Ein neues Verfahren zur Berechnung der Diffusionskoeffizienten in Multikomponentensystemen aus Meßdaten der quasistationären Diffusion / A new procedure for the determination of diffusion coefficients from quasi-stationary diffusion measurements in multicomponent systems

1975 ◽  
Vol 30 (4) ◽  
pp. 561-566
Author(s):  
W. Meiske ◽  
W. Schmidt ◽  
E. Kahrig
Keyword(s):  
Differential Equations ◽  
Diffusion Coefficients ◽  
Multicomponent Systems ◽  
Equivalent System ◽  
System Of Integral Equations ◽  
Component System ◽  
Flow Equations ◽  
Stationary Diffusion ◽  
Numerical Performance

Abstract Diffusion in an (n+1) -component system is described by Onsager's flow equations the integration of which leads in the case of quasi-stationarity to the differential equations d(Δc)/dt=-βD̅Δ c (Δc: vector of concentration differences between the compartments of the cell, D̅: matrix of integral diffusion coefficients, β: apparatus constant). Several procedures are known to determine these diffusion coefficients from such equations but all of them have certain disadvantages. In this paper a new method is described to compute the integral diffusion coefficients, which starts from the associated equivalent system of integral equations. The mathematical formalism is simple, and its numerical performance does not become more difficult with an increasing number of components of the system.

scholarly journals Rechnerische Bestimmung der lonenbeweglichkeit in Ziegelstein unter Zuhilfenahme von Ergebnissen aus nichtstationären Diffusionsversuchen / Numerical Determination of Ion Diffusivity in Bricks Based on Non-Stationary Diffusion Experiments

1999 ◽  
Vol 5 (1) ◽  
pp. 3-14
Author(s):  
H. Sadouki ◽  
A. Buchwald ◽  
F.H. Wittmann ◽  
Ch. Kaps
Keyword(s):  
Diffusion Coefficients ◽  
Inverse Analysis ◽  
Water Saturation ◽  
Optimization Technique ◽  
Ion Concentration ◽  
Ion Diffusion ◽  
Ion Migration ◽  
Numerical Studies ◽  
Stationary Diffusion

Abstract Ion concentration profiles in sandwich-brick specimens have been determined experimentally at different degrees of water saturation. Based on the experimental data, ion diffusion coefficients were determined by inverse analysis. The diffusion equation served as a basis for an optimization technique. It has been shown that the ion diffusivity in bricks decreases markedly as the moisture content decreases. The interface between two adjacent bricks slows down the ion migration at low water content in particular. It is planed to investigate the interface between mortar and bricks in further experimental and numerical studies.

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.

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

The Calculation of Turbulent Diffusion Coefficients in Aquatic Ecosystems

2019 ◽  
Vol 70 (11) ◽  
pp. 3903-3907
Author(s):  
Galina Marusic ◽  
Valeriu Panaitescu
Keyword(s):  
Transport Equation ◽  
Turbulent Diffusion ◽  
Diffusion Coefficients ◽  
Aquatic Ecosystems ◽  
Specific Area ◽  
Left Bank ◽  
The Right ◽  
Prut River

The paper deals with the issues related to the pollution of aquatic ecosystems. The influence of turbulence on the transport and dispersion of pollutants in the mentioned systems, as well as the calculation of the turbulent diffusion coefficients are studied. A case study on the determination of turbulent diffusion coefficients for some sectors of the Prut River is presented. A new method is proposed for the determination of the turbulent diffusion coefficients in the pollutant transport equation for specific sectors of a river, according to the associated number of P�clet, calculated for each specific area: the left bank, the right bank and the middle of the river.

scholarly journals Migration of mineral oil in elastomers

2021 ◽  
Author(s):  
Tobias Förster ◽  
Artur Blivernitz
Keyword(s):  
Diffusion Coefficients ◽  
Mineral Oil ◽  
Activation Energies ◽  
Concentration Profiles ◽  
Small Reservoir ◽  
Experimental Procedure ◽  
Mineral Oils ◽  
The Absolute ◽  
Suitable Measure

AbstractThis work describes a newly introduced experimental procedure to quantify the diffusion progress of mineral oils locally resolved in NBR. Diffusion of reference oils IRM 901, IRM 902 and IRM 903 in NBR with various acrylonitrile contents was investigated. Classical sorption experiments were performed as a basic characterization and compared to the newly introduced method. Here, elastomer specimens are only being dipped with the bottom in a relatively small reservoir of mineral oil. This provides a determination of locally resolved concentration profiles of mineral oils, and the calculation of diffusion coefficients. These diffusion coefficients follow the same trends like those determined via sorption experiments. Despite differences in the absolute numbers, activation energies of diffusion can be applied as a suitable measure for the compatibility of elastomers and fluids.

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