The Effect of Pressure Modulation on the Flow of Gas through a Solid Membrane: Permeation and Diffusion of Hydrogen through Nickel

Cummings, D.L.; Reuben, Robert Lewis; Blackburn, D. A.

doi:10.1007/bf02644195

Cited by 27 publications

(6 citation statements)

References 8 publications

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“…The propagation of flux and concentration modulations through a homogeneous foil was detailed in a previous paper /4/ in which the possible surface processes (adsorption, desorption, dissociation, association, solution and de-solution) are described by the single re-* Presented at the International Symposium on Metal -Hydrogen Systems, Fundamentals and Applications, Stuttgart, FRG, September [4][5][6][7][8][9]1988 (1) There, the approach is to link fluxes with pressures by a series of linear equations in which the diffusion and solubility coefficients appear as constants. Conditions in the bulk solid, at each surface, and in the entry and exit chamber are each described by matrices, their product giving the required vector relationship of output to input.…”

Section: Theorymentioning

confidence: 99%

“…By splitting terms into time independent and dependent parts and carrying through a calculation of the type described in /5/, the effective interface matrix can be shown to have (5) This equation has too many coefficients for complete experimental confirmation to be reasonable, so it is useful to begin with the case of rapid superficial reactions, and flow which is diffusion limited. In the limit kltks -» oo:…”

Section: Theorymentioning

confidence: 99%

See 1 more Smart Citation

Hydrogen Permeation in 304 and 316 Steels: Transport Mechanisms in Oxide Layers*

Grant¹,

Cummings²,

Blackburn³

1989

Zeitschrift Für Physikalische Chemie

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Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Hydrogen Permeation in 304 and 316 Steels: Transport Mechanisms in Oxide Layers*

Grant¹,

Cummings²,

Blackburn³

1989

Zeitschrift Für Physikalische Chemie

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“…The diffusion process is used to describe many types of particles or energy transfer in scattering media, including photon propagation in biological tissue [1], charge-carrier conveyance in semiconducting material [2], and neutron navigation in a nuclear reactor [3]. The diffusion model also applies to observances such as harmonic mass-transport [4], modulated eddy current [5], thermal waves [6], and the still-controversial viscosity waves [7]. Accurate and accessible quantitation of diffusion is fundamental to probing the properties of associated media and predicting processes [8].…”

Section: Introductionmentioning

confidence: 99%

Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator III Synthetic study of continuous-wave photon fluence rate along unique spiral paths

2012

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This is Part III of the work that examines photon diffusion in a scattering-dominant medium enclosed by a "concave" circular cylindrical applicator or enclosing a "convex" circular cylindrical applicator. In Part II of this work Zhang et al. [J. Opt. Soc. Am. A, 66 (2011)] predicted that, on the tissue-applicator interface of either "concave" or "convex" geometry, there exists a unique set of spiral paths, along which the steady-state photon fluence rate decays at a rate equal to that along a straight line on a planar semi-infinite interface, for the same line-of-sight source-detector distance. This phenomenon of steady-state photon diffusion is referred to as "straight-line-resembling-spiral paths" (abbreviated as "spiral paths"). This Part III study develops analytic approaches to the spiral paths associated with geometry of a large radial dimension and presents spiral paths found numerically for geometry of a small radial dimension. This Part III study also examines whether the spiral paths associated with a homogeneous medium are a good approximation for the medium containing heterogeneity. The heterogeneity is limited to an anomaly that is aligned azimuthally with the spiral paths and has either positive or negative contrast of the absorption or scattering coefficient over the background medium. For a weak-contrast anomaly the perturbation by it to the photon fluence rate along the spiral paths is found by applying a well-established perturbation analysis in cylindrical coordinates. For a strong-contrast anomaly the change by it to the photon fluence rate along the spiral paths is computed using the finite-element method. For the investigated heterogeneous-medium cases the photon fluence rate along the homogeneous-medium associated spiral paths is macroscopically indistinguishable from, and microscopically close to, that along a straight line on a planar semi-infinite interface.

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“…This technique is an extension of gas phase pressure modulation measurements where the entry flux is modulated as a function of frequency using a piston arrangement. [8][9][10][11] Theory In this section, we derive the relevant equations describing the modulated transport of hydrogen through a membrane taking into account trapping and surface effects. The equations for trapping are similar to those derived previously for gas phase modulated pressure measurements and hence are only summarized here.…”

mentioning

confidence: 99%

“…The equations for trapping are similar to those derived previously for gas phase modulated pressure measurements and hence are only summarized here. 9,10 The trapping of hydrogen can be described by the first order trapping and detrapping rate constants k t and…”

mentioning

confidence: 99%

Analysis of Hydrogen Trapping in Palladium by Modulated Permeation Spectroscopy

Buckley

Fagan

Searson

2000

J. Electrochem. Soc.

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The dynamics of transport processes, such as hydrogen transport in metals, can only be obtained from non-steady-state techniques. We have derived the relevant expressions for the phase shift and magnitude of the transfer function describing the response to a modulated flux at one surface of a foil. The expressions include the influence of trapping and surface effects. Experimental measurements of the phase shift and magnitude on annealed palladium foils agree with the model taking D ϭ 3 ϫ 10 Ϫ7 cm 2 s Ϫ1 and no trapping or surface effects. Experiments on palladium foils with poor surface treatment exhibited an increase in the phase shift and decrease in the magnitude across the accessible frequency range, consistent with surface effects. These results demonstrate that modulation permeation spectroscopy can be used to study transport in metallic foils.

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The Effect of Pressure Modulation on the Flow of Gas through a Solid Membrane: Permeation and Diffusion of Hydrogen through Nickel

Cited by 27 publications

References 8 publications

Hydrogen Permeation in 304 and 316 Steels: Transport Mechanisms in Oxide Layers*

Hydrogen Permeation in 304 and 316 Steels: Transport Mechanisms in Oxide Layers*

Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator III Synthetic study of continuous-wave photon fluence rate along unique spiral paths

Analysis of Hydrogen Trapping in Palladium by Modulated Permeation Spectroscopy

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