strain measurement data based on digital image correlation. First, the rigorous concept of semi-discretization for the direct problem is chosen, where—in the first step—the spatial discretization yields a large system of differential-algebraic equation (DAE-system). This is solved using a time-adaptive, high-order, singly diagonally-implicit Runge–Kutta method. Second, to study the fully analytical versus fully numerical determination of the sensitivities, required in a gradient-based optimization scheme, the force determination using the Lagrange-multiplier method and the strain computation must be provided explicitly. The consideration of the strains is necessary to circumvent the influence of rigid body motions occurring in the experimental data. This is done by applying an external strain determination tool which is based on the nodal displacements of the finite element program. Third, we apply the concept of local identifiability on the entire parameter identification procedure and show its influence on the choice of the parameters of the rate-type constitutive model. As a test example, a finite strain viscoelasticity model and biaxial tensile tests applied to a rubber-like material are chosen.

Diffusion Coefficients of Interest for the Simulation of Heat Treatment in Rare-Earth Transition Metal Magnets

2012 ◽  
Vol 727-728 ◽  
pp. 163-168 ◽  
Author(s):  
Marcos Flavio de Campos
Keyword(s):  
Experimental Data ◽  
Heat Treatment ◽  
Activation Energy ◽  
Rare Earth ◽  
Transition Metal ◽  
Impurity Atom ◽  
Diffusion Coefficients ◽  
Arrhenius Equation ◽  
Atom Diffusion ◽  
Essential Input

In the case of the modeling of sintering and heat treatments, the diffusion coefficients are an essential input. However, experimental data in the literature about diffusion coefficients for rare-earth transition metal intermetallics is scarce. In this study, the available data concerning diffusion coefficients relevant for rare-earth transition metal magnets are reviewed and commented. Some empirical rules are discussed, for example the activation energy is affected by the size of the diffusing impurity atom. Diffusion coefficients for Dy, Nd and Fe into Nd2Fe14B are given according an Arrhenius equation D=D0exp (-Q/RT). For Dy diffusion into Nd2Fe14B, Q 315 kJ/mol and D08 . 10-4m2/s.

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