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A generalized expression for lag-time in the gas-phase permeation of hollow tubes

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Abstract

A generalized expression for the nonsteady state parameter, lag-time, has been obtained from Fick’s second law for gas-phase transport through hollow, cylindrical membranes. This generalized expression is simplified for three limiting cases of practical interest: 1) diffusion controlled transport, 2) phase boundary reaction control at the inlet surface, and 3) phase boundary reaction control at the outlet surface. In all three cases the lagtime expressions were found to be inversely proportional only to the diffusion coefficient and functionally dependent on the membrane radii. Finally, the lag-time expressions were applied to experimentally obtained lag-time data for α-phase titanium and α-phase iron.

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Abbreviations

A :

Constant

a :

Inside radius of a hollow, cylindrical tube (cm)

B :

Constant

b :

Outside radius of a hollow, cylindrical tube

c :

Concentration

c g :

Molecular hydrogen concentration in the gas phase

D :

Coefficient for diffusion within the metal lattice (cm2 s-1)

D o :

Preexponential constant for diffusion

h a :

Reaction rate constant at r = a

h b :

Reaction rate constant at r = b

Q :

Quantity of gas passing out of the exit surface, r = b

Q D :

Activation energy for diffusion (J mol-1)

r :

Radius, a ≤ r ≤ b

s :

Constant of proportionality

t :

Time (s)

t L :

Lag-time parameter for nonsteady-state transport (s)

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Authors and Affiliations

  1. Metallurgy Option, Department of Mechanical Engineering, University of Nebraska-Lincota, 68520, USA

    Kiritkumar K. Shah (Graduate Student) & Donald L. Johnson (Associate Professor)

  2. Materials Science Branch, NASA-Ames Research Center, 94035, Moffett Field, California

    Howard G. Nelson (Research Scientist)

Authors
  1. Kiritkumar K. Shah
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  2. Howard G. Nelson
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  3. Donald L. Johnson
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  4. Frank M. Hamaker
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Formerly with NASA-Ames Research Center, Materials Science Branch.

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Shah, K.K., Nelson, H.G., Johnson, D.L. et al. A generalized expression for lag-time in the gas-phase permeation of hollow tubes. Metall Trans A 6, 373 (1975). https://doi.org/10.1007/BF02667292

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